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Instance-Dependent Label-Noise Learning With Manifold-Regularized Transition Matrix EstimationDe Cheng Tongliang Liu Yixiong Ning Nannan Wang Bo Han Gang Niu Xinbo Gao Masashi SugiyamaIEEE Conference on Computer Vision and Pattern Recognition
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/F112 8.9664 Tf 0.985 0 0 1 50.112 583.201 Tm [(Figure)-255(1.)-316(The)-255(proposed)-255(instance-dep)1(endent)-255(label-noise)-255(lea)1(rning)-255(frame)25(w)11(ork.)-317(W)81(e)-255(train)-254(a)-255(classi\002er)-254(in)-255(a)-254(statistically)-255(consistent)-254(manner)-255(through)]TJ/F112 8.9664 Tf 0.98 0 0 1 50.112 572.242 Tm [(the)-251(proposed)-251(IDTM)]TJ/F97 8.9664 Tf 1 0 0 1 122.13 572.242 Tm [(T)]TJ/F96 8.9664 Tf 6.655 0 Td [(\()]TJ/F111 8.9664 Tf 3.584 0 Td [(x)]TJ/F96 8.9664 Tf 4.483 0 Td [(\))]TJ/F112 8.9664 Tf 0.98 0 0 1 140.436 572.242 Tm [(,)-252(where)]TJ/F97 8.9664 Tf 1 0 0 1 168.517 572.242 Tm [(T)]TJ/F96 8.9664 Tf 6.656 0 Td [(\()]TJ/F111 8.9664 Tf 3.584 0 Td [(x)]TJ/F33 5.9776 Tf 4.483 -0.996 Td [(i)]TJ/F96 8.9664 Tf 3.162 0.996 Td [(\))]TJ/F98 8.9664 Tf 6.144 0 Td [(2)]TJ/F97 8.9664 Tf 8.703 0 Td [(R)]TJ/F33 5.9776 Tf 7.036 3.809 Td [(K)]TJ/F36 5.9776 Tf 6.545 0 Td [<02>]TJ/F33 5.9776 Tf 5.756 0 Td [(K)]TJ/F112 8.9664 Tf 0.98 0 0 1 229.834 572.242 Tm [(is)-251(estimated)-251(by)-251(the)-251(transition)-251(neural)-251(netw)11(ork.)-315(It)-251(is)-251(re)15(gularized)-251(by)-251(the)-251(manifold)-251(embedding)]TJ/F112 8.9664 Tf 0.986 0 0 1 50.112 561.283 Tm [(to)-254(reduce)-254(the)-254(de)15(gree)-254(of)-254(freedom)-254(of)]TJ/F97 8.9664 Tf 1 0 0 1 174.69 561.283 Tm [(T)]TJ/F96 8.9664 Tf 6.656 0 Td [(\()]TJ/F111 8.9664 Tf 3.584 0 Td [(x)]TJ/F96 8.9664 Tf 4.483 0 Td [(\))]TJ/F112 8.9664 Tf 0.986 0 0 1 195.243 561.283 Tm [(and)-254(mak)10(e)-254(it)-254(estimable)-254(in)-254(practice.)-316(In)-254(the)-254(manifold)-254(embedding)]TJ/F98 8.9664 Tf 1 0 0 1 415.329 561.283 Tm [(L)]TJ/F112 8.9664 Tf 0.986 0 0 1 421.677 561.283 Tm [(,)-254(the)-254(af)25(\002nity)-254(matrix)]TJ/F97 8.9664 Tf 1 0 0 1 492.079 561.283 Tm [(S)]TJ/F33 5.9776 Tf 5.63 -0.996 Td [(ij)]TJ/F112 8.9664 Tf 0.986 0 0 1 506.521 561.283 Tm [(is)-254(obtained)]TJ/F112 8.9664 Tf 1 0 0 1 50.112 550.325 Tm [(by)-250(\002nding)-250(the)]TJ/F97 8.9664 Tf 52.058 0 Td [(k)]TJ/F112 8.9664 Tf 5.061 0 Td [(-nearest)-250(neighbors)-250(in)-250(the)-250(instance)-250(feature)-250(space.)-310(Finally)65(,)-250(we)-250(use)-250(the)-250(cross-entrop)10(y)-250(to)-250(train)-250(the)-250(classi\002er)-250(assis)1(ted)-250(by)]TJ/F97 8.9664 Tf 411.238 0 Td [(T)]TJ/F96 8.9664 Tf 6.656 0 Td [(\()]TJ/F111 8.9664 Tf 3.584 0 Td [(x)]TJ/F96 8.9664 Tf 4.483 0 Td [(\))]TJ/F112 8.9664 Tf 3.584 0 Td [(.)]TJ
0 g 0 G
0 g 0 G
/F112 9.9626 Tf 1.02 0 0 1 50.112 528.488 Tm [(ha)20(v)14(e)-273(theoretical)-274(guarantees)-274(and)-274(ha)20(v)15(e)-274(achie)24(v)15(ed)-274(success)-273(un-)]TJ/F112 9.9626 Tf 1.011 0 0 1 50.112 516.532 Tm [(der)-247(some)-248(synthetic)-247(noisy)-248(labels)-247(or)-247(speci\002c)-248(conditions,)-247(the)15(y)]TJ/F112 9.9626 Tf 1.016 0 0 1 50.112 504.577 Tm [(are)-247(unable)-247(to)-247(cope)-247(with)-247(general)-247(real-w)10(orld)-247(noise,)-247(i.e.,)-247(IDN.)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 492.622 Tm [(Second,)-316(se)24(v)15(eral)-302(pioneer)-302(w)10(orks)-302(considered)-302(strong)-302(assump-)]TJ/F112 9.9626 Tf 0.99 0 0 1 50.112 480.667 Tm [(tions)-252(and)-253(focused)-252(on)-252(ho)25(w)-252(to)-252(simplify)]TJ/F11 9.9626 Tf 1 0 0 1 198.784 480.667 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.99 0 0 1 221.208 480.667 Tm [(and)-252(signi\002cantly)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 468.712 Tm [(reduce)-288(i)1(ts)-288(de)15(gree)-288(of)-287(freedom)-288(or)-287(comple)14(xity)64(.)-431(F)15(or)-288(e)15(xample,)]TJ 1.02 0 0 1 50.112 456.756 Tm [(in)-319(part-dependent)-318(noise)-319([)]TJ
0 1 0 rg 0 1 0 RG
[(44)]TJ
0 g 0 G
[(],)-337(it)-319(is)-319(assumed)-319(that)]TJ/F11 9.9626 Tf 1 0 0 1 248.658 456.756 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 271.833 456.756 Tm [(is)-319(a)]TJ/F112 9.9626 Tf 1.006 0 0 1 50.112 444.801 Tm [(con)40(v)15(e)15(x)-250(combinati)1(on)-250(of)-249(a)-249(prede\002ned)-249(number)-249(of)-249<0278>15(ed)-249(transi-)]TJ/F112 9.9626 Tf 0.984 0 0 1 50.112 432.846 Tm [(tion)-253(matrices,)-254(and)-253(their)-253(coef)25(\002cients)-254(come)-253(from)-253(non-ne)15(g)5(ati)26(v)15(e)]TJ/F112 9.9626 Tf 1.004 0 0 1 50.112 420.891 Tm [(matrix)-247(f)10(actorization.)-309(In)-247(such)-248(a)-247(w)10(ay)65(,)-248(the)-248(estimation)-247(problem)]TJ/F112 9.9626 Tf 0.987 0 0 1 50.112 408.936 Tm [(becomes)-252(parametric,)-253(and)-252(the)-253(de)15(gree)-252(of)-252(freedom)-253(of)]TJ/F11 9.9626 Tf 1 0 0 1 250.296 408.936 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.987 0 0 1 272.714 408.936 Tm [(can)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 396.981 Tm [(be)-342(reduced.)-595(The)-342(issue)-342(of)-342(those)-342(methods)-342(i)1(s)-342(that)-342(simplify-)]TJ 1.02 0 0 1 50.112 385.025 Tm [(ing)-255(the)-256(form)-255(of)]TJ/F11 9.9626 Tf 1 0 0 1 114.114 385.025 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 136.645 385.025 Tm [(too)-255(much)-256(will)-255(certainly)-255(cause)-256(a)-255(lar)18(ge)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 373.07 Tm [(approximation)-250(error)55(.)]TJ/F112 9.9626 Tf 1.006 0 0 1 62.067 358.542 Tm [(T)80(o)-249(address)-249(the)-249(problem)-248(of)-249(estimating)-249(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 241.282 358.542 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.006 0 0 1 263.71 358.542 Tm [(under)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 346.587 Tm [(IDN,)-280(i)1(n)-280(this)-279(paper)39(,)-288(we)-280(will)-279(not)-280(put)-279(an)14(y)-279(strong)-280(assumption)]TJ/F112 9.9626 Tf 1.018 0 0 1 50.112 334.632 Tm [(on)-246(the)-246(form)-246(of)]TJ/F11 9.9626 Tf 1 0 0 1 110.796 334.632 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.018 0 0 1 130.732 334.632 Tm [(,)-246(b)19(ut)-246(we)-246(will)-246(instead)-246(put)-246(some)-246(assump-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 322.676 Tm [(tion)-292(on)-291(the)]TJ/F117 9.9626 Tf 1.02 0 0 1 97.393 322.676 Tm [(g)10(eometry)]TJ/F112 9.9626 Tf 1.02 0 0 1 138.068 322.676 Tm [(of)]TJ/F11 9.9626 Tf 1 0 0 1 149.496 322.676 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 169.432 322.676 Tm [(.)-443(More)-292(speci\002cally)64(,)-303(we)-292(ha)20(v)14(e)]TJ 1.02 0 0 1 50.112 310.721 Tm [(noticed)-265(that,)-271(there)-265(are)-265(psychological)-265(and)-266(ph)5(ysiological)-265(e)25(v-)]TJ 1.02 0 0 1 50.112 298.766 Tm [(idences)-336([)]TJ
0 1 0 rg 0 1 0 RG
[(6)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-188(24)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-188(30)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-188(36)]TJ
0 g 0 G
[(])-336(sho)24(wing)-336(that)-336(we)-336(humans)-336(are)-336(more)]TJ 1.02 0 0 1 50.112 286.811 Tm [(lik)10(ely)-332(to)-331(annotate)-332(i)1(nstances)-332(of)-331(similar)-332(appearances)-331(to)-332(the)]TJ 1.02 0 0 1 50.112 274.856 Tm [(same)-295(class,)-307(and)-295(thus)-295(poor)20(-quality)-295(or)-295(ambiguous)-295(instances)]TJ 1.02 0 0 1 50.112 262.901 Tm [(of)-282(similar)-281(appearances)-282(are)-282(susceptible)-282(to)-281(be)-282(mislabeled)-282(to)]TJ 1.02 0 0 1 50.112 250.945 Tm [(correlated)-297(or)-297(same)-297(noisy)-297(classes.)-460(Therefore,)-311(according)-297(to)]TJ/F112 9.9626 Tf 1.003 0 0 1 50.112 238.99 Tm [(the)-248(basic)-248(principle)-248(that)-248(the)-248(noisy)-248(class-posterior)-248(probability)]TJ/F11 9.9626 Tf 1 0 0 1 50.112 227.035 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.382 2.518 Td [<16>]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F8 9.9626 Tf 10.865 0 Td [(=)]TJ/F11 9.9626 Tf 10.616 0 Td [(j)]TJ/F14 9.9626 Tf 4.673 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(X)]TJ/F8 9.9626 Tf 11.903 0 Td [(=)]TJ/F111 9.9626 Tf 10.616 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 124.606 227.035 Tm [(can)-250(be)-251(inferred)-250(by)-251(the)-250(latent)-250(clean)-251(class-)]TJ/F112 9.9626 Tf 0.985 0 0 1 50.112 215.08 Tm [(posterior)-253(probability)]TJ/F11 9.9626 Tf 1 0 0 1 133.037 215.08 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(i)]TJ/F14 9.9626 Tf 3.432 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(X)]TJ/F8 9.9626 Tf 11.803 0 Td [(=)]TJ/F111 9.9626 Tf 10.516 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.985 0 0 1 205.832 215.08 Tm [(and)-253(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 250.045 215.08 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.985 0 0 1 269.98 215.08 Tm [(,)-253(we)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 203.125 Tm [(propose)-316(an)-315(assumption)-316(that)-315<93746865>-316(closer)-315(tw)10(o)-316(instances)-315(are,)]TJ/F112 9.9626 Tf 0.984 0 0 1 50.112 191.17 Tm [(the)-253(more)-252(similar)-253(their)-252(corresponding)-253(transition)-253(matrices)-252(will)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 179.214 Tm [<6265942e>-506(This)-312(can)-313(be)-312(interpreted)-312(as)-313(that)-312(the)-312(instance)-313(adjacent)]TJ/F112 9.9626 Tf 1.002 0 0 1 50.112 167.259 Tm [(relationships)-249(of)-249(one)-249(cate)15(gory)-250(in)-249(the)-249(feature)-249(space)-249(should)-249(be)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 155.304 Tm [(consistent)-250(with)-250(those)-250(in)-250(the)-250(transition)-250(matrix)-250(space.)]TJ/F112 9.9626 Tf 1.006 0 0 1 62.067 140.776 Tm [(Moti)25(v)25(ated)-248(by)-248(this)-248(practically)-248(useful)-248(assumption,)-248(we)-247(pro-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 128.821 Tm [(pose)-286(to)-286(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 119.229 128.821 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 142.069 128.821 Tm [(by)-286(formulating)-286(the)-286(assumption)-285(into)]TJ 1.02 0 0 1 50.112 116.866 Tm [(the)]TJ/F117 9.9626 Tf 1.02 0 0 1 65.417 116.866 Tm [(manifold)-284(embedding)]TJ/F112 9.9626 Tf 1.02 0 0 1 151.917 116.866 Tm [(as)-284(sho)24(wn)-284(in)-284(Figure)]TJ
1 0 0 rg 1 0 0 RG
[-284(1)]TJ
0 g 0 G
[(.)-421(Speci\002cal-)]TJ 1.02 0 0 1 50.112 104.91 Tm [(ly)64(,)-334(we)-316(mak)9(e)-316(use)-316(of)-316(the)-316(manifold)-317(assumption,)-333(and)-317(require)]TJ 1.02 0 0 1 50.112 92.955 Tm [(that)-295(if)]TJ/F111 9.9626 Tf 1 0 0 1 77.564 92.955 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 88.862 92.955 Tm [(and)]TJ/F111 9.9626 Tf 1 0 0 1 106.536 92.955 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 118.715 92.955 Tm [(are)-295(close)-295(in)-296(the)-295(feature)-295(space,)-308(then)]TJ/F11 9.9626 Tf 1 0 0 1 264.275 92.955 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F112 9.9626 Tf 1.004 0 0 1 50.112 81 Tm [(and)]TJ/F11 9.9626 Tf 1 0 0 1 67.051 81 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(j)]TJ/F8 9.9626 Tf 4.198 1.494 Td [(\))]TJ/F112 9.9626 Tf 1.004 0 0 1 93.681 81 Tm [(should)-250(al)1(so)-250(be)-250(close)-249(\(in)-250(terms)-249(of)-250(a)-249(matrix)-250(norm\).)]TJ
0 g 0 G
0 g 0 G
/F112 9.9626 Tf 0.981 0 0 1 308.862 528.488 Tm [(Going)-255(along)-256(this)-255(line,)-256(though)-255(we)-256(do)-255(not)-256(reduce)-255(the)-255(comple)15(x-)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 516.532 Tm [(ity)-256(of)]TJ/F11 9.9626 Tf 1 0 0 1 333.257 516.532 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 355.793 516.532 Tm [(directly)-256(since)-256(we)-255(do)-256(not)-256(further)-256(simplify)-256(it,)-258(we)]TJ 1.02 0 0 1 308.862 504.577 Tm [(still)-280(ef)25(fecti)25(v)14(ely)-279(reduce)-280(the)-280(de)15(gree)-280(of)-280(freedom)-280(of)-280(the)-279(linear)]TJ 1.02 0 0 1 308.862 492.622 Tm [(system)]TJ/F11 9.9626 Tf 1 0 0 1 340.373 492.622 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()-69<16>]TJ/F11 9.9626 Tf 3.874 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F111 9.9626 Tf 2.768 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))-425(=)]TJ/F11 9.9626 Tf 20.087 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ/F11 9.9626 Tf 3.875 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 12.092 0 Td [(=)-425(1)]TJ/F11 9.9626 Tf 16.962 0 Td [(;)-167(::;)-166(N)]TJ/F112 9.9626 Tf 1.02 0 0 1 505.246 492.622 Tm [(and)-323(mak)10(e)]TJ/F11 9.9626 Tf 1 0 0 1 308.862 480.667 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 332.348 480.667 Tm [(stably)-349(estimable)-350(in)-349(practice.)-617(Here,)]TJ/F11 9.9626 Tf 1 0 0 1 481.202 480.667 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 504.688 480.667 Tm [(can)-349(be)-350(re-)]TJ/F112 9.9626 Tf 0.984 0 0 1 308.862 468.712 Tm [(g)5(arded)-253(as)-253(practically)-253(stable,)-254(since)-253(adding)-253(such)-253(a)-253(smoothness)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 456.756 Tm [(assumption)-315(stops)]TJ/F11 9.9626 Tf 1 0 0 1 382.456 456.756 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 405.594 456.756 Tm [(from)-315(changing)-315(too)-315(much)-315(in)-315(a)-316(tin)15(y)]TJ 1.02 0 0 1 308.862 444.801 Tm [(neighborhood)-310(and)-310(then)-311(it)-310(should)-310(be)-310(Lipschitz)-310(continuous.)]TJ/F112 9.9626 Tf 0.981 0 0 1 308.553 432.846 Tm [(Thus,)-255(it)-254(should)-255(be)-255(uniquely)-254(determined)-255(gi)26(v)15(en)-255(in\002nite)-254(data)-255(or)]TJ/F112 9.9626 Tf 1.008 0 0 1 308.862 420.891 Tm [(the)-247(underlying)-248(data)-247(distrib)20(ution.)-307(Finally)64(,)-247(we)-248(conduct)-247(e)15(xten-)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 408.936 Tm [(si)25(v)14(e)-272(e)15(xperiments)-273(on)-272(v)24(arious)-272(datasets,)-279(which)-272(illustrates)-273(the)]TJ/F112 9.9626 Tf 1.018 0 0 1 308.862 396.981 Tm [(proposed)-244(method)-245(is)-244(superior)-245(to)-244(state-of-the-art)-244(approaches)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 385.025 Tm [(for)-250(label-noise)-250(learning)-250(under)-250(IDN.)]TJ 11.955 -11.955 Td [(The)-250(main)-250(contrib)20(utions)-250(are)-250(summarized)-250(as)-250(follo)25(ws:)]TJ
0 g 0 G
/F14 9.9626 Tf -1.992 -19.194 Td [<0f>]TJ
0 g 0 G
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[(].)-626(The)-352(IDN)-352(model)-353(considers)]TJ 1.02 0 0 1 50.112 590.486 Tm [(more)-277(general)-278(case)-277(of)-278(label)-277(noise,)-285(where)-278(the)-277(probability)-278(of)]TJ 1.02 0 0 1 50.112 578.531 Tm [(an)-296(instance)-295(being)-296(mislabeled)-295(depends)-296(on)-295(the)-296(features)-296(and)]TJ/F112 9.9626 Tf 0.998 0 0 1 50.112 566.575 Tm [(class)-250(of)-251(the)-250(instance)-250(itself.)-311(Intuiti)25(v)15(ely)65(,)-250(IDN)-250(is)-251(quite)-250(realistic)]TJ/F112 9.9626 Tf 0.986 0 0 1 50.112 554.62 Tm [(and)-253(applicable,)-252(as)-253(the)-253(poor)21(-quality)-253(and)-253(ambiguous)-252(instances)]TJ/F112 9.9626 Tf 0.991 0 0 1 50.112 542.665 Tm [(are)-251(more)-251(prone)-252(to)-251(be)-251(labeled)-251(wrongly)-251(in)-252(real-w)11(orld)-252(datasets.)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 530.71 Tm [(Ho)25(we)24(v)15(er)39(,)-422(it)-387(is)-387(v)15(ery)-387(comple)15(x)-387(to)-387(model)-386(IDN)-387(without)-387(an)15(y)]TJ 1.02 0 0 1 50.112 518.755 Tm [(additional)-392(as)1(sumption.)-744(Our)-391(w)9(ork)-391(in)-392(this)-391(paper)39(,)-428(aims)-392(to)]TJ 1.02 0 0 1 50.112 506.799 Tm [(estimate)-274(this)-274(realistic)-274(IDN)-274(model)-274(by)-275(considering)-274(practical)]TJ/F112 9.9626 Tf 0.997 0 0 1 50.112 494.844 Tm [(useful)-251(assumptions)-252(on)-251(the)]TJ/F117 9.9626 Tf 0.997 0 0 1 155.56 494.844 Tm [(g)10(eometry)]TJ/F112 9.9626 Tf 0.997 0 0 1 194.916 494.844 Tm [(of)]TJ/F11 9.9626 Tf 1 0 0 1 205.687 494.844 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.997 0 0 1 225.622 494.844 Tm [(,)-252(which)-251(aims)-251(to)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 482.889 Tm [(reduce)-298(the)-297(de)14(gree)-298(of)-297(freedom)-298(of)]TJ/F11 9.9626 Tf 1 0 0 1 185.487 482.889 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 205.422 482.889 Tm [(,)-311(and)-298(mak)10(e)-298(it)-297(stably)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 470.934 Tm [(estimable)-250(in)-250(practice.)]TJ/F111 9.9626 Tf 11.955 -15.639 Td [(Estimating)-282(the)-283(transition)-282(matrix)]TJ/F112 9.9626 Tf 1.02 0 0 1 203.382 455.295 Tm [(is)-277(one)-277(popular)-277(direc-)]TJ 1.02 0 0 1 50.112 443.339 Tm [(tion)-350(to)-351(b)20(uild)-350(statistically)-350(consistent)-351(classi\002er)54(.)-619(It)-350(helps)-351(to)]TJ/F112 9.9626 Tf 0.986 0 0 1 50.112 431.384 Tm [(signi\002cantly)-252(reduce)-253(the)-252(side-ef)25(fects)-252(of)-253(noisy)-252(labels,)-253(by)-252(infer)20(-)]TJ/F112 9.9626 Tf 0.982 0 0 1 50.112 419.429 Tm [(ring)-254(clean)-253(distrib)20(ution)-253(based)-254(on)-253(the)-254(transition)-253(matrix)-254(and)-253(the)]TJ/F112 9.9626 Tf 1.016 0 0 1 50.112 407.474 Tm [(noisy)-246(class-posterior)-247(probabilitie)1(s,)-247(statistically)64(.)-306(W)79(e)-246<02727374>-247(re-)]TJ/F112 9.9626 Tf 0.98 0 0 1 49.863 395.519 Tm [(vie)26(w)-242(representa)1(ti)25(v)15(e)-241(w)10(orks)-241(under)-241(the)-241(CCN.)-241(By)-241(le)26(v)15(eraging)-241(the)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 383.564 Tm [(class-dependent)-270(transition)-270(matrix)-270(\(CDTM\))]TJ/F11 9.9626 Tf 1 0 0 1 227.036 383.564 Tm [(T)]TJ/F112 9.9626 Tf 1.02 0 0 1 234.241 383.564 Tm [(,)-276(the)-270(training)]TJ/F112 9.9626 Tf 0.985 0 0 1 50.112 371.608 Tm [(loss)-255(on)-254(the)-255(noisy)-254(data)-255(can)-254(be)-255(corrected.)-317(There)-255(e)16(xist)-255(man)15(y)-254(al-)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 359.653 Tm [(gorithms)-231(to)-231(estimate)-231(the)-232(CDTM)]TJ/F11 9.9626 Tf 1 0 0 1 176.389 359.653 Tm [(T)]TJ/F112 9.9626 Tf 0.98 0 0 1 185.852 359.653 Tm [([)]TJ
0 1 0 rg 0 1 0 RG
[(13)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-93(19)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-93(22)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-92(37)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-93(45)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-93(51)]TJ
0 g 0 G
[(].)-308(F)15(or)]TJ 0.98 0 0 1 50.112 347.698 Tm [(e)15(xample,)-222(Liu)]TJ/F117 9.9626 Tf 0.98 0 0 1 103.314 347.698 Tm [(et)-215(al)]TJ/F112 9.9626 Tf 0.98 0 0 1 120.065 347.698 Tm [(.)-215([)]TJ
0 1 0 rg 0 1 0 RG
[(22)]TJ
0 g 0 G
[(])-214(introduced)-215(the)-215(anchor)-215(point)1(s)-215(assump-)]TJ/F112 9.9626 Tf 1.002 0 0 1 50.112 335.743 Tm [(tion)-250(to)-250(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 114.167 335.743 Tm [(T)]TJ/F112 9.9626 Tf 1.002 0 0 1 121.373 335.743 Tm [(,)-250(Li)]TJ/F117 9.9626 Tf 1.002 0 0 1 137.734 335.743 Tm [(et)-250(al)]TJ/F112 9.9626 Tf 1.002 0 0 1 155.213 335.743 Tm [(.)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(19)]TJ
0 g 0 G
[(])-250(tried)-250(to)-250(optimize)-250(the)-250(transi-)]TJ/F112 9.9626 Tf 0.989 0 0 1 50.112 323.788 Tm [(tion)-253(matrix)-254(by)-254(mi)1(n)-1(i)1(mizing)-254(the)-253(v)20(olume)-254(of)]TJ/F11 9.9626 Tf 1 0 0 1 213.557 323.788 Tm [(T)]TJ/F112 9.9626 Tf 0.989 0 0 1 220.763 323.788 Tm [(.)-316(T)81(o)-253(estimate)-254(the)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 311.833 Tm [(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 77.429 311.833 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 97.365 311.833 Tm [(,)-245(e)15(xisting)-243(w)10(orks)-243(rely)-243(on)-242(v)25(arious)-243(assumptions,)-245(for)]TJ/F112 9.9626 Tf 1.003 0 0 1 50.112 299.877 Tm [(e)15(xample,)-250(Cheng)]TJ/F117 9.9626 Tf 1.003 0 0 1 117.398 299.877 Tm [(et)-250(al)]TJ/F112 9.9626 Tf 1.003 0 0 1 134.892 299.877 Tm [(.)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(5)]TJ
0 g 0 G
[(])-250(proposed)-249(to)-250(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 239.232 299.877 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.003 0 0 1 261.663 299.877 Tm [(with)-250(a)]TJ/F112 9.9626 Tf 0.993 0 0 1 50.112 287.922 Tm [(bounded)-253(noise)-252(rate,)-253(Xia)]TJ/F117 9.9626 Tf 0.993 0 0 1 146.649 287.922 Tm [(et)-253(al)]TJ/F112 9.9626 Tf 0.993 0 0 1 163.996 287.922 Tm [(.)-253([)]TJ
0 1 0 rg 0 1 0 RG
[(44)]TJ
0 g 0 G
[(])-252(proposed)-253(to)-252(approximate)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 275.967 Tm [(the)-312(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 94.826 275.967 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 117.929 275.967 Tm [(by)-312(utilizing)-311(the)-312(part)-311(re)14(gularization)-311(of)-312(the)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 264.012 Tm [(transition)-201(matrices.)-298(Berthon)]TJ/F117 9.9626 Tf 0.98 0 0 1 160.804 264.012 Tm [(et)-201(al)]TJ/F112 9.9626 Tf 0.98 0 0 1 177.418 264.012 Tm [(.)-201([)]TJ
0 1 0 rg 0 1 0 RG
[(3)]TJ
0 g 0 G
[(])-200(introduced)-201(the)-201(instance-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 252.057 Tm [(le)25(v)14(el)-252(forw)10(ard)-253(correction)-252(method)-253(to)-253(esti)1(mate)]TJ/F11 9.9626 Tf 1 0 0 1 230.384 252.057 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 250.319 252.057 Tm [(,)-254(Y)98(ang)]TJ/F117 9.9626 Tf 1.02 0 0 1 279.025 252.057 Tm [(et)]TJ/F117 9.9626 Tf 1.008 0 0 1 50.112 240.101 Tm [(al)]TJ/F112 9.9626 Tf 1.008 0 0 1 57.935 240.101 Tm [(.)-249([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(])-248(proposed)-249(to)-249(infer)-248(the)-249(Bayes)-249(optimal)-248(distrib)20(ution)-249(in-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 228.146 Tm [(stead)-303(of)-304(the)-303(clean)-303(distrib)20(ution.)-479(Although)-303(abo)14(v)15(e)-303(adv)24(anced)]TJ/F112 9.9626 Tf 0.991 0 0 1 50.112 216.191 Tm [(methods)-252(achie)25(v)15(ed)-251(success)-252(empirically)65(,)-252(some)-252(strong)-252(assump-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 204.236 Tm [(tions)-319(limit)-320(their)-319(applications)-319(in)-320(practice)-319([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(].)-527(In)-319(contrast,)]TJ/F112 9.9626 Tf 0.987 0 0 1 50.112 192.281 Tm [(our)-254(w)10(ork)-254(proposes)-254(a)-255(manifold-re)16(gularized)-255(method)-254(to)-254(reduce)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 180.326 Tm [(the)-319(estimation)-320(error)-319(without)-320(hurting)-319(much)-320(approximation)]TJ 1.02 0 0 1 50.112 168.37 Tm [(error)-359(of)]TJ/F11 9.9626 Tf 1 0 0 1 85.627 168.37 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 105.563 168.37 Tm [(,)-388(which)-359(achie)24(v)15(es)-360(superior)-359(performances)-360(for)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 156.415 Tm [(label-noise)-250(learning.)]TJ/F111 9.9626 Tf 11.955 -15.639 Td [(Extracting)-287(con\002dent)-287(clean)-287(examples)]TJ/F112 9.9626 Tf 1.02 0 0 1 219.615 140.776 Tm [(is)-281(crucial)-282(for)-281(op-)]TJ 1.02 0 0 1 50.112 128.821 Tm [(timizing)-321(the)-320(transition)-321(matrix)]TJ/F11 9.9626 Tf 1 0 0 1 174.365 128.821 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 197.559 128.821 Tm [(when)-321(only)-320(noisy)-321(data)]TJ 1.02 0 0 1 50.112 116.866 Tm [(is)-332(a)20(v)25(ailable.)-564(T)79(o)-332(accurately)-332(estimate)-331(the)-332(transition)-331(matrix,)]TJ 1.02 0 0 1 49.753 104.91 Tm [(we)-318(usually)-318(require)-318(that)-318(some)-318(clean)-318(data)-318(of)-318(each)-318(class)-318(are)]TJ/F112 9.9626 Tf 0.989 0 0 1 50.112 92.955 Tm [(gi)25(v)15(en.)-313(When)-252(clean)-253(data)-252(is)-252(not)-253(a)21(v)25(ailable,)-253(the)16(y)-253(are)-252(required)-252(to)]TJ/F112 9.9626 Tf 1.002 0 0 1 50.112 81 Tm [(be)-250(e)15(xtracted)-250(from)-250(the)-250(noisy)-250(data)-250(automatically)65(,)-250(to)-250(construct)]TJ
0 g 0 G
0 g 0 G
/F112 9.9626 Tf 1.02 0 0 1 308.862 710.037 Tm [(con\002dent)-342(clean)-342(dataset)-343(for)-342(optimizing)]TJ/F11 9.9626 Tf 1 0 0 1 469.623 710.037 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 489.559 710.037 Tm [(.)-595(The)-343(curren-)]TJ 1.02 0 0 1 308.862 698.082 Tm [(t)-340(ef)25(f)1(ecti)24(v)15(e)-340(methods)-339(mainly)-340(include)-339(b)19(ut)-339(not)-340(limited)-339(to)-340(the)]TJ 1.02 0 0 1 308.862 686.127 Tm [(follo)25(wing)-367(approaches:)-547(the)-366(distillation)-367(method)-366([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(],)-397(sam-)]TJ 1.02 0 0 1 308.862 674.172 Tm [(ple)-364(sie)24(v)15(e)-365(approach)-364([)]TJ
0 1 0 rg 0 1 0 RG
[(5)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-207(25)]TJ
0 g 0 G
[(],)-394(loss)-365(distrib)20(ution)-365(modeling)-364(by)]TJ 1.02 0 0 1 308.862 662.217 Tm [(a)-304(Gaussian)-303(mixture)-304(model)-304([)]TJ
0 1 0 rg 0 1 0 RG
[(18)]TJ
0 g 0 G
[(],)-318(con\002dence-based)-304(sample)]TJ 1.02 0 0 1 308.862 650.262 Tm [(collection)-390([)]TJ
0 1 0 rg 0 1 0 RG
[(3)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-225(9)]TJ
0 g 0 G
[(],)-427(small-loss-based)-390(methods)-390([)]TJ
0 1 0 rg 0 1 0 RG
[(11)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-225(41)]TJ
0 g 0 G
[(],)-427(and)]TJ 1.02 0 0 1 308.862 638.306 Tm [(some)-344(early)-345(stopping)-344(techniques)-345([)]TJ
0 1 0 rg 0 1 0 RG
[(2)]TJ
0 g 0 G
[(].)-602(When)-344(the)-345(con\002dent)]TJ 1.02 0 0 1 308.862 626.351 Tm [(clean)-307(e)15(xamples)-307(are)-307(obtained,)-322(the)-307(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 475.723 626.351 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 498.776 626.351 Tm [(for)-307(each)-307(in-)]TJ/F112 9.9626 Tf 1.014 0 0 1 308.862 614.396 Tm [(stance)-246(can)-245(be)-246(learned.)-306(Besides,)-246(there)-245(also)-246(e)15(xist)-246(man)15(y)-246(other)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 602.441 Tm [(semi-supervised)-279(learning)-279(methods)-278([)]TJ
0 1 0 rg 0 1 0 RG
[(5)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-150(8)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-150(10)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-150(18)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-150(28)]TJ
0 g 0 G
[(],)-288(which)]TJ/F112 9.9626 Tf 1.007 0 0 1 308.862 590.486 Tm [(transform)-249(the)-250(label-noise)-249(learning)-250(into)-249(the)-250(semi-supervised)]TJ/F112 9.9626 Tf 0.985 0 0 1 308.862 578.531 Tm [(learning)-253(by)-252(using)-253(the)-252(e)15(xtracted)-253(con\002dent)-252(clean)-253(e)15(xa)1(mples.)-315(In)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 566.575 Tm [(this)-267(paper)39(,)-273(we)-267(also)-267(need)-268(to)-267(adopt)-267(such)-268(a)-267(method)-267(to)-267(e)14(xtract)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 554.62 Tm [(con\002dent)-250(clean)-250(e)15(xamples)-250(for)-250(optimizing)-250(the)-250(IDTM)]TJ/F11 9.9626 Tf 205.438 0 Td [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F111 11.9552 Tf -225.373 -20.313 Td [(3.)-250(Label-Noise)-250(Lear)15(ning)-250(Method)]TJ/F112 9.9626 Tf 1.02 0 0 1 320.817 514.688 Tm [(In)-289(this)-288(section,)-300(we)-288(obtain)-289(a)-289(statistically)-288(consistent)-289(clas-)]TJ 1.02 0 0 1 308.862 502.732 Tm [(si\002er)-332(through)-331(the)-332(estimated)-331(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 454.978 502.732 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 474.914 502.732 Tm [(.)-564(S)1(peci\002cally)63(,)-353(as)]TJ/F112 9.9626 Tf 0.988 0 0 1 308.862 490.777 Tm [(illustrated)-254(in)-253(Figure)]TJ
1 0 0 rg 1 0 0 RG
[-254(1)]TJ
0 g 0 G
[(,)-254(the)-254(proposed)-253(method)-254(mainly)-254(consists)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 478.822 Tm [(of)-253(the)-253(follo)26(wing)-253(components:)-315(the)-253(input)-253(noisy)-252(data,)-254(con\002dent)]TJ/F112 9.9626 Tf 0.995 0 0 1 308.862 466.867 Tm [(clean)-252(e)15(xample-e)15(xtracting)-252(module,)-253(where)-252(we)-252(ha)20(v)15(e)-253(cast)-252(them)]TJ/F112 9.9626 Tf 0.987 0 0 1 308.862 454.912 Tm [(as)-254(a)-254(whole)-254(i)1(n)-254(Figure)]TJ
1 0 0 rg 1 0 0 RG
[-254(1)]TJ
0 g 0 G
[(,)-254(the)-254(backbone)-254(netw)10(ork)-254(and)-253(the)-254(transi-)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 442.957 Tm [(tion)-246(neural)-246(netw)10(ork)-245(aiming)-246(to)-246(learn)-246(the)-246(instance)-246(features)-246(and)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 431.001 Tm [(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 345.518 431.001 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 368.24 431.001 Tm [(respecti)25(v)14(ely)64(,)-282(the)-274(cross-entrop)10(y)-274(loss)-274(training)]TJ 1.02 0 0 1 308.503 419.046 Tm [(with)-329(noisy)-330(labels,)-350(and)-329(the)-329(proposed)-330(manifold-re)15(gularized)]TJ 1.02 0 0 1 308.862 407.091 Tm [(objecti)25(v)14(e.)-427(Finally)63(,)-296(we)-287(jointly)-286(train)-286(the)-287(DNN)-286(to)-286(learn)]TJ/F11 9.9626 Tf 1 0 0 1 526.342 407.091 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.017 0 0 1 308.862 395.136 Tm [(for)-247(each)-246(instance,)-247(and)-247(obtain)-247(a)-246(consistent)-247(classi\002er)]TJ/F11 9.9626 Tf 1 0 0 1 515.977 395.136 Tm [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf -233.541 -11.955 Td [(on)-250(the)-250(gi)25(v)15(en)-250(noisy)-250(data.)]TJ/F111 10.9589 Tf 0 -19.163 Td [(3.1.)-250(Pr)18(oblem)-250(Setting)]TJ/F112 9.9626 Tf 1.02 0 0 1 320.817 345.395 Tm [(De\002ne)]TJ/F11 9.9626 Tf 1 0 0 1 351.108 345.395 Tm [(D)]TJ/F112 9.9626 Tf 1.02 0 0 1 362.833 345.395 Tm [(be)-315(the)-315(distrib)20(ution)-315(of)-315(pair)20(-wise)-315(random)-315(v)25(ari-)]TJ 1.02 0 0 1 308.862 333.44 Tm [(ables)]TJ/F8 9.9626 Tf 1 0 0 1 333.201 333.44 Tm [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(X)]TJ/F11 9.9626 Tf 7.193 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(Y)]TJ/F8 9.9626 Tf 7.193 0 Td 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[(1)]TJ
0 g 0 G
[(\),)-245(only)-244(the)-244(noisy)-245(class-posterior)-244(probability)]TJ/F11 9.9626 Tf 1 0 0 1 50.112 536.736 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.382 2.518 Td [<16>]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F14 9.9626 Tf 7.998 0 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(X)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 86.583 536.736 Tm [(can)-294(be)-293(obtained)-294(by)-293(e)14(xploiting)-293(the)-294(noisy)-294(data.)-449(T)78(o)]TJ/F112 9.9626 Tf 0.991 0 0 1 50.112 524.781 Tm [(accurately)-251(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 128.545 524.781 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.991 0 0 1 148.481 524.781 Tm [(,)-251(there)-251(contain)-252(tw)10(o)-251(important)-251(steps:)]TJ/F112 9.9626 Tf 1.02 0 0 1 49.365 512.826 Tm [(1\))-315(e)14(xtracting)-315(con\002dent)-316(clean)-315(e)14(xamples;)-350(2\))-316(optimizing)-315(the)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 500.87 Tm [(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 77.112 500.87 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 99.103 500.87 Tm [(based)-210(on)-211(the)-210(gi)25(v)15(en)-210(noisy)-211(labels)-210(and)-211(the)-210(e)15(xtracted)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 488.915 Tm [(con\002dent)-250(clean)-250(e)15(xamples.)]TJ/F111 9.9626 Tf 11.955 -11.955 Td [(Extracting)-239(con\002dent)-240(clean)-239(examples)]TJ/F112 9.9626 Tf 0.98 0 0 1 217.716 476.96 Tm [(is)-244(v)15(ery)-244(crucial)-244(for)]TJ/F112 9.9626 Tf 1.012 0 0 1 50.112 465.005 Tm [(optimizing)-247(the)-246(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 139.347 465.005 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.012 0 0 1 161.769 465.005 Tm [(as)-247(can)-246(be)-247(inferred)-246(from)-247(Eq.)-247(\()]TJ
1 0 0 rg 1 0 0 RG
[(1)]TJ
0 g 0 G
[(\).)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 453.05 Tm [(In)-386(the)-385(related)-386(w)10(ork)-386(section,)-421(we)-386(ha)20(v)15(e)-386(listed)-386(man)15(y)-386(useful)]TJ/F112 9.9626 Tf 1.004 0 0 1 50.112 441.095 Tm [(sample-sie)25(v)15(e)-249(approaches.)-309(In)-249(this)-249(paper)40(,)-249(we)-249(adopt)-249(the)-249(e)14(xam-)]TJ/F112 9.9626 Tf 0.996 0 0 1 50.112 429.139 Tm [(ple)-251(distillation)-251(method)-251([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(])-251(to)-251(e)15(xtract)-251(con\002dent)-252(clean)-251(e)15(xam-)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 417.184 Tm [(ples.)-307(This)-229(method)-228(can)-229(e)15(xtract)-228(a)-229(distilled)-228(sub-dataset)-229(with)-228(the-)]TJ/F112 9.9626 Tf 1.012 0 0 1 50.112 405.229 Tm [(oretically)-246(guaranteed)-246(Bayes)-247(optimal)-246(labels)-246(out)-247(of)-246(the)-246(noisy)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 393.274 Tm [(dataset.)-503(Note)-312(that)-311(our)-312(method)-311(is)-312(not)-311(limited)-312(to)-312(the)-311(abo)15(v)14(e)]TJ/F112 9.9626 Tf 0.991 0 0 1 50.112 381.319 Tm [(distillation-based)-254(e)15(xample)-254(e)15(xtraction)-254(method,)-255(b)21(ut)-255(man)16(y)-255(oth-)]TJ/F112 9.9626 Tf 1.003 0 0 1 50.112 369.364 Tm [(er)-249(sample-sie)25(v)15(e)-249(approaches)-249(can)-249(also)-249(be)-250(used.)-309(Then,)-249(we)-249(can)]TJ/F112 9.9626 Tf 1.001 0 0 1 50.112 357.408 Tm [(train)-249(a)-249(DNN)-248(on)-249(the)-249(e)15(xtracted)-249(sub-dataset)-248(to)-249(learn)-249(the)-249(transi-)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 345.453 Tm [(tion)-246(matrix)]TJ/F11 9.9626 Tf 1 0 0 1 95.604 345.453 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 117.944 345.453 Tm [(to)-246(model)-246(the)-247(relationships)-246(between)-246(the)-246(con-)]TJ/F112 9.9626 Tf 1.013 0 0 1 50.112 333.498 Tm [(\002dent)-246(clean)-246(data)-246(distrib)20(ution)]TJ/F11 9.9626 Tf 1 0 0 1 167.486 333.498 Tm [(D)]TJ/F112 9.9626 Tf 1.013 0 0 1 178.493 333.498 Tm [(and)-246(the)-246(noisy)-246(data)-246(distrib)20(u-)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 321.543 Tm [(tion)]TJ/F8 9.9626 Tf 20.321 2.518 Td [<16>]TJ/F11 9.9626 Tf -2.326 -2.518 Td [(D)]TJ/F112 9.9626 Tf 8.525 0 Td [(.)-311(Here,)-250(we)-251(denote)-250(as)]TJ/F8 9.9626 Tf 86.208 2.518 Td [<16>]TJ/F14 9.9626 Tf -2.321 -2.518 Td [(D)]TJ/F7 6.9738 Tf 7.962 3.615 Td [(s)]TJ/F8 9.9626 Tf 6.428 -3.615 Td [(:=)]TJ/F14 9.9626 Tf 13.289 0 Td [(f)]TJ/F8 9.9626 Tf 4.981 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F7 6.9738 Tf 4.982 3.615 Td [(s)]TJ/F10 6.9738 Tf 0 -6.208 Td [(i)]TJ/F11 9.9626 Tf 3.654 2.593 Td [(;)]TJ/F8 9.9626 Tf 5.112 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.495 Td [(\))]TJ/F14 9.9626 Tf 3.875 0 Td [(g)]TJ/F10 6.9738 Tf 4.981 3.615 Td [(N)]TJ/F6 4.9813 Tf 7.058 3.007 Td [(s)]TJ/F10 6.9738 Tf -7.058 -9.215 Td [(i)]TJ/F7 6.9738 Tf 2.819 0 Td [(=1)]TJ/F112 9.9626 Tf 13.079 2.593 Td [(the)-250(e)15(xtract-)]TJ/F112 9.9626 Tf 0.983 0 0 1 50.112 309.588 Tm [(ed)-254(e)15(xamples.)-316(F)15(or)-254(simplicity)66(,)-255(we)-254(still)-255(use)]TJ/F8 9.9626 Tf 1 0 0 1 212.621 312.106 Tm [<16>]TJ/F14 9.9626 Tf -2.321 -2.518 Td [(D)]TJ/F8 9.9626 Tf 10.733 0 Td [(:=)]TJ/F14 9.9626 Tf 13.286 0 Td [(f)]TJ/F8 9.9626 Tf 4.981 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.495 Td [(;)]TJ/F8 9.9626 Tf 5.112 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.495 Td [(\))]TJ/F14 9.9626 Tf 3.875 0 Td [(g)]TJ/F10 6.9738 Tf 4.981 3.615 Td [(N)]TJ 0 -6.209 Td [(i)]TJ/F7 6.9738 Tf 2.819 0 Td [(=1)]TJ/F112 9.9626 Tf -225.665 -9.362 Td [(in)-250(the)-250(follo)25(wing)-250(descriptions.)]TJ/F111 10.9589 Tf 0 -18.463 Td [(3.2.)-250(The)-250(LabelNoise)-250(Lear)15(ning)-250(Framew)10(ork)]TJ/F112 9.9626 Tf 1.012 0 0 1 62.067 261.236 Tm [(Gi)25(v)15(en)-248(the)-248(e)15(xtracted)-247(training)-248(e)15(xamples)]TJ/F14 9.9626 Tf 1 0 0 1 217.208 261.236 Tm [(f)]TJ/F8 9.9626 Tf 4.981 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F7 6.9738 Tf 4.982 3.616 Td [(s)]TJ/F10 6.9738 Tf 0 -6.209 Td [(i)]TJ/F11 9.9626 Tf 3.654 2.593 Td [(;)]TJ/F8 9.9626 Tf 5.112 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F14 9.9626 Tf 3.875 0 Td [(g)]TJ/F10 6.9738 Tf 4.981 3.616 Td [(N)]TJ/F6 4.9813 Tf 7.058 3.006 Td [(s)]TJ/F10 6.9738 Tf -7.058 -9.215 Td [(i)]TJ/F7 6.9738 Tf 2.819 0 Td [(=1)]TJ/F112 9.9626 Tf 1.012 0 0 1 269.588 261.236 Tm [(,)-248(we)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 249.281 Tm [(train)-340(the)-340(transition)-340(neural)-340(netw)10(ork)-340(parameterized)-340(by)]TJ/F11 9.9626 Tf 1 0 0 1 270.047 249.281 Tm [<12>]TJ/F112 9.9626 Tf 1.02 0 0 1 278.456 249.281 Tm [(to)]TJ 1.02 0 0 1 50.112 237.326 Tm [(estimate)]TJ/F11 9.9626 Tf 1 0 0 1 86.846 237.326 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 106.782 237.326 Tm [(,)-291(which)-282(models)-282(the)-282(probability)-282(of)-282(observing)]TJ 1.02 0 0 1 50.112 225.371 Tm [(a)-266(noisy)-266(label)]TJ/F8 9.9626 Tf 1 0 0 1 105.185 225.371 Tm [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F112 9.9626 Tf 1.02 0 0 1 112.444 225.371 Tm [(from)-266(the)-266(gi)25(v)15(en)-266(input)-266(instance)]TJ/F111 9.9626 Tf 1 0 0 1 234.494 225.371 Tm [(x)]TJ/F112 9.9626 Tf 1.02 0 0 1 242.176 225.371 Tm [(and)-266(its)-266(cor)20(-)]TJ 1.02 0 0 1 50.112 213.416 Tm [(responding)-287(estimated)-287(latent)-287(clean)-287(label)]TJ/F8 9.9626 Tf 1 0 0 1 213.266 213.416 Tm [(^)]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F112 9.9626 Tf 1.02 0 0 1 217.824 213.416 Tm [(.)-430(Then,)-297(it)-288(can)-287(be)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 201.46 Tm [(e)15(xpressed)-238(as)]TJ/F11 9.9626 Tf 1 0 0 1 101.246 201.46 Tm [(T)]TJ/F10 6.9738 Tf 5.822 -1.494 Td [(ij)]TJ/F8 9.9626 Tf 7.016 1.494 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.953 0 Td [(\))-278(=)]TJ/F11 9.9626 Tf 17.158 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.383 2.519 Td [<16>]TJ/F11 9.9626 Tf -1.509 -2.519 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(j)]TJ/F14 9.9626 Tf 4.673 0 Td [(j)]TJ/F8 9.9626 Tf 4.276 2.519 Td [(^)]TJ/F11 9.9626 Tf -1.508 -2.519 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(i;)]TJ/F111 9.9626 Tf 7.86 0 Td [(X)]TJ/F8 9.9626 Tf 9.96 0 Td [(=)]TJ/F111 9.9626 Tf 10.517 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.953 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 257.71 201.46 Tm [(,)-242(where)]TJ/F11 9.9626 Tf 1 0 0 1 50.112 188.177 Tm [(T)]TJ/F10 6.9738 Tf 5.822 -1.494 Td [(ij)]TJ/F8 9.9626 Tf 7.016 1.494 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F14 9.9626 Tf 7.692 0 Td [(2)]TJ/F62 9.9626 Tf 10.46 0 Td [(R)]TJ/F10 6.9738 Tf 7.195 3.615 Td [(K)]TJ/F13 6.9738 Tf 7.183 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(K)]TJ/F112 9.9626 Tf 1.02 0 0 1 127.626 188.177 Tm [(,)]TJ/F8 9.9626 Tf 1 0 0 1 134.874 190.695 Tm [(^)]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F112 9.9626 Tf 1.02 0 0 1 144.422 188.177 Tm [(is)-301(the)-301(v)25(ariable)-301(for)-301(the)-301(labels)-301(of)-301(the)]TJ 1.02 0 0 1 50.112 176.222 Tm [(e)15(xtracted)-301(con\002dent)-302(clean)-301(data.)-472(T)78(o)-301(e)15(xtract)-301(con\002dent)-302(clean)]TJ/F112 9.9626 Tf 1.014 0 0 1 50.112 164.267 Tm [(data,)-246(we)-246(need)-246(to)-245(learn)-246(the)-246(noisy)-246(class-posterior)-246(probability)65(,)]TJ/F112 9.9626 Tf 0.994 0 0 1 49.753 152.311 Tm [(which)-251(can)-250(be)-251(obtained)-251(by)-250(a)-251(classi\002er)]TJ/F11 9.9626 Tf 1 0 0 1 198.034 152.311 Tm [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F14 9.9626 Tf 3.875 0 Td [<0f>]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 0.994 0 0 1 230.818 152.311 Tm [(parameterised)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 140.356 Tm [(by)]TJ/F111 9.9626 Tf 12.453 0 Td [(w)]TJ/F112 9.9626 Tf 7.193 0 Td [(,)-250(i.e.,)]TJ/F11 9.9626 Tf 22.137 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.382 2.519 Td [(^)]TJ/F11 9.9626 Tf -1.508 -2.519 Td [(Y)]TJ/F14 9.9626 Tf 7.998 0 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))-278(=)]TJ/F11 9.9626 Tf 17.157 0 Td [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F112 9.9626 Tf 1.02 0 0 1 62.067 128.401 Tm [(The)-289(probability)-290(of)-289(observing)-289(a)-290(noisy)-289(label)]TJ/F8 9.9626 Tf 1 0 0 1 239.392 130.919 Tm [<16>]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F112 9.9626 Tf 1.02 0 0 1 248.822 128.401 Tm [(gi)24(v)15(en)-289(the)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 116.446 Tm [(input)-250(instance)]TJ/F111 9.9626 Tf 58.111 0 Td [(x)]TJ/F112 9.9626 Tf 7.472 0 Td [(can)-250(be)-250(inferred)-250(as,)]TJ/F11 9.9626 Tf -57.115 -27.676 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.383 2.518 Td [<16>]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(j)]TJ/F14 9.9626 Tf 4.673 0 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))-278(=)]TJ/F10 6.9738 Tf 20.762 12.453 Td [(K)]TJ/F1 9.9626 Tf -3.604 -2.989 Td [(X)]TJ/F10 6.9738 Tf 0.743 -21.219 Td [(i)]TJ/F7 6.9738 Tf 2.818 0 Td [(=1)]TJ/F11 9.9626 Tf 12.49 11.755 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.383 2.518 Td [<16>]TJ/F11 9.9626 Tf -1.509 -2.518 Td [(Y)]TJ/F8 9.9626 Tf 10.766 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(j)]TJ/F14 9.9626 Tf 4.673 0 Td [(j)]TJ/F8 9.9626 Tf 4.275 2.518 Td [(^)]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(i;)]TJ/F111 9.9626 Tf 7.86 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ 5.382 2.518 Td [(^)]TJ/F11 9.9626 Tf -1.508 -2.518 Td [(Y)]TJ/F8 9.9626 Tf 10.765 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(i)]TJ/F14 9.9626 Tf 3.433 0 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F11 9.9626 Tf 3.875 0 Td [(:)]TJ/F112 9.9626 Tf 11.236 0 Td [(\(2\))]TJ
0 g 0 G
0 g 0 G
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[(\))]TJ 1.02 0 0 1 308.862 559.879 Tm [(directly)-332(to)-331(obtain)-332(the)-332(parameter)-331(set)]TJ/F8 9.9626 Tf 1 0 0 1 457.774 559.879 Tm [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(w)]TJ/F11 9.9626 Tf 7.193 0 Td [(;)-167<12>]TJ/F8 9.9626 Tf 9.382 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 482.097 559.879 Tm [(.)-564(Ho)25(we)24(v)15(er)39(,)-353(the)]TJ 1.02 0 0 1 308.862 547.924 Tm [(transition)-434(matrix)]TJ/F11 9.9626 Tf 1 0 0 1 382.615 547.924 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.953 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 416.348 547.924 Tm [(must)-434(be)-435(hard)-434(to)-435(learn)-434(without)]TJ 1.02 0 0 1 308.862 535.968 Tm [(an)15(y)-476(assumption,)-534(the)-475(ultimate)-476(reason)-476(is)-476(that)-476(the)-475(de)14(gree)]TJ 1.02 0 0 1 308.862 524.013 Tm [(of)-364(freedom)-364(of)]TJ/F11 9.9626 Tf 1 0 0 1 370.754 524.013 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.953 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 403.772 524.013 Tm [(is)-364(too)-364(high,)-394(and)-365(the)-364(linear)-364(system)]TJ/F11 9.9626 Tf 1 0 0 1 308.862 512.058 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()-69<16>]TJ/F11 9.9626 Tf 3.874 0 Td [(y)]TJ/F14 9.9626 Tf 5.242 0 Td [(j)]TJ/F111 9.9626 Tf 2.768 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))-303(=)]TJ/F11 9.9626 Tf 17.654 0 Td [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()-69(^)]TJ/F11 9.9626 Tf 3.875 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.316 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.875 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 10.875 0 Td [(=)-303(1)]TJ/F11 9.9626 Tf 15.746 0 Td [(;)-167(:::;)-166(N)]TJ/F112 9.9626 Tf 1.02 0 0 1 465.396 512.058 Tm [(,)-262(has)-258(the)-258(same)-258(num-)]TJ 1.02 0 0 1 308.862 500.103 Tm [(ber)-292(of)-291(equations)-292(and)-291(v)24(ariables.)-443(Existing)-292(methods)-292(focused)]TJ 1.02 0 0 1 308.862 488.148 Tm [(on)-275(ho)24(w)-275(to)-276(simplify)]TJ/F11 9.9626 Tf 1 0 0 1 389.253 488.148 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 411.987 488.148 Tm [(itself)-275(and)-276(signi\002cantly)-275(reduce)-275(its)]TJ/F112 9.9626 Tf 0.985 0 0 1 308.862 476.193 Tm [(de)15(gree)-255(of)-254(freedom)-255(or)-255(comple)15(xity)66(,)-255(which)-254(will)-255(certainly)-255(cause)]TJ/F112 9.9626 Tf 1.005 0 0 1 308.862 464.237 Tm [(an)-249(approximation)-249(error)54(.)-309(While)-249(in)-250(our)-249(w)10(ork,)-249(we)-249(will)-250(not)-249(put)]TJ/F112 9.9626 Tf 1.002 0 0 1 308.862 452.282 Tm [(an)15(y)-249(strong)-249(restrictions)-250(on)-249(the)-249(form)-249(of)]TJ/F11 9.9626 Tf 1 0 0 1 459.764 452.282 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.002 0 0 1 479.699 452.282 Tm [(,)-249(instead)-250(we)-249(will)]TJ/F112 9.9626 Tf 0.984 0 0 1 308.862 440.327 Tm [(put)-254(a)-255(mild)-254(assumption)-255(on)-254(the)]TJ/F117 9.9626 Tf 0.984 0 0 1 425.134 440.327 Tm [(g)10(eometry)]TJ/F112 9.9626 Tf 0.984 0 0 1 464.006 440.327 Tm [(of)]TJ/F11 9.9626 Tf 1 0 0 1 474.667 440.327 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.984 0 0 1 497.097 440.327 Tm [(by)-254(using)-255(the)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 428.372 Tm [(manifold)-250(re)15(gularization.)]TJ/F111 10.9589 Tf 0 -18.605 Td [(3.3.)-250(Manif)25(oldRegularized)-250(T)74(ransition)-250(Matrix)]TJ/F112 9.9626 Tf 0.984 0 0 1 320.817 391.834 Tm [(Manifold)-253(learning)-253(typically)-254(aims)-253(to)-253(retain)-253(intrinsic)-253(neigh-)]TJ/F112 9.9626 Tf 1.002 0 0 1 308.862 379.879 Tm [(bouring)-249(structures)-248(in)-249(the)-249(underlying)-248(lo)25(wer)20(-dimensional)-249(fea-)]TJ/F112 9.9626 Tf 0.997 0 0 1 308.862 367.924 Tm [(ture)-251(space.)-312(The)-251(classical)-251(manifold)-251(learning)-251(techniques)-251(such)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 355.969 Tm [(as)-263(LLE)-262([)]TJ
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[(34)]TJ
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[(])-263(and)-263(Isomap)-262([)]TJ
0 1 0 rg 0 1 0 RG
[(40)]TJ
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[(])-263(estimate)-262(the)-263(local)-263(manifolds)]TJ 1.02 0 0 1 308.613 344.014 Tm [(via)-263(justi\002able)-263(assumptions.)-357(Therefore,)-267(we)-263(adopt)-263(the)-263(mani-)]TJ 1.02 0 0 1 308.862 332.059 Tm [(fold)-249(embedding)-250(techniques)-249(to)-250(ful\002ll)-249(our)-250(proposed)-249(assump-)]TJ 1.02 0 0 1 308.862 320.103 Tm [(tion)-346<93746865>-346(closer)-346(tw)10(o)-347(instances)-346(are,)-371(the)-346(more)-346(similar)-346(their)]TJ/F112 9.9626 Tf 0.988 0 0 1 308.862 308.148 Tm [(corresponding)-253(transition)-254(matrices)-253(will)-253<6265942c>-254(to)-253(mak)10(e)-253(the)-254(IDT)93(-)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 296.193 Tm [(M)]TJ/F11 9.9626 Tf 1 0 0 1 321.205 296.193 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 344.451 296.193 Tm [(practically)-326(learnable.)-546(W)40(ith)-326(the)-326(manifold)-326(re)15(gular)20(-)]TJ 1.02 0 0 1 308.862 284.238 Tm [(ization,)-353(though)-331(we)-331(do)-331(not)-332(r)1(educe)-332(the)-331(comple)15(xity)-331(of)]TJ/F11 9.9626 Tf 1 0 0 1 526.342 284.238 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 272.283 Tm [(directly)-382(since)-383(we)-382(do)-382(not)-383(further)-382(model)-382(it,)-417(we)-382(still)-382(ef)24(f)1(ec-)]TJ 1.02 0 0 1 308.862 260.328 Tm [(ti)25(v)14(ely)-355(reduce)-355(the)-356(de)15(gree)-355(of)-356(freedom)-355(of)-355(the)-355(linear)-356(system)]TJ/F11 9.9626 Tf 1 0 0 1 308.862 248.372 Tm [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()-69<16>]TJ/F11 9.9626 Tf 3.874 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))-279(=)]TJ/F11 9.9626 Tf 17.175 0 Td [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F11 9.9626 Tf 3.874 0 Td [(P)]TJ/F8 9.9626 Tf 7.78 0 Td [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F111 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\))]TJ/F112 9.9626 Tf 0.991 0 0 1 417.501 248.372 Tm [(and)-253(mak)10(e)]TJ/F11 9.9626 Tf 1 0 0 1 458.033 248.372 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.991 0 0 1 480.463 248.372 Tm [(stably)-253(estimable.)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 236.417 Tm [(Meanwhile,)]TJ/F11 9.9626 Tf 1 0 0 1 360.464 236.417 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 383.572 236.417 Tm [(can)-312(be)-312(re)14(g)5(arded)-312(as)-312(practically)-312(stable,)-329(s-)]TJ/F112 9.9626 Tf 0.991 0 0 1 308.862 224.462 Tm [(ince)-253(adding)-252(such)-253(a)-253(smoothness)-253(assumption)-252(stops)]TJ/F11 9.9626 Tf 1 0 0 1 503.488 224.462 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 0.991 0 0 1 525.919 224.462 Tm [(from)]TJ/F112 9.9626 Tf 0.992 0 0 1 308.862 212.507 Tm [(changing)-253(too)-253(much.)-315(It)-253(should)-253(be)-253(uniquely)-253(determined)-253(gi)25(v)15(en)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 200.552 Tm [(in\002nite)-250(data)-250(or)-250(the)-250(underlying)-250(data)-250(distrib)20(ution.)]TJ/F112 9.9626 Tf 0.984 0 0 1 320.817 188.597 Tm [(More)-254(speci\002cally)66(,)-254(we)-255(construct)-254(an)-254(intrinsic)-255(af)26(\002nity)-255(graph)]TJ/F112 9.9626 Tf 1.01 0 0 1 308.862 176.641 Tm [(to)-248(characterize)-247(the)-248(within-manifold)-248(consistenc)15(y)-248(and)-247(the)-248(e)15(x-)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 164.686 Tm [(trinsic)-262(af)24<02>1(nity)-262(graph)-262(to)-262(characterize)-262(the)-263(between)-262(manifold)]TJ 1.02 0 0 1 308.862 152.731 Tm [(relationships)-253([)]TJ
0 1 0 rg 0 1 0 RG
[(36)]TJ
0 g 0 G
[(],)-256(respecti)25(v)14(ely)64(.)-329(The)-253(intrinsic)-254(graph)-253(is)-253(con-)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 140.776 Tm [(structed)-234(by)-234(node)-234(adjacenc)15(y)-233(relationships)-234(in)-234(all)-234(the)-234(manifolds,)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.503 128.821 Tm [(where)-258(each)-257(node)-258(is)-258(connected)-258(to)-257(its)]TJ/F11 9.9626 Tf 1 0 0 1 455.516 128.821 Tm [(k)]TJ/F7 6.9738 Tf 5.186 -1.495 Td [(1)]TJ/F112 9.9626 Tf 1.02 0 0 1 465.172 128.821 Tm [(-nearest)-258(neighbours)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.503 116.866 Tm [(within)-242(the)-241(same)-242(manifold.)-311(The)-242(e)15(xtrinsic)-241(graph)-242(is)-241(constructed)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 104.91 Tm [(using)-309(the)-309(between-manifold)-309(node)-309(adjacenc)14(y)-309(relationships)]TJ/F112 9.9626 Tf 1.017 0 0 1 308.862 92.955 Tm [(from)-246(dif)25(ferent)-245(manifolds.)-305(W)79(e)-246(use)-246(the)]TJ/F11 9.9626 Tf 1 0 0 1 460.939 92.955 Tm [(k)]TJ/F7 6.9738 Tf 5.186 -1.494 Td [(2)]TJ/F112 9.9626 Tf 1.017 0 0 1 470.595 92.955 Tm [(-nearest)-246(neighbors)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 81 Tm [(between)-250(the)]TJ/F11 9.9626 Tf 50.351 0 Td [(k)]TJ/F112 9.9626 Tf 5.5 0 Td [(-th)-250(manifold)-250(and)-250(the)-250(other)-250(manifolds.)]TJ
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Td [(N)]TJ/F1 9.9626 Tf -3.666 -2.989 Td [(X)]TJ/F10 6.9738 Tf -2.291 -21.219 Td [(i;j)]TJ/F7 6.9738 Tf 8.885 0 Td [(=1)]TJ/F11 9.9626 Tf 11.747 11.754 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.761 -7.952 Td [(ij)]TJ/F14 9.9626 Tf 11.372 2.777 Td [(jj)]TJ/F11 9.9626 Tf 5.535 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.316 1.494 Td [(\))]TJ/F14 9.9626 Tf 6.089 0 Td [<00>]TJ/F11 9.9626 Tf 9.962 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(j)]TJ/F8 9.9626 Tf 4.197 1.494 Td [(\))]TJ/F14 9.9626 Tf 3.875 0 Td [(jj)]TJ/F7 6.9738 Tf 5.535 4.114 Td [(2)]TJ/F11 9.9626 Tf 4.469 -4.114 Td [(;)]TJ/F112 9.9626 Tf 36.376 0 Td [(\(4\))]TJ/F11 9.9626 Tf -200.851 -39.132 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.114 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.761 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 14.139 2.777 Td [(=)]TJ/F1 9.9626 Tf 10.517 14.047 Td [<1a>]TJ/F8 9.9626 Tf 12.453 -7.97 Td [(1)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 12.73 0 Td [(if)]TJ/F111 9.9626 Tf 8.301 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(j)]TJ/F14 9.9626 Tf 6.966 1.494 Td [(2)-278(N)]TJ/F8 9.9626 Tf 19.051 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.494 Td [(;)-167(k)]TJ/F7 6.9738 Tf 9.614 -1.494 Td [(1)]TJ/F8 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F112 9.9626 Tf 6.089 0 Td [(and)]TJ/F8 9.9626 Tf 17.283 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F8 9.9626 Tf 6.084 1.494 Td [(=)-346<16>]TJ/F11 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(j)]TJ/F11 9.9626 Tf 4.198 1.494 Td [(;)]TJ/F8 9.9626 Tf -136.522 -11.955 Td [(0)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 64.39 0 Td [(else)]TJ/F11 9.9626 Tf 15.491 0 Td [(;)]TJ/F112 9.9626 Tf 72.771 5.878 Td [(\(5\))]TJ/F112 9.9626 Tf 1.02 0 0 1 49.753 577.471 Tm [(where)]TJ/F11 9.9626 Tf 1 0 0 1 77.737 577.471 Tm [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.114 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.761 -7.952 Td [(ij)]TJ/F112 9.9626 Tf 1.02 0 0 1 98.377 577.471 Tm [(refers)-311(to)-311(element)]TJ/F8 9.9626 Tf 1 0 0 1 171.058 577.471 Tm [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [(i;)-167(j)]TJ/F8 9.9626 Tf 12.533 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 194.498 577.471 Tm [(in)-311(the)-311(intrinsic)-310(af)24<02>1(nity)]TJ 1.02 0 0 1 50.112 561.937 Tm [(graph)-264(matrix)]TJ/F111 9.9626 Tf 1 0 0 1 105.14 561.937 Tm [(S)]TJ/F10 6.9738 Tf 5.539 4.401 Td [(I)]TJ/F8 9.9626 Tf 7.687 -4.401 Td [(=)-313(\()]TJ/F11 9.9626 Tf 14.738 0 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.761 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 11.372 2.777 Td 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216.587 549.981 Tm [(k)]TJ/F7 6.9738 Tf 5.187 -1.494 Td [(1)]TJ/F112 9.9626 Tf 1.02 0 0 1 226.243 549.981 Tm [(-nearest)-359(neigh-)]TJ 1.02 0 0 1 50.112 538.026 Tm [(bours)-313(of)-313(the)-314(instance)]TJ/F111 9.9626 Tf 1 0 0 1 139.605 538.026 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 147.903 538.026 Tm [(,)]TJ/F8 9.9626 Tf 1 0 0 1 154.483 538.026 Tm [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F8 9.9626 Tf 7.366 1.494 Td [(=)-475<16>]TJ/F11 9.9626 Tf 11.797 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 190.112 538.026 Tm [(indicates)-313(that)]TJ/F111 9.9626 Tf 1 0 0 1 247.845 538.026 Tm [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 259.326 538.026 Tm [(and)]TJ/F111 9.9626 Tf 1 0 0 1 277.183 538.026 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 526.071 Tm [(are)-259(in)-259(the)-259(same)-260(manifol)1(d,)-263(the)-259(distance)-259(used)-260(for)-259(computing)]TJ/F112 9.9626 Tf 0.984 0 0 1 50.112 514.116 Tm [(nearest)-254(neighbours)-255(is)-254(the)-255(Euclidean)-254(distance)-255(between)]TJ/F111 9.9626 Tf 1 0 0 1 261.413 514.116 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F112 9.9626 Tf 0.984 0 0 1 272.206 514.116 Tm [(and)]TJ/F111 9.9626 Tf 1 0 0 1 49.863 502.161 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 61.736 502.161 Tm [(in)-265(the)-265(feature)-265(space.)-364(Ob)15(viously)64(,)-271(m)1(inimizing)-266(t)1(he)-266(within-)]TJ 1.02 0 0 1 50.112 490.206 Tm [(manifold)-320(consistenc)15(y)-321(encourages)-320(the)-320(learned)-320(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 267.592 490.206 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.004 0 0 1 50.112 478.25 Tm [(to)-249(be)-248(close,)-249(if)-248(their)-249(corresponding)-248(instances)-249(are)-248(close)-249(in)-248(the)]TJ/F112 9.9626 Tf 1.009 0 0 1 50.112 466.295 Tm [(same)-248(cate)15(gory)65(.)-308(This)-247(k)10(eeps)-248(the)-248(manifold)-248(in)-247(the)-248(instance)-248(fea-)]TJ/F112 9.9626 Tf 1.004 0 0 1 50.112 454.34 Tm [(ture)-248(space)-248(to)-248(be)-248(consistent)-248(with)-247(that)-248(in)-248(the)-248(transition)-248(matrix)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 442.385 Tm [(space.)]TJ/F112 9.9626 Tf 1.02 0 0 1 62.067 430.43 Tm [(Meanwhile,)-332(since)-315(instances)-315(with)-315(dif)25(ferent)-314(noisy)-315(labels)]TJ/F112 9.9626 Tf 0.991 0 0 1 50.112 418.475 Tm [(correspond)-252(to)-253(dif)25(ferent)-252(ef)25(fecti)25(v)15(e)-253(ro)26(w)-253(v)25(alues)-252(in)-253(the)-252(transition)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 406.519 Tm [(matrix,)-279(we)-273(also)-272(construct)-273(a)-272(e)15(xtrinsic)-273(graph)-272(to)-273(characterize)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 394.564 Tm [(the)-250(mar)18(gin)-250(between)-250(manifolds.)-310(It)-250(can)-250(be)-250(e)15(xpressed)-250(as:)]TJ/F14 9.9626 Tf 42.938 -30.951 Td [(M)]TJ/F10 6.9738 Tf 11.965 -1.495 Td [(B)]TJ/F8 9.9626 Tf 9.624 1.495 Td [(=)]TJ/F10 6.9738 Tf 16.473 12.453 Td [(N)]TJ/F1 9.9626 Tf -3.666 -2.989 Td [(X)]TJ/F10 6.9738 Tf -2.291 -21.219 Td [(i;j)]TJ/F7 6.9738 Tf 8.885 0 Td [(=1)]TJ/F11 9.9626 Tf 11.747 11.755 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(B)]TJ/F7 6.9738 Tf 6.359 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F14 9.9626 Tf 13.659 2.777 Td [(jj)]TJ/F11 9.9626 Tf 5.534 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.495 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.495 Td [(\))]TJ/F14 9.9626 Tf 6.088 0 Td [<00>]TJ/F11 9.9626 Tf 9.962 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.495 Td [(j)]TJ/F8 9.9626 Tf 4.198 1.495 Td [(\))]TJ/F14 9.9626 Tf 3.874 0 Td [(jj)]TJ/F7 6.9738 Tf 5.535 4.113 Td [(2)]TJ/F11 9.9626 Tf 4.469 -4.113 Td [(;)]TJ/F112 9.9626 Tf 34.09 0 Td [(\(6\))]TJ/F11 9.9626 Tf -207.802 -39.133 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(B)]TJ/F7 6.9738 Tf 6.36 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 16.425 2.777 Td [(=)]TJ/F1 9.9626 Tf 10.517 14.048 Td [<1a>]TJ/F8 9.9626 Tf 12.453 -7.971 Td [(1)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 12.73 0 Td [(if)]TJ/F111 9.9626 Tf 8.301 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(j)]TJ/F14 9.9626 Tf 6.966 1.494 Td [(2)-278(N)]TJ/F8 9.9626 Tf 19.051 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.494 Td [(;)-167(k)]TJ/F7 6.9738 Tf 9.614 -1.494 Td [(2)]TJ/F8 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F112 9.9626 Tf 6.089 0 Td [(and)]TJ/F8 9.9626 Tf 17.283 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F14 9.9626 Tf 6.084 1.494 Td [(6)]TJ/F8 9.9626 Tf 0 0 Td [(=)-346<16>]TJ/F11 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(j)]TJ/F11 9.9626 Tf 4.197 1.494 Td [(;)]TJ/F8 9.9626 Tf -136.521 -11.955 Td [(0)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 64.39 0 Td [(else)]TJ/F11 9.9626 Tf 15.491 0 Td [(;)]TJ/F112 9.9626 Tf 77.436 5.878 Td [(\(7\))]TJ/F112 9.9626 Tf 0.98 0 0 1 49.753 297.864 Tm [(where)]TJ/F11 9.9626 Tf 1 0 0 1 75.842 297.864 Tm [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.114 0 Td [(B)]TJ/F7 6.9738 Tf 6.359 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F112 9.9626 Tf 0.98 0 0 1 97.846 297.864 Tm [(denotes)-229(element)]TJ/F8 9.9626 Tf 1 0 0 1 163.057 297.864 Tm [(\()]TJ/F11 9.9626 Tf 3.875 0 Td [(i;)-167(j)]TJ/F8 9.9626 Tf 12.533 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 185.576 297.864 Tm [(of)-229(the)-229(between-class)-229(af)25<026e2d>]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 282.329 Tm [(ity)-322(matrix)]TJ/F111 9.9626 Tf 1 0 0 1 93.916 282.329 Tm [(S)]TJ/F10 6.9738 Tf 5.539 4.401 Td [(B)]TJ/F8 9.9626 Tf 11.069 -4.401 Td [(=)-423(\()]TJ/F11 9.9626 Tf 15.835 0 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(B)]TJ/F7 6.9738 Tf 6.359 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 13.658 2.777 Td [(\))]TJ/F10 6.9738 Tf 3.875 -1.494 Td [(N)]TJ/F13 6.9738 Tf 7.058 0 Td [<02>]TJ/F10 6.9738 Tf 6.227 0 Td [(N)]TJ/F112 9.9626 Tf 1.02 0 0 1 170.842 282.329 Tm [(,)]TJ/F14 9.9626 Tf 1 0 0 1 176.848 282.329 Tm [(N)]TJ/F8 9.9626 Tf 9.643 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.494 Td [(;)-167(k)]TJ/F7 6.9738 Tf 9.615 -1.494 Td [(2)]TJ/F8 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 219.892 282.329 Tm [(indicates)-322(the)]TJ/F11 9.9626 Tf 1 0 0 1 274.976 282.329 Tm [(k)]TJ/F7 6.9738 Tf 5.186 -1.494 Td [(2)]TJ/F112 9.9626 Tf 1.02 0 0 1 284.632 282.329 Tm [(-)]TJ 1.02 0 0 1 50.112 270.374 Tm [(nearest)-246(neighbours)-246(of)-246(instance)]TJ/F111 9.9626 Tf 1 0 0 1 175.817 270.374 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 184.115 270.374 Tm [(,)]TJ/F8 9.9626 Tf 1 0 0 1 189.843 270.374 Tm [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(i)]TJ/F14 9.9626 Tf 6.103 1.494 Td [(6)]TJ/F8 9.9626 Tf 0 0 Td [(=)-348<16>]TJ/F11 9.9626 Tf 10.535 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 222.264 270.374 Tm [(indicates)]TJ/F111 9.9626 Tf 1 0 0 1 260.889 270.374 Tm [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 271.688 270.374 Tm [(and)]TJ/F111 9.9626 Tf 1 0 0 1 49.863 258.419 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(j)]TJ/F112 9.9626 Tf 6.689 1.495 Td [(are)-250(from)-250(dif)25(ferent)-250(manifolds.)]TJ/F112 9.9626 Tf 1.01 0 0 1 62.067 246.464 Tm [(Therefore,)-245(the)-245(o)14(v)15(erall)-245(proposed)-245(manifold-re)15(gularization)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 234.508 Tm [(on)-250(the)-250(IDTM)]TJ/F11 9.9626 Tf 55.063 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F112 9.9626 Tf 6.365 0 Td [(can)-250(be)-250(e)15(xpressed)-250(as:)]TJ/F14 9.9626 Tf -16.188 -21.538 Td [(M)]TJ/F8 9.9626 Tf 11.964 0 Td [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))-278(=)]TJ/F14 9.9626 Tf 17.158 0 Td [(M)]TJ/F10 6.9738 Tf 11.964 -1.495 Td [(I)]TJ/F14 9.9626 Tf 6.785 1.495 Td [<00>-222(M)]TJ/F10 6.9738 Tf 21.927 -1.495 Td [(B)]TJ/F11 9.9626 Tf 6.857 1.495 Td [(:)]TJ/F112 9.9626 Tf 65.151 0 Td [(\(8\))]TJ/F112 9.9626 Tf 1.02 0 0 1 49.644 191.431 Tm [(W)78(e)-730(can)-730(clearly)-731(see)-730(that,)-852(minimizing)-730(the)-730(manifold-)]TJ/F112 9.9626 Tf 0.98 0 0 1 50.112 179.476 Tm [(re)15(gularization)-245(objecti)26(v)15(e)]TJ/F14 9.9626 Tf 1 0 0 1 144.37 179.476 Tm [(M)]TJ/F8 9.9626 Tf 11.965 0 Td [(\()]TJ/F11 9.9626 Tf 3.874 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F112 9.9626 Tf 0.98 0 0 1 171.432 179.476 Tm [(is)-245(equi)25(v)26(alent)-245(to)-246(k)11(eep)-246(the)-245(man-)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 167.521 Tm [(ifold)-281(in)-281(the)-281(transition)-280(matrix)-281(space)-281(be)-281(consistent)-281(with)-281(that)]TJ 1.02 0 0 1 50.112 155.566 Tm [(in)-365(the)-366(feature/label)-365(space.)-665(Thus,)-395(we)-366(ful\002ll)-365(the)-366(proposed)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 143.61 Tm [(practical)-250(useful)-250(assumption)-250(on)-250(the)]TJ/F117 9.9626 Tf 138.628 0 Td [(g)10(eometry)]TJ/F112 9.9626 Tf 39.462 0 Td [(of)]TJ/F11 9.9626 Tf 10.789 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F111 9.9626 Tf -196.86 -14.789 Td [(Remarks)]TJ/F112 9.9626 Tf 1.02 0 0 1 100.801 128.821 Tm [(:)-412(The)-299(manifold)-299(embedding)-299(is)-299(usually)-299(used)-299(in)]TJ 1.02 0 0 1 50.112 116.866 Tm [(the)-348(unsupervised)-349(or)-348(semi-supervised)-348(learning,)-375(its)-348(af)25(\002nity)]TJ/F112 9.9626 Tf 1.015 0 0 1 50.112 104.91 Tm [(matrix)-245(is)-246(constructed)-245(by)-246(the)]TJ/F11 9.9626 Tf 1 0 0 1 164.753 104.91 Tm [(k)]TJ/F112 9.9626 Tf 1.015 0 0 1 170.254 104.91 Tm [(-nearest)-245(neighbours)-246(in)-245(an)-246(un-)]TJ/F112 9.9626 Tf 1.003 0 0 1 50.112 92.955 Tm [(supervised)-248(manner)-248(traditionally)65(.)-309(Ho)25(we)25(v)15(er)39(,)-248(in)-248(this)-248(w)10(ork,)-249(we)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 81 Tm [(construct)-349(the)-349(af)25(\002nity)-349(matrix)-349(for)-349(the)-349(manifold)-349(embedding)]TJ
0 g 0 G
0 g 0 G
/F112 9.9626 Tf 0.991 0 0 1 308.503 710.037 Tm [(while)-252(considering)-252(t)1(he)-252(gi)25(v)15(en)-252(noisy)-251(labels)-252(as)-252(sho)25(wn)-251(in)-252(Eq.)-252(\()]TJ
1 0 0 rg 1 0 0 RG
[(5)]TJ
0 g 0 G
[(\))]TJ/F112 9.9626 Tf 0.988 0 0 1 308.862 698.082 Tm [(and)-253(Eq.)-252(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\).)-314(The)-252(main)-253(reason)-252(is)-253(that)-253(dif)26(f)-1(erent)-252(instances)-253(with)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 686.127 Tm [(dif)25(ferent)-338(gi)25(v)14(en)-338(noisy)-338(labels)-338(correspond)-338(to)-337(dif)24(f)1(erent)-338(ef)24(f)1(ec-)]TJ 1.02 0 0 1 308.862 674.172 Tm [(ti)25(v)14(e)-333(ro)25(ws)-333(in)-333(their)-333(corresponding)-333(transition)-333(matrices)]TJ/F11 9.9626 Tf 1 0 0 1 524.379 674.172 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 544.315 674.172 Tm [(.)]TJ 1.02 0 0 1 308.394 662.217 Tm [(W)78(e)-275(only)-275(used)-275(one)-276(ro)25(w)-276(of)]TJ/F11 9.9626 Tf 1 0 0 1 413.874 662.217 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 436.607 662.217 Tm [(to)-275(generate)-276(the)-275(noisy)-275(label.)]TJ 1.02 0 0 1 308.553 650.262 Tm [(Then)-316(e)24(v)15(en)-317(tw)10(o)-316(instances,)]TJ/F111 9.9626 Tf 1 0 0 1 416.205 650.262 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(i)]TJ/F112 9.9626 Tf 1.02 0 0 1 427.719 650.262 Tm [(and)]TJ/F111 9.9626 Tf 1 0 0 1 445.609 650.262 Tm [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(j)]TJ/F112 9.9626 Tf 1.02 0 0 1 454.788 650.262 Tm [(,)-334(are)-317(v)15(ery)-317(close)-316(in)-317(the)]TJ/F112 9.9626 Tf 1.002 0 0 1 308.862 638.306 Tm [(feature)-250(space)-251(and)-250(ha)20(v)15(e)-250(the)-251(same)-250(con\002dent)-250(clean)-251(label,)-250(their)]TJ/F112 9.9626 Tf 0.992 0 0 1 308.862 626.351 Tm [(corresponding)-253(transition)-253(matrices)-253(should)-254(be)-253(f)10(ar)-253(apart)-253(if)-253(the)15(y)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 614.396 Tm [(ha)20(v)16(e)-238(dif)26(f)-1(erent)-237(gi)25(v)16(en)-238(noisy)-237(labels.)-310(Therefore,)-241(we)-238(specially)-237(de-)]TJ 0.98 0 0 1 308.862 602.441 Tm [(sign)-249(the)-248(af)25(\002nity)-249(matrix)-249(in)-249(the)-248(proposed)-249(manifold-re)15(gularized)]TJ/F112 9.9626 Tf 0.998 0 0 1 308.862 590.486 Tm [(label-noise)-251(learning)-250(frame)25(w)10(ork,)-251(as)-251(sho)25(wn)-250(in)-251(Eq.\()]TJ
1 0 0 rg 1 0 0 RG
[(5)]TJ
0 g 0 G
[(\),)-251(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\),)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(9)]TJ
0 g 0 G
[(\))]TJ/F112 9.9626 Tf 1 0 0 1 308.862 578.531 Tm [(and)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(10)]TJ
0 g 0 G
[(\),)-250(for)-250(optimizing)-250(the)-250(IDTM)]TJ/F11 9.9626 Tf 140.841 0 Td [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F111 10.9589 Tf -160.776 -19.669 Td [(3.4.)-250(K)25(er)15(nel)-250(T)74(rick)-250(to)-250(the)-250(Manif)25(old)-250(Embedding)]TJ/F112 9.9626 Tf 1.02 0 0 1 320.817 540.929 Tm [(T)78(o)-265(impro)15(v)15(e)-265(the)-266(ef)25(fecti)25(v)15(eness)-266(of)-265(the)-265(proposed)-265(manifold-)]TJ 1.02 0 0 1 308.862 528.974 Tm [(re)15(gularization)-276(on)-276(the)-275(IDTM)]TJ/F11 9.9626 Tf 1 0 0 1 424.898 528.974 Tm [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.495 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 460.333 528.974 Tm [(,)-283(we)-276(further)-276(consider)]TJ 1.02 0 0 1 308.862 517.019 Tm [(to)-279(adopt)-279(the)-279(k)10(ernel)-279(trick)-278(to)-279(pre-compute)-279(the)-279(af)25(\002nity)-279(graph)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 503.46 Tm [(matrix)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(36)]TJ
0 g 0 G
[(].)-310(Concretely)65(,)]TJ/F11 9.9626 Tf 98.729 0 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.76 -7.952 Td [(ij)]TJ/F112 9.9626 Tf 13.862 2.777 Td [(and)]TJ/F11 9.9626 Tf 16.877 0 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.114 0 Td [(B)]TJ/F7 6.9738 Tf 6.359 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F112 9.9626 Tf 16.149 2.777 Td [(can)-250(be)-250(de\002ned)-250(as,)]TJ/F11 9.9626 Tf -153.854 -31.991 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.761 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 14.14 2.777 Td [(=)]TJ/F1 9.9626 Tf 10.516 17.036 Td [(\()]TJ/F11 9.9626 Tf 13.007 -14.054 Td [(e)]TJ/F13 6.9738 Tf 4.639 4.514 Td [<00>]TJ/F12 4.9813 Tf 7.422 4.824 Td [(jj)]TJ/F111 4.9813 Tf 4.566 0 Td [(x)]TJ/F9 4.9813 Tf 2.491 -1.604 Td [(i)]TJ/F12 4.9813 Tf 3.156 1.604 Td [<00>]TJ/F111 4.9813 Tf 5.396 0 Td [(x)]TJ/F9 4.9813 Tf 2.491 -1.604 Td [(j)]TJ/F12 4.9813 Tf 3.722 1.604 Td [(jj)]TJ/F6 4.9813 Tf 4.566 2.01 Td [(2)]TJ
ET
q
1 0 0 1 368.676 480.708 cm
[]0 d 0 J 0.339 w 0 0 m 30.276 0 l S
Q
BT
/F9 4.9813 Tf 379.75 475.523 Td [<1b>]TJ/F6 4.9813 Tf 4.24 1.467 Td [(2)]TJ/F11 9.9626 Tf 16.656 -2.539 Td [(;)]TJ/F112 9.9626 Tf 12.73 0 Td [(if)]TJ/F111 9.9626 Tf 8.301 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(j)]TJ/F14 9.9626 Tf 6.965 1.494 Td [(2)-278(N)]TJ/F8 9.9626 Tf 19.052 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.494 Td [(;)-167(k)]TJ/F7 6.9738 Tf 9.615 -1.494 Td [(1)]TJ/F8 9.9626 Tf 4.469 1.494 Td [(\))]TJ/F112 9.9626 Tf 6.088 0 Td [(and)]TJ/F8 9.9626 Tf 17.284 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F8 9.9626 Tf 6.084 1.494 Td [(=)-346<16>]TJ/F11 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.494 Td [(j)]TJ/F11 9.9626 Tf 4.198 1.494 Td [(;)]TJ/F8 9.9626 Tf -136.521 -11.955 Td [(0)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 64.389 0 Td [(else)]TJ/F11 9.9626 Tf 15.492 0 Td [(;)]TJ/F112 9.9626 Tf 52.969 -11.338 Td [(\(9\))]TJ/F11 9.9626 Tf -222.903 -20.32 Td [(S)]TJ/F7 6.9738 Tf 6.684 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(B)]TJ/F7 6.9738 Tf 6.359 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F8 9.9626 Tf 16.426 2.777 Td [(=)]TJ/F1 9.9626 Tf 10.516 17.036 Td [(\()]TJ/F11 9.9626 Tf 13.007 -14.054 Td [(e)]TJ/F13 6.9738 Tf 4.639 4.514 Td [<00>]TJ/F12 4.9813 Tf 7.422 4.825 Td [(jj)]TJ/F111 4.9813 Tf 4.566 0 Td [(x)]TJ/F9 4.9813 Tf 2.491 -1.605 Td [(i)]TJ/F12 4.9813 Tf 3.156 1.605 Td [<00>]TJ/F111 4.9813 Tf 5.396 0 Td [(x)]TJ/F9 4.9813 Tf 2.491 -1.605 Td [(j)]TJ/F12 4.9813 Tf 3.722 1.605 Td [(jj)]TJ/F6 4.9813 Tf 4.566 2.01 Td [(2)]TJ
ET
q
1 0 0 1 368.712 440.078 cm
[]0 d 0 J 0.339 w 0 0 m 30.276 0 l S
Q
BT
/F9 4.9813 Tf 379.786 434.893 Td [<1b>]TJ/F6 4.9813 Tf 4.24 1.467 Td [(2)]TJ/F11 9.9626 Tf 16.656 -2.539 Td [(;)]TJ/F112 9.9626 Tf 14.944 0 Td [(if)]TJ/F111 9.9626 Tf 8.301 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(j)]TJ/F14 9.9626 Tf 6.965 1.495 Td [(2)-278(N)]TJ/F8 9.9626 Tf 19.052 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 4.981 -1.495 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.495 Td [(;)-167(k)]TJ/F7 6.9738 Tf 9.615 -1.495 Td [(2)]TJ/F8 9.9626 Tf 4.469 1.495 Td [(\))]TJ/F112 9.9626 Tf 6.088 0 Td [(and)]TJ/F8 9.9626 Tf 17.284 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.495 Td [(i)]TJ/F14 9.9626 Tf 6.084 1.495 Td [(6)]TJ/F8 9.9626 Tf 0 0 Td [(=)-346<16>]TJ/F11 9.9626 Tf 10.516 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(j)]TJ/F11 9.9626 Tf 4.198 1.495 Td [(;)]TJ/F8 9.9626 Tf -138.735 -11.956 Td [(0)]TJ/F11 9.9626 Tf 4.981 0 Td [(;)]TJ/F112 9.9626 Tf 65.496 0 Td [(else)]TJ/F11 9.9626 Tf 15.492 0 Td [(;)]TJ/F112 9.9626 Tf 46.844 -11.337 Td [(\(10\))]TJ/F112 9.9626 Tf 1.02 0 0 1 308.503 398.573 Tm [(where)]TJ/F11 9.9626 Tf 1 0 0 1 335.828 398.573 Tm [<1b>]TJ/F112 9.9626 Tf 1.02 0 0 1 344.379 398.573 Tm [(is)-246(one)-246(h)5(yper)20(-parameter)-246(to)-246(adjust)-246(the)-246(weight)-246(distri-)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 386.618 Tm [(b)20(ution)-250(in)-250(the)-250(af)25(\002nity)-250(graph)-250(matrix.)]TJ/F111 10.9589 Tf 0 -19.669 Td [(3.5.)-250(Ov)10(erall)-250(Objecti)10(v)10(e)-250(Function)]TJ/F112 9.9626 Tf 1.02 0 0 1 320.817 349.016 Tm [(Finally)64(,)-271(the)-265(o)15(v)14(erall)-265(objecti)25(v)14(e)-265(function)-265(can)-266(be)-265(e)15(xpressed)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 337.061 Tm [(as)-250(Eq.\()]TJ
1 0 0 rg 1 0 0 RG
[(11)]TJ
0 g 0 G
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0 g 0 G
0 g 0 G
BT
/F111 9.9626 Tf 64.558 510.126 Td [(Input)]TJ/F112 9.9626 Tf 23.81 0 Td [(:)]TJ
0 g 0 G
[-310(Noisy)-250(training)-250(dataset)]TJ/F8 9.9626 Tf 98.11 2.519 Td [<16>]TJ/F14 9.9626 Tf -2.32 -2.519 Td [(D)]TJ/F8 9.9626 Tf 10.729 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(f)]TJ/F111 9.9626 Tf 4.981 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.316 1.494 Td [(;)]TJ/F8 9.9626 Tf 5.112 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.885 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(g)]TJ/F10 6.9738 Tf 4.981 3.616 Td [(N)]TJ 0 -6.209 Td [(i)]TJ/F7 6.9738 Tf 2.819 0 Td [(=1)]TJ
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0 g 0 G
[-310(The)-250<026e616c>-250(classi\002er)]TJ/F11 9.9626 Tf 81.952 0 Td [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F111 9.9626 Tf 4.427 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 6.365 0 Td [(and)-250(the)-250(transition)]TJ -108.885 -11.955 Td [(matrix)]TJ/F11 9.9626 Tf 28.503 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F11 9.9626 Tf 4.428 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F111 9.9626 Tf -95.179 -11.955 Td [(W)65(armup)]TJ/F112 9.9626 Tf 38.097 0 Td [(:)-310(T)35(rain)-250(the)-250(DNN)-250(on)-250(the)-250(noisy)-250(dataset)]TJ/F8 9.9626 Tf 151.988 2.518 Td [<16>]TJ/F14 9.9626 Tf -2.321 -2.518 Td [(D)]TJ/F112 9.9626 Tf 10.453 0 Td [(with)]TJ -197.719 -11.955 Td [(the)-250(early-stop)-250(strate)15(gy)-250(to)-250(obtain)-250(the)-250(initial)-250(classi\002er)]TJ/F11 9.9626 Tf 0 -11.956 Td [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(;)]TJ/F111 9.9626 Tf -30.66 -11.955 Td [(while)]TJ/F117 9.9626 Tf 25.186 0 Td [(Number)-250(of)-250(tr)15(aining)-250(epoc)15(h)]TJ/F14 9.9626 Tf 105.414 0 Td [<14>]TJ/F117 9.9626 Tf 10.239 0 Td [(Max-Epoc)15(h)]TJ/F111 9.9626 Tf 48.817 0 Td [(do)]TJ
ET
q
1 0 0 1 67.246 306.012 cm
[]0 d 0 J 0.398 w 0 0 m 0 128.797 l S
Q
BT
/F14 9.9626 Tf 77.406 428.054 Td [<0f>]TJ/F112 9.9626 Tf 7.472 0 Td [(Extract)-250(con\002dent)-250(clean)-250(e)15(xamples)-250(using)-250(e)15(xample)]TJ -7.472 -11.955 Td [(distillation)-250(method)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(])-250(with)-250(current)-250(classi\002er)]TJ/F11 9.9626 Tf 0 -11.955 Td [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F111 9.9626 Tf 4.427 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf 6.365 0 Td [(to)-250(form)-250(the)-250(sub-dataset)]TJ/F8 9.9626 Tf 96.397 2.518 Td [<16>]TJ/F14 9.9626 Tf -2.321 -2.518 Td [(D)]TJ/F10 6.9738 Tf 7.962 3.615 Td [(s)]TJ/F8 9.9626 Tf 7.026 -3.615 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(f)]TJ/F111 9.9626 Tf 4.981 0 Td [(x)]TJ/F10 6.9738 Tf 4.982 3.615 Td [(s)]TJ 0 -6.208 Td [(i)]TJ/F11 9.9626 Tf 4.258 2.593 Td [(;)]TJ/F8 9.9626 Tf 5.112 0 Td [<16>]TJ/F11 9.9626 Tf -0.684 0 Td [(y)]TJ/F10 6.9738 Tf 4.884 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(g)]TJ/F10 6.9738 Tf 4.982 3.615 Td [(N)]TJ/F9 4.9813 Tf 7.058 3.007 Td [(s)]TJ/F10 6.9738 Tf -7.058 -9.215 Td [(i)]TJ/F7 6.9738 Tf 2.818 0 Td [(=1)]TJ/F112 9.9626 Tf 10.586 2.593 Td [(;)]TJ/F14 9.9626 Tf -197.607 -11.955 Td [<0f>]TJ/F112 9.9626 Tf 0.997 0 0 1 84.878 392.189 Tm [(Input)-251(the)-250(e)15(xtracted)-251(con\002dent)-251(clean)-251(e)15(xamples)-250(into)]TJ/F112 9.9626 Tf 1 0 0 1 77.406 380.233 Tm [(the)-250(backbone)-250(netw)10(ork;)]TJ/F14 9.9626 Tf 0 -11.955 Td [<0f>]TJ/F112 9.9626 Tf 7.472 0 Td [(Compute)-250(the)-250(af)25(\002nity)-250(graph)-250(matrix)]TJ/F11 9.9626 Tf 138.39 0 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(I)]TJ/F7 6.9738 Tf 4.073 0 Td [(\))]TJ/F10 6.9738 Tf -7.76 -7.952 Td [(ij)]TJ/F112 9.9626 Tf 13.862 2.777 Td [(and)]TJ/F11 9.9626 Tf 16.877 0 Td [(S)]TJ/F7 6.9738 Tf 6.683 5.175 Td [(\()]TJ/F10 6.9738 Tf 3.113 0 Td [(B)]TJ/F7 6.9738 Tf 6.36 0 Td [(\))]TJ/F10 6.9738 Tf -10.047 -7.952 Td [(ij)]TJ/F112 9.9626 Tf -188.819 -9.178 Td [(based)-250(on)-250(current)-250(instance)-250(features)-250(according)-250(to)]TJ 0 -11.955 Td [(Eq.)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(5)]TJ
0 g 0 G
[(\))-250(and)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\))-250(or)-250(Eq.)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(9)]TJ
0 g 0 G
[(\))-250(and)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(10)]TJ
0 g 0 G
[(\);)]TJ/F14 9.9626 Tf 0 -11.955 Td [<0f>]TJ/F112 9.9626 Tf 7.472 0 Td [(Optimize)-250(the)-250(DNN)-250(based)-250(on)-250(the)-250(loss)-250(function)]TJ -7.472 -11.955 Td [(sho)25(wn)-250(in)-250(Eq.)-250(\()]TJ
1 0 0 rg 1 0 0 RG
[(11)]TJ
0 g 0 G
[(\))-250(to)-250(obtain)-250(ne)25(w)-250(classi\002er)]TJ/F11 9.9626 Tf 168.018 0 Td [(f)]TJ/F8 9.9626 Tf 5.95 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(;)]TJ/F111 9.9626 Tf 4.428 0 Td [(w)]TJ/F8 9.9626 Tf 7.193 0 Td [(\))]TJ/F112 9.9626 Tf -194.445 -11.956 Td [(and)-250(transition)-250(matrix)]TJ/F11 9.9626 Tf 85.508 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(\()]TJ/F111 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 4.982 0 Td [(;)]TJ/F11 9.9626 Tf 4.427 0 Td [<12>]TJ/F8 9.9626 Tf 4.954 0 Td [(\))]TJ/F112 9.9626 Tf 3.874 0 Td [(.)]TJ/F111 9.9626 Tf -130.164 -11.855 Td [(end)]TJ
0 g 0 G
ET
q
1 0 0 1 50.112 290.669 cm
[]0 d 0 J 0.797 w 0 0 m 236.25 0 l S
Q
0 g 0 G
BT
/F111 11.9552 Tf 50.112 268.778 Td [(4.)-250(Experiments)]TJ/F112 9.9626 Tf 1.02 0 0 1 62.067 249.849 Tm [(In)-298(this)-297(section,)-311(we)-298<02727374>-298(introduce)-297(the)-298(e)14(xperim)1(ent)-298(setup)]TJ/F112 9.9626 Tf 0.984 0 0 1 50.112 237.894 Tm [(including)-254(the)-254(dataset,)-254(noisy)-254(type)-254(and)-254(implementation)-254(details.)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 225.939 Tm [(Ne)15(xt,)-312(we)-299(compare)-299(the)-299(proposed)-298(method)-299(with)-299(the)-298(state-of-)]TJ/F112 9.9626 Tf 1.01 0 0 1 50.112 213.984 Tm [(the-art)-248(methods)-247(on)-248(four)-248(synthetic)-247(and)-248(tw)10(o)-248(real-w)10(orld)-248(noisy)]TJ/F112 9.9626 Tf 1.02 0 0 1 50.112 202.028 Tm [(datasets,)-279(then)-273(conduct)-272(an)-272(ablation)-273(study)-272(to)-272(analyze)-273(the)-272(e)15(x-)]TJ/F112 9.9626 Tf 1 0 0 1 50.112 190.073 Tm [(perimental)-250(results)-250(and)-250(some)-250(useful)-250(h)5(yper)20(-parameters.)]TJ/F111 10.9589 Tf 0 -19.409 Td [(4.1.)-250(Experiment)-250(Setup)]TJ/F111 9.9626 Tf 11.955 -17.933 Td [(Datasets)]TJ/F112 9.9626 Tf 1.02 0 0 1 98.032 152.731 Tm [(.)-732(Extensi)25(v)15(e)-388(e)15(xperiments)-388(are)-387(conducted)-388(to)-388(il-)]TJ 1.02 0 0 1 50.112 140.776 Tm [(lustrate)-269(the)-269(ef)25(fecti)25(v)14(eness)-268(of)-269(our)-269(method,)-275(on)-269(four)-269(manually)]TJ/F112 9.9626 Tf 1.003 0 0 1 50.112 128.821 Tm [(corrupted)-249(datasets)-250(\(i.e.,)-249(F-MNIST)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(46)]TJ
0 g 0 G
[(],SVHN)-249([)]TJ
0 1 0 rg 0 1 0 RG
[(27)]TJ
0 g 0 G
[(],CIF)74(AR-)]TJ/F112 9.9626 Tf 0.989 0 0 1 49.365 116.866 Tm [(10)-252([)]TJ
0 1 0 rg 0 1 0 RG
[(16)]TJ
0 g 0 G
[(],)-252(C)1(IF)74(AR-100)-251([)]TJ
0 1 0 rg 0 1 0 RG
[(16)]TJ
0 g 0 G
[(]\))-252(and)-252(tw)11(o)-252(real-w)10(orld)-252(noisy)-251(datasets)]TJ/F112 9.9626 Tf 1.02 0 0 1 49.783 104.91 Tm [(\()-341(i.e.,)-365(Clothing1M)-341([)]TJ
0 1 0 rg 0 1 0 RG
[(47)]TJ
0 g 0 G
[(])-341(and)-341(F)15(ood-101N)-341([)]TJ
0 1 0 rg 0 1 0 RG
[(17)]TJ
0 g 0 G
[(]\).)-591(F-MNIST)]TJ/F112 9.9626 Tf 1.013 0 0 1 50.112 92.955 Tm [(has)]TJ/F8 9.9626 Tf 1 0 0 1 66.05 92.955 Tm [(28)]TJ/F14 9.9626 Tf 12.156 0 Td [<02>]TJ/F8 9.9626 Tf 9.942 0 Td [(28)]TJ/F112 9.9626 Tf 1.013 0 0 1 100.596 92.955 Tm [(gray)-246(scale)-246(images)-247(of)-246(10)-246(classes)-246(including)-247(60K)]TJ/F112 9.9626 Tf 1.002 0 0 1 50.112 81 Tm [(for)-250(training)-250(and)-249(10K)-250(for)-250(testing.)-310(SVHN)-250(contains)-250(10)-249(classes)]TJ
0 g 0 G
0 g 0 G
/F112 9.9626 Tf 1.02 0 0 1 308.862 710.037 Tm [(of)-267(images)-266(with)]TJ/F8 9.9626 Tf 1 0 0 1 372.308 710.037 Tm [(73)]TJ/F11 9.9626 Tf 9.963 0 Td [(;)]TJ/F8 9.9626 Tf 4.428 0 Td [(257)]TJ/F112 9.9626 Tf 1.02 0 0 1 404.352 710.037 Tm [(for)-267(t)1(raining)-267(and)]TJ/F8 9.9626 Tf 1 0 0 1 470.613 710.037 Tm [(26)]TJ/F11 9.9626 Tf 9.963 0 Td [(;)]TJ/F8 9.9626 Tf 4.428 0 Td [(032)]TJ/F112 9.9626 Tf 1.02 0 0 1 502.656 710.037 Tm [(for)-267(testing.)]TJ/F112 9.9626 Tf 1.003 0 0 1 308.862 698.082 Tm [(CIF)74(AR-10)-248(contains)-248(10)-248(classes)-248(and)-248(CIF)73(AR-100)-248(contain)-248(100)]TJ/F112 9.9626 Tf 1.016 0 0 1 308.862 686.127 Tm [(classes,)-245(and)-245(both)-245(of)-245(them)-245(contain)-245(50K)-244(training)-245(images)-245(and)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.115 674.172 Tm [(10K)-320(testing)-320(images)-320(of)-320(size)-319(32)]TJ/F14 9.9626 Tf 1 0 0 1 432.186 674.172 Tm [<02>]TJ/F112 9.9626 Tf 1.02 0 0 1 443.186 674.172 Tm [(32.)-528(Clothing1M)-320(has)-320(1M)]TJ/F112 9.9626 Tf 0.991 0 0 1 308.862 662.217 Tm [(images)-251(with)-251(real-w)10(orld)-251(noisy)-251(labels)-251(from)-251(14)-251(f)10(ashion)-251(classes)]TJ 0.991 0 0 1 308.862 650.262 Tm [(for)-252(training)-251(and)-252(10K)-252(test)-251(images)-252(with)-252(clean)-252(label,)-251(where)-252(the)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 638.306 Tm [(estimated)-297(noisy)-297(label)-297(rate)-297(is)]TJ/F8 9.9626 Tf 1 0 0 1 426.692 638.306 Tm [(38)]TJ/F11 9.9626 Tf 9.963 0 Td [(:)]TJ/F8 9.9626 Tf 2.767 0 Td [(46%)]TJ/F112 9.9626 Tf 1.02 0 0 1 457.687 638.306 Tm [(.)-460(F)15(ood101N)-297(contains)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.115 626.351 Tm [(101)-212(food)-211(cate)15(gories)-212(wit)1(h)-212(310k)-212(training)-211(images)-212(and)-212(55K)-211(clean)]TJ/F112 9.9626 Tf 1.013 0 0 1 308.862 614.396 Tm [(images)-248(for)-247(testing,)-248(which)-247(is)-248(also)-248(a)-247(real-w)10(orld)-248(noisy)-247(dataset)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 602.441 Tm [(and)-250(has)-250(about)]TJ/F8 9.9626 Tf 57.275 0 Td [(19)]TJ/F11 9.9626 Tf 9.962 0 Td [(:)]TJ/F8 9.9626 Tf 2.768 0 Td [(66%)]TJ/F112 9.9626 Tf 20.755 0 Td [(noisy)-250(labels)-250(in)-250(the)-250(training)-250(dataset.)]TJ/F111 9.9626 Tf -78.805 -12.331 Td [(Noisy)-353(type)]TJ/F112 9.9626 Tf 1.02 0 0 1 366.397 590.11 Tm [(.)-607(F)14(or)-346(the)-346(manually)-346(corrupted)-346(datasets)-346(\(i.e.,)]TJ 1.02 0 0 1 308.862 578.155 Tm [(F-MNIST)73(,)-254(SVHN,)-253(CIF)73(AR-10,)-256(and)-253(CIF)73(AR-100\),)-255(we)-254(adopt)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 566.199 Tm [(e)15(xactly)-255(the)-256(same)-256(strate)15(gy)-255(to)-256(generate)-256(the)-256(instance-dependent)]TJ/F112 9.9626 Tf 0.997 0 0 1 308.862 554.244 Tm [(label)-251(noise)-251(as)-251(pre)25(vious)-251(methods)-251([)]TJ
0 1 0 rg 0 1 0 RG
[(5)]TJ
0 g 0 G
[(,)]TJ
0 1 0 rg 0 1 0 RG
[-131(44)]TJ
0 g 0 G
[(].)-312(The)-251(basic)-251(idea)-251(is)-251(to)]TJ/F112 9.9626 Tf 1.014 0 0 1 308.862 542.289 Tm [(randomly)-246(g)-1(e)1(nerate)-247(one)-247(v)15(ector)-246(for)-247(each)-246(class)-247(\(K)-246(v)14(ect)1(ors)-247(for)]TJ/F112 9.9626 Tf 1.004 0 0 1 308.862 530.334 Tm [(all)-249(the)-250(classes\))-249(and)-250(project)-249(each)-250(instance)-249(feature)-250(onto)-250(t)1(he)-250(K)]TJ/F112 9.9626 Tf 1.005 0 0 1 308.613 518.379 Tm [(v)15(ectors.)-310(The)-250(noise)-249(label)-249(is)-250(generated)-249(by)-249(jointly)-250(considering)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 506.424 Tm [(its)-218(clean)-217(label)-218(and)-218(the)-217(projected)-218(results.)-304(W)82(e)-218(ha)20(v)16(e)-218(set)-218(dif)26(f)-1(erent)]TJ/F112 9.9626 Tf 1.017 0 0 1 308.862 494.468 Tm [(noisy)-246(rate)-247(for)-246(all)-246(the)-246(datasets)-247(from)]TJ/F8 9.9626 Tf 1 0 0 1 449.574 494.468 Tm [(10%)]TJ/F112 9.9626 Tf 1.017 0 0 1 470.334 494.468 Tm [(to)]TJ/F8 9.9626 Tf 1 0 0 1 480.712 494.468 Tm [(50%)]TJ/F112 9.9626 Tf 1.017 0 0 1 501.473 494.468 Tm [(to)-246(e)24(v)25(aluate)]TJ/F112 9.9626 Tf 1 0 0 1 308.862 482.513 Tm [(all)-250(the)-250(methods.)]TJ/F111 10.9589 Tf 0 -21.053 Td [(4.2.)-250(Implementation)-250(Details)]TJ/F112 9.9626 Tf 1.02 0 0 1 320.817 443.151 Tm [(F)15(or)-287(f)10(air)-287(comparison,)-298(we)-287(conduct)-287(all)-287(e)15(xperiments)-287(on)-287(N-)]TJ/F112 9.9626 Tf 0.991 0 0 1 308.503 431.196 Tm [(VIDIA)-252(GeF)15(orce)-253(R)61(TX)-252(3090,)-253(and)-252(all)-252(methods)-253(are)-252(implement-)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 419.241 Tm [(ed)-277(on)-277(the)-277(same)-277(PyT)79(orch)-277(platform.)-400(The)-277(backbone)-277(netw)10(ork)]TJ 1.02 0 0 1 308.503 407.286 Tm [(we)-247(used)-247(on)-248(F-MNIST)-247(dataset)-247(is)-247(ResNet-18,)-248(while)-247(ResNet-)]TJ 1.02 0 0 1 308.862 395.331 Tm [(34)-269(netw)9(ork)-269(is)-269(used)-269(on)-270(SVHN,)-269(CIF)72(AR-10)-269(and)-269(CIF)72(AR-100)]TJ 1.02 0 0 1 308.862 383.376 Tm [(datasets.)-428(F)15(or)-287(the)-286(tw)9(o)-286(real-w)10(orld)-287(dataset)-286(\(Clothing1M)-287(and)]TJ/F112 9.9626 Tf 1.014 0 0 1 308.862 371.42 Tm [(F)15(ood101\),)-246(we)-246(adopt)-246(the)-246(ResNet-50)-245(netw)9(ork)-245(pre-trained)-246(on)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 359.465 Tm [(ImageNet)-376(as)-376(the)-377(backbone)-376(netw)10(ork.)-697(The)-376(transition)-376(neu-)]TJ/F112 9.9626 Tf 1.019 0 0 1 308.862 347.51 Tm [(ral)-245(netw)10(ork)-245(in)-245(the)-245(frame)25(w)9(ork)-245(is)-245(implement)1(ed)-245(by)-245(one)-245(fully-)]TJ/F112 9.9626 Tf 0.98 0 0 1 308.862 335.555 Tm [(connected)-243(layer)41(,)-245(where)-243(the)-243(input)-242(is)-243(the)-243(instance)-242(features,)-246(and)]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 323.6 Tm [(the)-338(number)-338(of)-338(output)-337(nodes)-338(is)]TJ/F11 9.9626 Tf 1 0 0 1 437.848 323.6 Tm [(K)]TJ/F14 9.9626 Tf 12.086 0 Td [<02>]TJ/F11 9.9626 Tf 10.661 0 Td [(K)]TJ/F112 9.9626 Tf 1.02 0 0 1 473.202 323.6 Tm [(where)]TJ/F11 9.9626 Tf 1 0 0 1 501.46 323.6 Tm [(K)]TJ/F112 9.9626 Tf 1.02 0 0 1 514.068 323.6 Tm [(denotes)]TJ 1.02 0 0 1 308.862 311.645 Tm [(the)-281(number)-280(of)-281(classes)-281(on)-281(each)-280(dataset.)-411(The)-281(obtained)]TJ/F11 9.9626 Tf 1 0 0 1 526.342 311.645 Tm [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(\()]TJ/F111 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 4.981 0 Td [(\))]TJ/F112 9.9626 Tf 1.02 0 0 1 308.862 299.689 Tm [(is)-270(normalized)-270(in)-270(each)-271(ro)25(w)64(.)-380(The)]TJ/F11 9.9626 Tf 1 0 0 1 438.709 299.689 Tm [(k)]TJ/F112 9.9626 Tf 1.02 0 0 1 444.209 299.689 Tm [(-nearest)-270(neighbor)-270(param-)]TJ 1.02 0 0 1 308.862 287.734 Tm [(eters)-339(in)-338(Eq.)-339(\()]TJ
1 0 0 rg 1 0 0 RG
[(5)]TJ
0 g 0 G
[(\))-339(and)-339(Eq.)-338(\()]TJ
1 0 0 rg 1 0 0 RG
[(7)]TJ
0 g 0 G
[(\))-339(are)-339(set)-338(as)]TJ/F11 9.9626 Tf 1 0 0 1 468.567 287.734 Tm [(k)]TJ/F7 6.9738 Tf 5.186 -1.494 Td [(1)]TJ/F8 9.9626 Tf 8.999 1.494 Td [(=)]TJ/F11 9.9626 Tf 12.278 0 Td [(k)]TJ/F7 6.9738 Tf 5.186 -1.494 Td [(2)]TJ/F8 9.9626 Tf 8.999 1.494 Td [(=)-455(7)]TJ/F112 9.9626 Tf 1.02 0 0 1 526.474 287.734 Tm [(,)-362(the)]TJ/F112 9.9626 Tf 1.004 0 0 1 308.862 275.779 Tm [(h)5(yper)20(-parameter)]TJ/F11 9.9626 Tf 1 0 0 1 377.196 275.779 Tm [<1b>]TJ/F112 9.9626 Tf 1.004 0 0 1 385.734 275.779 Tm [(in)-249(Eq.)-248(\()]TJ
1 0 0 rg 1 0 0 RG
[(9)]TJ
0 g 0 G
[(\))-249(and)-249(Eq.)-248(\()]TJ
1 0 0 rg 1 0 0 RG
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/F112 9.9626 Tf 154.839 648.961 Td [(90.78)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.30)-1200(89.01)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.44)-1200(86.51)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.20)-1200(78.17)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.32)-1200(68.31)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.07)]TJ
ET
q
1 0 0 1 459.087 645.374 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
1 0 0 rg 1 0 0 RG
BT
/F111 9.9626 Tf 465.064 648.961 Td [(91.71)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.08)-1200(89.62)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.14)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.389 0 Td [(86.93)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.15)-1200(80.29)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.27)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(65.91)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.22)]TJ -675.723 -11.955 Td [(CoT)70(eaching)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(11)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 633.419 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 637.006 Td [(90.54)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.35)-1200(88.53)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.09)-1200(87.37)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.14)-1200(78.36)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.82)-1200(67.81)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.02)]TJ
ET
q
1 0 0 1 459.087 633.419 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 637.006 Td [(90.80)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.05)-1200(88.43)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.08)-1200(86.40)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.41)-1200(80.85)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.97)-1200(62.63)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.51)]TJ -681.342 -11.956 Td [(CoT)70(eaching++)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(52)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 621.464 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 156.084 625.05 Td [(90.67)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.49)-1325(88.52)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.44)-1200(87.33)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.87)-1200(79.85)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.03)-1200(68.86)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.39)]TJ
ET
q
1 0 0 1 459.087 621.464 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 625.05 Td [(91.47)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.59)-1200(89.78)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.34)-1200(85.72)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.35)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(81.00)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.82)-1200(61.46)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.36)]TJ -663.624 -11.955 Td [(JoCor)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(43)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 609.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
1 0 0 rg 1 0 0 RG
BT
/F111 9.9626 Tf 154.839 613.095 Td [(91.48)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.11)-1200(89.24)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.09)-1200(86.50)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.10)-1325(77.15)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.04)-1450(67.85)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.84)]TJ
ET
q
1 0 0 1 459.087 609.509 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 613.095 Td [(91.42)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.11)-1200(89.30)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.27)-1200(85.54)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.82)-1200(80.87)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.91)-1200(64.11)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.57)]TJ -669.985 -11.955 Td [(PeerLoss)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(23)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 597.553 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 156.084 601.14 Td [(90.76)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.41)-1325(87.06)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.74)-1200(84.40)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.93)-1200(73.95)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.37)-1200(65.79)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.49)]TJ
ET
q
1 0 0 1 459.087 597.553 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 601.14 Td [(90.89)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.07)-1200(89.21)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.63)-1200(85.70)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.56)-1200(78.51)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.23)-1200(59.08)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.05)]TJ -669.985 -11.955 Td [(TMDNN)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 585.598 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 589.185 Td [(91.33)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.27)-1200(89.70)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.14)-1200(87.63)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.28)-1200(78.40)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(3.69)-1200(66.55)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(7.52)]TJ
ET
q
1 0 0 1 459.087 585.598 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 589.185 Td [(90.45)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.72)-1200(88.14)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.66)-1325(84.55)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.48)-1325(79.71)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.95)-1200(63.33)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.75)]TJ -662.717 -11.955 Td [(P)15(artT)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(44)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 573.643 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 577.23 Td [(91.27)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.38)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(89.78)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.43)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(88.30)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.51)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(80.75)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.86)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(72.22)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(4.22)]TJ
ET
q
1 0 0 1 459.087 573.643 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 577.23 Td [(90.32)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.15)-1200(89.33)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.70)-1325(85.33)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.86)-1325(80.59)]TJ/F14 9.9626 Tf 53.051 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.41)-1200(64.58)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(2.86)]TJ
ET
q
1 0 0 1 52.603 573.444 cm
[]0 d 0 J 0.398 w 0 0 m 710.732 0 l S
Q
BT
/F112 9.9626 Tf 69.275 564.876 Td [(MEIDTM)-250(\(Ours\))]TJ
ET
q
1 0 0 1 148.861 561.289 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 564.876 Td [(91.78)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.87)-1200(90.49)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.35)-1200(88.74)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.25)-1200(84.21)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.52)-1200(73.67)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(3.76)]TJ
ET
q
1 0 0 1 459.087 561.289 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 465.064 564.876 Td [(92.17)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.21)-1200(91.38)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.34)-1200(87.68)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.26)-1200(82.63)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.24)-1200(72.17)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(1.51)]TJ -679.116 -11.955 Td [(kMEIDTM)-250(\(Ours\))]TJ
ET
q
1 0 0 1 148.861 549.334 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F111 9.9626 Tf 156.084 552.921 Td [(91.96)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.08)]TJ/F111 9.9626 Tf 30.635 0 Td [(90.83)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.05)]TJ/F111 9.9626 Tf 29.39 0 Td [(89.61)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.65)]TJ/F111 9.9626 Tf 29.39 0 Td [(85.81)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.44)]TJ/F111 9.9626 Tf 29.39 0 Td [(76.43)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(4.88)]TJ
ET
q
1 0 0 1 459.087 549.334 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F111 9.9626 Tf 465.064 552.921 Td [(92.91)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.07)]TJ/F111 9.9626 Tf 29.389 0 Td [(92.26)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.25)]TJ/F111 9.9626 Tf 29.389 0 Td [(90.73)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.24 0 Td [(0.34)]TJ/F111 9.9626 Tf 29.39 0 Td [(85.94)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.92)]TJ/F111 9.9626 Tf 29.39 0 Td [(73.77)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 10.239 0 Td [(0.82)]TJ
ET
q
1 0 0 1 52.603 547.22 cm
[]0 d 0 J 0.797 w 0 0 m 710.732 0 l S
Q
1 0 0 1 50.112 631.664 cm
Q
0 g 0 G
0 g 0 G
0 g 0 G
1 0 0 1 -50.112 -631.664 cm
BT
/F112 8.9664 Tf 0.98 0 0 1 49.834 553.357 Tm [(T)82(able)-257(2.)-319(Comparison)-256(with)-256(state-of-the-art)-256(methods)-257(on)-256(SVHN)-256(and)-256(CIF)75(AR-100)-256(datasets.)-319(The)-256(mean)-257(and)-256(standard)-256(de)26(viation)-257(comp)1(uted)-257(o)16(v)15(er)-256<02>25(v)16(e)]TJ/F112 8.9664 Tf 1 0 0 1 50.112 542.399 Tm [(runs)-250(are)-250(presented.)-310(\223IDN-xx)]TJ/F96 8.9664 Tf 102.117 0 Td [(%)]TJ/F112 8.9664 Tf 7.68 0 Td [<94>-250(means)-250(the)-250(noise)-250(rate)-250(is)-250(xx)]TJ/F96 8.9664 Tf 98.611 0 Td [(%)]TJ/F112 8.9664 Tf 9.921 0 Td [(and)-250(noise)-250(type)-250(is)-250<9349444e942e>]TJ
0 g 0 G
ET
1 0 0 1 50.112 470.913 cm
q
.71144 0 0 .71144 0 0 cm
q
1 0 0 1 2.491 89.425 cm
[]0 d 0 J 0.797 w 0 0 m 690.807 0 l S
Q
1 0 0 1 -50.112 -470.913 cm
BT
/F112 9.9626 Tf 88.224 536.828 Td [(Method)]TJ
ET
q
1 0 0 1 148.861 545.197 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 284.188 548.783 Td [(SVHN)]TJ
ET
q
1 0 0 1 446.633 545.197 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 571.589 548.783 Td [(CIF)74(AR-100)]TJ
ET
q
1 0 0 1 148.861 544.997 cm
[]0 d 0 J 0.398 w 0 0 m 594.548 0 l S
Q
q
1 0 0 1 148.861 533.241 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 158.995 536.828 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(10%)]TJ/F112 9.9626 Tf 38.534 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(20%)]TJ/F112 9.9626 Tf 38.533 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(30%)]TJ/F112 9.9626 Tf 38.534 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(40%)]TJ/F112 9.9626 Tf 38.533 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(50%)]TJ
ET
q
1 0 0 1 446.633 533.241 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 456.768 536.828 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(10%)]TJ/F112 9.9626 Tf 38.533 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(20%)]TJ/F112 9.9626 Tf 38.534 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(30%)]TJ/F112 9.9626 Tf 38.533 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(40%)]TJ/F112 9.9626 Tf 41.024 0 Td [(IDN-)]TJ/F8 9.9626 Tf 21.021 0 Td [(50%)]TJ
ET
q
1 0 0 1 52.603 533.042 cm
[]0 d 0 J 0.398 w 0 0 m 690.807 0 l S
Q
BT
/F112 9.9626 Tf 76.468 524.474 Td [(CE)-250(\(baseline\))]TJ
ET
q
1 0 0 1 148.861 520.888 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 524.474 Td [(90.47)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.27)-1200(89.85)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.16)-1200(86.31)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.79)-1200(80.59)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.56)-1200(64.93)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.03)]TJ
ET
q
1 0 0 1 446.633 520.888 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 524.474 Td [(66.55)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.23)-1200(63.94)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.51)-1200(61.97)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.16)-1200(58.70)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.56)-1450(56.63)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.69)]TJ
ET
q
1 0 0 1 52.603 520.689 cm
[]0 d 0 J 0.398 w 0 0 m 690.807 0 l S
Q
BT
/F112 9.9626 Tf 84.214 512.121 Td [(GCE)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(54)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 508.534 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 512.121 Td [(90.82)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.12)-1200(89.48)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.66)-1200(86.92)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.24)-1200(81.95)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.45)-1200(63.20)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.75)]TJ
ET
q
1 0 0 1 446.633 508.534 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
1 0 0 rg 1 0 0 RG
BT
/F111 9.9626 Tf 452.611 512.121 Td [(69.18)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.14)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.389 0 Td [(68.35)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.33)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(66.35)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.13)-1200(62.09)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.09)-1450(56.68)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.75)]TJ -638.991 -11.955 Td [(DMI)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(48)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 496.579 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 500.166 Td [(92.66)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.58)-1200(91.88)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.42)-1200(88.44)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.85)-1200(82.27)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.54)-1200(68.72)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.32)]TJ
ET
q
1 0 0 1 446.633 496.579 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 500.166 Td [(67.06)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.46)-1200(64.72)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.64)-1450(62.8)]TJ/F14 9.9626 Tf 49.315 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.46)-1450(60.24)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.63)-1450(56.52)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.18)]TJ -646.06 -11.956 Td [(F)15(orw)10(ard)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(32)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 484.624 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 488.21 Td [(92.01)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(1.10)-1200(90.67)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.27)-1200(86.04)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.40)-1200(83.18)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.95)-1200(70.72)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.00)]TJ
ET
q
1 0 0 1 446.633 484.624 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 488.21 Td [(67.81)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.48)-1200(67.23)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.29)-1200(65.42)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.63)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.389 0 Td [(62.18)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.26)-1450(58.61)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.44)]TJ -653.307 -11.955 Td [(CoT)70(eaching)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(11)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 472.669 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 476.255 Td [(91.11)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.16)-1200(90.88)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.17)-1200(88.21)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.62)-1200(86.46)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.33)-1200(70.04)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.05)]TJ
ET
q
1 0 0 1 446.633 472.669 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 476.255 Td [(67.91)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.34)-1200(67.40)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.44)-1200(64.13)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.43)-1200(59.98)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.28)-1200(57.48)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.740)]TJ -656.436 -11.955 Td [(CoT)70(eaching++)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(52)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 460.713 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 464.3 Td [(92.64)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.43)-1200(91.59)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.43)-1200(87.55)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.26)-1200(87.69)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.06)-1200(72.36)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.39)]TJ
ET
q
1 0 0 1 446.633 460.713 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 464.3 Td [(68.67)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.25)-1200(68.30)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.69)-1200(65.77)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.30)-1200(61.75)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.53)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 31.881 0 Td [(57.94)]TJ
0 g 0 G
/F14 9.9626 Tf 22.415 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.15)]TJ -641.208 -11.955 Td [(JoCor)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(43)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 448.758 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 452.345 Td [(93.52)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.47)-1200(93.47)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.40)-1200(89.47)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.04)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(88.56)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.28)-1200(73.70)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.92)]TJ
ET
q
1 0 0 1 446.633 448.758 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 452.345 Td [(68.48)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.49)-1200(67.87)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.80)-1200(65.73)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.55)-1200(61.64)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.54)-1450(57.75)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.80)]TJ -647.569 -11.955 Td [(PeerLoss)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(23)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 436.803 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 440.39 Td [(92.59)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.56)-1200(91.67)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.72)-1200(89.86)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.67)-1200(85.44)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.97)-1200(73.91)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.30)]TJ
ET
q
1 0 0 1 446.633 436.803 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 440.39 Td [(65.64)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.07)-1200(63.83)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.48)-1200(61.64)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.67)-1200(58.30)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.80)-1450(55.41)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.28)]TJ -647.569 -11.955 Td [(TMDNN)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(50)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 424.848 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 428.435 Td [(95.51)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.13)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(94.83)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.64)-1200(92.43)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.91)-1200(86.91)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.17)-1200(76.53)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.15)]TJ
ET
q
1 0 0 1 446.633 424.848 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 428.435 Td [(68.42)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.42)-1200(66.62)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.85)-1200(64.72)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.64)-1200(59.38)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.65)-1450(55.68)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.43)]TJ -640.301 -11.956 Td [(P)15(artT)-250([)]TJ
0 1 0 rg 0 1 0 RG
[(44)]TJ
0 g 0 G
[(])]TJ
ET
q
1 0 0 1 148.861 412.893 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
1 0 0 rg 1 0 0 RG
BT
/F111 9.9626 Tf 154.839 416.479 Td [(95.56)]TJ
0 g 0 G
/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.45)-1200(94.19)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.20)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(92.56)]TJ
0 g 0 G
/F14 9.9626 Tf 22.415 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.83)-1200(88.13)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.56)]TJ
1 0 0 rg 1 0 0 RG
/F111 9.9626 Tf 29.39 0 Td [(77.04)]TJ
0 g 0 G
/F14 9.9626 Tf 22.415 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.56)]TJ
ET
q
1 0 0 1 446.633 412.893 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 416.479 Td [(67.33)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.33)-1200(65.33)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.59)-1200(64.56)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.55)-1200(59.73)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.76)-1450(56.80)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(1.32)]TJ
ET
q
1 0 0 1 52.603 412.694 cm
[]0 d 0 J 0.398 w 0 0 m 690.807 0 l S
Q
BT
/F112 9.9626 Tf 69.275 404.126 Td [(MEIDTM)-250(\(Ours\))]TJ
ET
q
1 0 0 1 148.861 400.539 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 154.839 404.126 Td [(95.72)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.40)-1200(95.48)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.01)-1200(94.23)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.27)-1200(92.00)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.10)-1200(78.25)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.35)]TJ
ET
q
1 0 0 1 446.633 400.539 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F112 9.9626 Tf 452.611 404.126 Td [(68.19)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.32)-1200(67.21)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.38)-1200(66.06)]TJ/F14 9.9626 Tf 51.806 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.77)-1200(62.34)]TJ/F14 9.9626 Tf 51.805 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.18)-1450(57.69)]TJ/F14 9.9626 Tf 54.296 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.51)]TJ -656.7 -11.955 Td [(kMEIDTM)-250(\(Ours\))]TJ
ET
q
1 0 0 1 148.861 388.584 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
/F111 9.9626 Tf 154.839 392.171 Td [(96.38)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.748 0 Td [(0.07)]TJ/F111 9.9626 Tf 29.39 0 Td [(95.66)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.02)]TJ/F111 9.9626 Tf 29.39 0 Td [(94.68)]TJ/F14 9.9626 Tf 22.415 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.17)]TJ/F111 9.9626 Tf 29.39 0 Td [(92.20)]TJ/F14 9.9626 Tf 22.416 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(0.23)]TJ/F111 9.9626 Tf 29.39 0 Td [(80.22)]TJ/F14 9.9626 Tf 22.415 0 Td [<06>]TJ/F112 9.9626 Tf 7.749 0 Td [(2.00)]TJ
ET
q
1 0 0 1 446.633 388.584 cm
[]0 d 0 J 0.398 w 0 0 m 0 11.955 l S
Q
BT
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