ERATO100913

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いぶきなかじゅく
4 years ago
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1 ERATO September 13, 2010, DC2 1/25

2 /25

3 3/25

4 3/25

5 2 3/25

6 2 3/25

7 /25

8 (0, 0) /25

9 (0, 0) ( 1, 0) /25

10 1 (1, 1) (0, 0) ( 1, 0) /25

11 1 (1, 1) (1, 1) (0, 0) ( 1, 0) /25

12 1 (1, 1) (1, 1) (0, 0) ( 1, 0) 4/10 + 4/10 = /25

13 1 (1, 1) (1, 1) (0, 0) ( 1, 0) 4/10 + 4/10 = (00, 01) (01, 00) ( 10, 01) 4/25

14 1 (1, 1) (1, 1) (01, 10) 1 (1, 1) (1 1, 01) (0, 0) ( 1, 0) 4/10 + 4/10 = (00, 01) (01, 00) ( 10, 01) 4/25

15 1 (1, 1) (1, 1) (01, 10) 1 (1, 1) (1 1, 01) (0, 0) ( 1, 0) 4/10 + 4/10 = (00, 01) (01, 00) ( 10, 01) 12/ /10 = 2.2 4/25

16 t [Johnson, 99] p 2 1 FPAI 5/25

17 6/25

18 7/25

19 A B /25

20 A B /25

21 A B A B /25

22 A B A B /25

23 9/25

24 y = 3x 10/25

25 0, 1, [Tsuiki, 2002] /25

26 5 3 2 Position γ(1/4) 1/2 = γ((5/8, 7/8)) = (1 1 ω ) 1 12/25

27 (01 1 ω ) (1 1 ω ) /25

28 14/25

29 X Y I = [0, 1] [0, 1] R d X, Y γ(x), γ(y) R d γ γ(x) γ(y) 15/25

30 C(X, Y) { if X Y, D(X; Y) + D(Y; X) otherwise, D D(X; Y) 1 X X X R (P, Q) R P R Q = min { O O (γ(x), γ(y)) } 16/25

31 function MAIN(γ(X), γ(y)) LEARNING(γ(X), γ(y), 0, 0, X, Y, 0) function LEARNING(P, Q, D 1, D 2, m, n, k) V DISCRETIZE(P, k), W DISCRETIZE(Q, k) V sep {v V v W}, W sep {w W w V} D 1 D 1 + min V V v V v (V = {V V sep f P (V ) = f P (V sep )}) D 2 D 2 + min W W w W w (W = {W W sep f P (W ) = f P (W sep )}) output D 1 /m + D 2 /n P {p P p f P (V sep )}, Q {q Q q f Q (W sep )} if P = and Q = then halt else return LEARNING(P, Q, D 1, D 2, m, n, k + 1) function DISCRETIZE(P, k) return {w w = n, p (w ω ), p P} (n = (k + 1)d 1) f P (V) = {p P v V. p (v ω )}, P Σ ω,d, V Σ 17/25

32 : X : Y Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

33 : X : Y Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

34 : X : Y Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

35 : X : Y Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

36 : X : Y Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

37 : X : Y Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

38 : X : Y Level-3 Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

39 : X : Y Level-3 Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 18/25

40 : X : Y Level-4 Level-3 Level Level D(X; Y) { 10, 11} D(Y; X) {0 1, 101} C(X, Y) = 4/5 + 5/5 = /25

41 19/25

42 X Y A B Z A B Z { A B if C(X, Z) > C(Y, Z), otherwise. 20/25

43 21/25

44 R UCI abalon, sonar,... 10,000 sensitivity specificity accuracy n 2 X, T + Y, T X, Y T +, T min-max normalization T + T t pos t neg (t pos + t neg )/20000 accuracy 22/25

45 n = abalon 0.65 sonar Accuracy Number of attributes Number of attributes Gray-coding div. Binary-coding div. SVM (RBF) SVM (Polynomial) 1-nearest neighbor 5-nearest neighbor 23/25

46 n = ecoli 1.0 glass Accuracy Number of attributes Number of attributes Gray-coding div. Binary-coding div. SVM (RBF) SVM (Polynomial) 1-nearest neighbor 5-nearest neighbor 23/25

47 n = segmentation 0.9 ionosphere Accuracy Number of attributes Number of attributes Gray-coding div. Binary-coding div. SVM (RBF) SVM (Polynomial) 1-nearest neighbor 5-nearest neighbor 23/25

48 n = madelon 0.7 magic Accuracy Number of attributes Number of attributes Gray-coding div. Binary-coding div. SVM (RBF) SVM (Polynomial) 1-nearest neighbor 5-nearest neighbor 23/25

49 n = yeast Accuracy Number of attributes Gray-coding div. Binary-coding div. SVM (RBF) SVM (Polynomial) 1-nearest neighbor 5-nearest neighbor 23/25

50 24/25

51 Computable Analysis Computational Learning Theory 25/25

橡点検記録(集約).PDF

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