Self-Organizing Map:SOM SOM..
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1 2016 3
2 Self-Organizing Map:SOM SOM SOM SOM SOM (S-SOM) S-SOM S-SOM S-SOM U-matrix (HMM) HMM Forward algorithm Backward algorithm Viterbi algorithm Baum-Welch algorithm HMM (HMM-S-SOM) 51 1
3 4.1 HMM-S-SOM HMM-S-SOM (F-HMM-S-SOM) F-HMM-S-SOM F-HMM-S-SOM F-HMM-S-SOM DNA
4 1 1.1,,,,,,,,,,,,,k-means,,,, 3
5 1.2,,,,,,,,,,,, Siri,,,,,,, [1][2],,, [3],,,,,,,,,,, 4
6 ,,,,,,, [4], [5], 5
7 1.3,,,,,, [6][7],,,,,,,, 3,, 3 6
8 2 Self-Organizing Map:SOM 2.1 SOM, (TKohonen) SOM,,,, 1, data 2, data3, (data1, data2),,,, 1: SOM 7
9 2.2 SOM, ( 2) SOM,,,data2 data3,data2,data3,data1 2 2: SOM SOM,data1, 2,SOM data1data3, ,, SOM,,1 1,,,, ( 3), 8
10 ,, 3: SOM,data1,data1 3, (winner node) data1, 4,,,, data1 data1 data1,data2, 9
11 4: data1 data2, data1 5, data2 data2, data2 data3 data2 6,,,data3 data2,data2 data1,,,,,, 10
12 5: data2 6: data3 11
13 , SOM,,, SOM SOM STEP 1: ()v j SOM STEP 2: v j w N j k N j k N j k = min f j (k) (1) k f j (k) = n (a jt w kt ) 2 (2) STEP 3: N j k w k v j t=1 h(p jx, P jx ) = exp( P jx P jx 2 σ 2 ) (3) w k = β h(p jx, P jx )f j (k) (4) w new k = w k + w k (5) 12
14 P jx N j k P jx P jx P jx σ β 7 7: 24 w 2.3 SOM Data1Data R,G,B SOM Data2 Data5,, 13
15 , SOM SOMPlane-SOM,,,, SOM ( 9:), SOM,, SOM ( 9:), 14
16 8: SOM 2.4 (S-SOM) SOM SOM [8][9][10][11] [9] OpenGL Windows Windows API DirectX [12][13] 15
![[8][9][10][11] [9]](/docs-images/51/20162934/images/page_16.jpg "OpenGL Windows Windows")
17 9: SOM S-SOM DirectX D 10, 16
18 10: 11 11: S-SOM SOM 17
19 SOM SOM S-SOM SOM SOM 12 12: S-SOM S-SOM n m v j = {a j1, a j2, a j3,..., a jn }(j = 1, 2, 3,..., m) S- SOM l N k (k = 1, 2, 3,..., l) w k = {w k1, w k2, w k3,..., w kn } 18
20 S-SOM STEP 1: w w STEP 2: v v j SOM STEP 3: v j w N j k N j k N j k = min k f j (k) (6) f j (k) = n (a jt w kt ) 2 (7) t=1 STEP 4: N j k w k v j h(p jx, P jx ) = exp( P jx P jx θ 2 ) (8) w k = β h(p jx, P jx )f j (k) (9) w new k = w k + w k (10) P jx N j k P jx P jx P jx θ β 19
21 θ 13β 13: S-SOM 20
22 2.4.3 S-SOM U-matrix SOM S-SOM : S-SOM U-matrix 21
23 S-SOM U-matrix S-SOM n n-1 S-SOM n U-matrix T g U g ab U g ab N a N b U g ab = U g ba U g ab, U g ba U g N k (k = 1, 2, 3,..., l) w k = {w k1, w k2, w k3,..., w kn } SOM U g ab n U g ab = (w aj w bj ) 2 (11) j=1 T g N a V a, V g L V g = L (αu g + max h(u h ) M min h (U h ) ) (12) max h (U h ) min h (U h ) V a = L 1 6 j (αu g aj + max h(u h ) M min h (U h ) max h (U h ) min h (U h ) ) (13) α = M 1 max h (U h ) min h (U h ) (14) V g min(u h ) 0, max (U h ) M U g L h h 22
24 M L V a N a 6 U a L 15: S-SOM U-matrix 16: S-SOM U-matrix 23
25 3 3.1 (HMM) Baum-Welch algorithm Viterbi algorithm 3.2 HMM HMM Q = {q 1, q 2, q 3,..., q k } : q a i,j : q i q j j a i,j = 1 s i (x) : i x x s i (x) = 1 w[t] : t 24
26 Θ : HMM Forward algorithm Forward algorithm HMM w w N R N R R M R R m (W ) = {r m [0], r m [1], r m [2],..., r m [N]} (m = 1, 2, 3,..., M) (15) r m [t] R m (W ) t S L w M N L w = s g(m,t 1) (w[t]) a g(m,t 1),j g(m, t) = r m [t] (16) m=1 t=1 17 A, B, C HMM w AABC w 1 25
27 17: 26
28 1: w R 1 R 3 w R 1 : a 0,0 s 0 (w[1]) a 0,1 s 0 (w[2]) a 1,2 s 1 (w[3]) a 2,3 s 2 (w[4]) = a 0,0 s 0 (A) a 0,1 s 0 (A) a 1,2 s 1 (B) a 2,3 s 2 (C) = = (17) R 2 : a 0,1 s 0 (w[1]) a 1,1 s 1 (w[2]) a 1,2 s 1 (w[3]) a 2,3 s 2 (w[4]) = a 0,1 s 0 (A) a 1,1 s 1 (A) a 1,2 s 1 (B) a 2,3 s 2 (C) = = (18) R 3 : 27
29 a 0,1 s 0 (w[1]) a 1,2 s 1 (w[2]) a 2,2 s 2 (w[3]) a 2,3 s 2 (w[4]) = a 0,1 s 0 (A) a 1,2 s 1 (A) a 2,2 s 2 (B) a 2,3 s 2 (C) = = (19) w L w L w = = (20) Forward algorithm f j (t) = s i (w[t]) q i Q f i (t 1)a i,j t 1 (21) f 0 (0) = 1 f j (t) t q j w = {w[1], w[2],..., w[t]} 28
30 Forward algorithm, L w f 0 (0) = 1.0 f 0 (1) = f 0 (0) a 0,0 s 0 (w[1]) = f 0 (0) a 0,0 s 0 (A) = = 0.06 f 1 (1) = f 0 (0) a 0,1 s 0 (w[1]) = f 0 (0) a 0,1 s 0 (A) = = 0.24 f 1 (2) = f 0 (1) a 0,1 s 0 (w[2]) + f 1 (1) a 1,1 s 1 (w[2]) = f 0 (1) a 0,1 s 0 (A) + f 1 (1) a 1,1 s 1 (A) = = f 2 (2) = f 1 (1) a 1,2 s 1 (w[2]) = f 1 (1) a 1,2 s 1 (A) = = f 2 (3) = f 1 (2) a 1,2 s 1 (w[3]) + f 2 (2) a 2,2 s 2 (w[3]) = f 1 (2) a 1,2 s 1 (B) + f 2 (2) a 2,2 s 2 (B) = = f 3 (4) = f 2 (3) a 2,3 s 2 (w[4]) = f 2 (3) a 2,3 s 2 (C) = = L w = f 3 (4) =
31 3.2.2 Backward algorithm Forward algorithm w q j Backward algorithm q j w = {w[n], w[n 1],..., w[t + 1]} b j (t) b i (t) = q j Q b j (t + 1)a i,j s i (w[t + 1]) (22) 17 AABC L w Backward algorithm 30
32 b 3 (4) = 1.0 b 2 (3) = b 3 (4) a 2,3 s 2 (w[4]) = b 3 (4) a 2,3 s 2 (C) = = 0.06 b 2 (2) = b 2 (3) a 2,2 s 2 (w[3]) = b 2 (3) a 2,2 s 2 (B) = = b 1 (2) = b 2 (3) a 1,2 s 1 (w[3]) = b 2 (3) a 1,2 s 1 (B) = = b 1 (1) = b 2 (2) a 1,2 s 1 (w[2]) + b 1 (2) a 1,1 s 1 (w[2]) = b 2 (2) a 1,2 s 1 (A) + b 1 (2) a 1,1 s 1 (A) = = b 0 (1) = b 1 (2) a 0,1 s 0 (w[2]) = b 1 (2) a 0,1 s 0 (A) = = b 0 (0) = b 1 (1) a 0,1 s 0 (w[1]) + b 0 (1) a 0,0 s 0 (w[1]) = b 1 (1) a 0,1 s 0 (A) + b 0 (1) a 0,0 s 0 (A) = = L w = b 0 (0) = Backward algorithm b 0 (0) Forward algorithm f 3 (4) b 0 (0) = f 3 (4) 31
33 3.2.3 Viterbi algorithm Forward algorithm f j (t) = s i (w[t]) f i (t 1)a i,j q i Q w Viterbi algorithm W Rm(w) N L w = arg max s g(m,t) (w[t]) a g(m,t),j g(m, t) = r m [t] (23) t=0 f j (t) = s i (w[t]) max q Q f i(t 1)a i,j (24) 32
34 3.2.4 Baum-Welch algorithm HMM Viterbi algorithm HMM Θ Θ w Viterbi algorithm w Θ Baum-Welch algorithm Θ HMM w Θ Θ Forward algorithm L w 18 left-to-light 33
35 18: Baum-Welch algorithm Baum-Welch algorithm O i,j : W = {w 1, w 2,..., w l } q i q j E i (x) : W = {w 1, w 2,..., w l } x q i P (w k Θ) : W = {w 1, w 2,..., w l } Θ w k L w P (w k Θ) = L w W P (W Θ) P (W Θ) = l k=1 L k l 34
36 , O i,j E i (x) t 1 O i,j = l k=1 1 fi k (t 1) a i,j s i (w k [t]) b k j (t) (25) P (w k Θ) t E i (x) = l k=1 1 P (w k Θ) t:w k [t]=x f k i (t 1) b k i (t 1) (26) O i,j E i (x) a i,j s i (x) a i,j = s i (x) = O i,j j O i,j E i(x) x E i (x ) (27) (28) 35
37 17 AABC AABC L w O i,j = = = t 1 1 f i (t 1) a i,j s i (w 1 [t]) b j (t) P (w k Θ) k=1 t 1 f i (t 1) a i,j s i (w 1 [t]) b j (t) P (w 1 Θ) t f i (t 1) a i,j s i (w 1 [t]) b j (t) L w t q i q j ξ t (i, j) ξ t (i, j) = f i(t 1) a i,j s i (w k [t]) b j (t) L w O i,j = t ξ t (i, j) PROCESS1PROCESS4 36
38 PROCESS 1 ξ t (i, j) ξ t (i, j) ξ 1 (0, 0) = f 0(0) a 0,0 s 0 (w 1 [1]) b 0 (1) = f 0(0) a 0,0 s 0 (A) b 0 (1) L w L w = = ξ 1 (0, 1) = f 0(0) a 0,1 s 0 (w 1 [1]) b 1 (1) = f 0(0) a 0,1 s 0 (A) b 1 (1) L w L w = = ξ 2 (0, 1) = f 0(1) a 0,1 s 0 (w 1 [2]) b 1 (2) = f 0(1) a 0,1 s 0 (A) b 1 (2) L w L w = = ξ 2 (1, 1) = f 1(1) a 1,1 s 1 (w 1 [2]) b 1 (2) = f 1(1) a 1,1 s 1 (A) b 1 (2) L w L w = = ξ 2 (1, 2) = f 1(1) a 1,2 s 1 (w 1 [2]) b 2 (2) = f 1(1) a 1,2 s 1 (A) b 2 (2) L w L w = = ξ 3 (1, 2) = f 1(2) a 1,2 s 1 (w 1 [3]) b 2 (3) = f 1(2) a 1,2 s 1 (B) b 2 (3) L w L w = = ξ 3 (2, 2) = f 2(2) a 2,2 s 2 (w 1 [3]) b 2 (3) = f 2(2) a 2,2 s 2 (B) b 2 (3) L w L w = = ξ 4 (2, 3) = f 2(3) a 2,3 s 2 (w 1 [4]) b 3 (4) = f 2(3) a 2,3 s 2 (C) b 3 (4) L w L w = =
39 ξ 1 (0, 0) + ξ 1 (0, 1) = 1.0 ξ 2 (0, 1) + ξ 2 (1, 1) + ξ 2 (1, 2) = 1.0 ξ 3 (1, 2) + ξ 3 (2, 2) = 1.0 ξ 4 (2, 3) = 1.0 PROCESS 2 a i,j PROCESS 1 ξ t (i, j) a i,j = O i,j j O i,j O i,j O i,j = ξ t (i, j) t j 29 O i,j = t ξ t (i, j) a i,j j a i,j = t ξ t(i, j) j ξ t(i, j) t (29) a i,j 38
40 a 0,0 = = a 0,1 = = a 1,1 = = a 1,2 = = a 2,2 = = a 2,3 = = ξ 1 (0, 0) ξ 1 (0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) ξ 1 (0, 1) + ξ 2 (0, 1) ξ 1 (0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) ξ 2 (1, 1) ξ 2 (1, 1) + ξ 2 (1, 2) + ξ 3 (1, 2) ξ 2 (1, 2) + ξ 3 (1, 2) ξ 2 (1, 1) + ξ 2 (1, 2) + ξ 3 (1, 2) ξ 3 (2, 2) ξ 3 (2, 2) + ξ 4 (2, 3) ξ 4 (2, 3) ξ 3 (2, 2) + ξ 4 (2, 3) a i,j a i,j 39
41 PROCESS 3 s i (x) s i (x) l 1 L w P (w k Θ) k=1 l 1 1 P (w k Θ) = 1 P (w 1 Θ) = 1 L w k=1 k=1 26 E i (x) = 1 L w t:w k [t]=x f i (t 1) b i (t 1) (30) 3022 E i (x) = 1 L w = 1 = = t:w k [t]=x L w t:w k [t]=x f i (t 1) b i (t 1) f i (t 1) b j (t)a i,j s i (w[t]) q j Q t:w k [t]=x f i(t 1) q j Q b j(t)a i,j s i (w[t]) t:w k [t]=x q j Q L w f i (t 1) b j (t)a i,j s i (w[t]) L w (31) ξ t (i, j) = f i(t 1) a i,j s i (w k [t]) b j (t) L w 31 E i (x) = t:w k [t]=x q j Q f i (t 1) b j (t)a i,j s i (w[t]) L w = t:w k [t]=x q j Q ξ t (i, j) (32) 40
42 28 s i (x) = = = E i (x) x E i (x ) t:w k [t]=x x t:w k [t]=x t t:w k [t]=x q j Q ξ t(i, j) q j Q ξ t(i, j) q j Q ξ t(i, j) q j Q ξ t(i, j) (33) 41
43 33 s i (x) s 0 (A) = ξ 1(0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) ξ 1 (0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) = 1.0 s 0 (B) = 0 ξ 1 (0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) = 0.0 s 0 (C) = 0 ξ 1 (0, 0) + ξ 1 (0, 1) + ξ 2 (0, 1) = 0.0 s 1 (A) = = s 1 (B) = = s 1 (C) = s 2 (A) = s 2 (B) = = s 2 (C) = = ξ 2 (1, 1) + ξ 2 (1, 2) ξ 2 (1, 1) + ξ 2 (1, 2) + ξ 3 (1, 2) ξ 3 (1, 2) ξ 2 (1, 1) + ξ 2 (1, 2) + ξ 3 (1, 2) ξ 2 (1, 1) + ξ 2 (1, 2) + ξ 3 (1, 2) = ξ 3 (2, 2) + ξ 4 (2, 3) = 0.0 ξ 3 (2, 2) ξ 3 (2, 2) + ξ 4 (2, 3) ξ 4 (2, 3) ξ 3 (2, 2) + ξ 4 (2, 3)
44 3.3 HMM Forward algorithmbackward algorithmbaum-welch algorithm 17 AABC 1 t G = {G 1, G 2,...G t,...g l } k G t t k k G t = Γ t (0, 0) Γ t (0, 1) Γ t (0, k 1) Γ t (1, 0) Γ t (1, 1) Γ t (1, k 1) Γ t (k 1, 0) Γ t (k 1, 1) Γ t (k 1, k 1) 4 k = 4 G t Γ t (i, j) t i s i (w[t]) i j 0 i s i (w[t]) i j t = 1 A i A Γ 1 (i, j) = 1, i 43
45 A i j Γ 1 (i, j) = 1 i j t = 1 t = 4 44
46 t = 1 t = 1 0 i = 0 G 1 i 0 1 t = 4 t = 4 4 i 3(... k 1 = 4 1 = 3) a i,3 0 i 1, 0 i = 0 1 Γ 1 (0, 0) = 0 (... s 0 (A) a 0,0 0) Γ 1 (0, 1) = 0 (... s 0 (A) a 0,1 0) Γ 1 (0, 2) = 1 (... s 0 (A) a 0,1 = 0) Γ 1 (0, 3) = 1 (... s 0 (A) a 0,1 = 0) 45
47 Γ 1 (1, 0) = 1 Γ 1 (2, 0) = 1 Γ 1 (3, 0) = 1 Γ 1 (1, 1) = 1 Γ 1 (2, 1) = 1 Γ 1 (3, 1) = 1 Γ 1 (1, 2) = 1 Γ 1 (2, 2) = 1 Γ 1 (3, 2) = 1 Γ 1 (1, 3) = 1 Γ 1 (2, 3) = 1 Γ 1 (3, 3) = 1 t G t 19 46
48 19: G t G t STEP 1 G 1 j 1 2 G 2 j 1 20 G 1 G 2 G 3, G 4 t = 1 G t j 1 G t+1 j 1 t = l 1 G 47
49 20: G STEP t = l G t i 1 G t 1 i 1 t = 2 G 21 48
50 21: G STEP STEP t i j G t Γ t (i, j) AABC
51 22: G 50
52 4 隠れマルコフ球面自己組織化マップ (HMM-S-SOM) 隠れマルコフ球面自己組織化マップとは,S-SOM のノードに隠れマルコフモデル を用いたものであり 図 23, 入力データには, ベクトルではなく文字列集合を用い る. ノード上に内包された隠れマルコフモデルは, すべて同じ構造を持つ この自 己組織化マップは, データを直接分類するのではなくデータの背景にある確率モデ ルにもとづいて, 確率モデルを球面上にクラスタリングし, その分類結果を視覚的に も容易に提示することのできる学習モデルである S-SOM と HMM-S-SOM の違い については表 2 に示す ノードや入力データの形式の違い以外に, 勝者ノードの決 定方法や, ノードの更新の方法が異なる その詳細については, 次の HMM-S-SOM の学習アルゴリズムの説明に記す 図 23: 隠れマルコフ球面自己組織化マップ 51
53 2: S-SOM HMM-S-SOM 4.1 HMM-S-SOM STEP 0: HMM Θ k STEP 1: STEP 2: Baum-Welch algorithm STEP 3,, STEP 3: HMM Baum-Welch algorithm, HMM SOM 52
54 SOM, STEP1STEP3, STEP2,,,, 24,,,Baum-Welch algorithm HMM,,,,Baum-Welch algorithm HMM,STEP3 24: 53
55 4.2, left to right, Ergodic, U-matrix, U-matrix U-matrix,,,, A,B,C 3 HMM HMM M 1, M 3,..., M 10,,,, ,
56 3: M 1 4: M 2 5: M 3 6: M 4 7: M 5 8: M 6 55
57 9: M 7 10: M 8 11: M 9 12: M 10 13: M 1 14: M 2 56
58 15: M 3 16: M 4 17: M 5 18: M 6 19: M 7 20: M 8 57
59 21: M 9 22: M 10 25: HMM-S-SOM HMM-S-SOM M 1 Data1 M 1 M 10 M 1 M 10 M 3, M 8, M 9, M 7, M 2, M 5, M 6, M 4 M 1,U-matrix HMM, U-matrix HMM 58
60 26:, HMM,, 27,,,,model 1 model 4,HMM -matrix,, 59
61 27: 60
62 5 (F-HMM-S-SOM), Baum-Welch algorithm,,som,hmm,, SOM HMM, (F-HMM-S-SOM) ( 28) 28: F-HMM-S-SOM,, HMM,, 61
63 , F-S-HMM-SOM, A,B,C, n, n + 1,A,B,C,,, A,B,C, l, l 1 l, 12 (l 1) m, l max, (m 2 + m)(l max 1) ACCB, BCC,,, 2,ACCB, AC, 29 AC, 0, , CC , CB ACCB 62
64 ,BCC :,,, 30,, 0( 30: ) Θ k : HMMS-SOMHMMΘ k = {A k, S k } 63
65 30: A k = a k 01 a k 02 a k 0j a k 11 a k 12 a k 1j S k = s k 01 s k 02 s k 0h s k 11 a k 12 s k 1h a k i1 a k i2 a k ij s k i1 s k i2 s k ih a i,j i j s i,h i x h X : X = {x 1, x 2, x 3,..., x h } V = {v 1, v 2, v 3,..., v h } STEP 1: HMM Θ k STEP 2: W n Baum-Welch algorithm N i HMM L i, N i E i STEP 3:, 64
66 (1 E i E max ) L i,e max E i STEP 4: Baum-Welch algorithm, STEP 5:,SOM N n k Θ k STEP 4 Nk n HMM Θ n k = {An k, Sn k } A = β h(p nx, P nx )(A n k A k) A new k = A k + A S = β h(p nx, P nx )(Sk n S k) S new k = S k + S Θ new k Θ k Θ new k = {A new k, Sk new } h(p nx, P nx ) = exp( P nx P nx θ 2 ) P jx N j k P jx 65
67 P jx P jx β,baum-welch algorithm STEP 6: SOM SOM STEP2STEP5,,, U-matrix, 66
68 5.1 F-HMM-S-SOM,, HMM-S-SOM, F-HMM-S-SOM HMM U-matrix 31,, 31: HMM U-matrix, ( 32),, 67
![32: U-matrix 5.2 F-HMM-S-SOM,,,DNA (HMM-S-SOM) 5.2.1 DNA, DNA ATGC,ATGC [14], 1024, 6](/docs-images/39/20162934/images/69-0.png "1024, (Hsall), Mmuall, (Cfaall), Ecoall, (Dmaall), (Osaall),HMM- S-SOM, U-matrix 33")
69 32: U-matrix 5.2 F-HMM-S-SOM,,,DNA (HMM-S-SOM) DNA, DNA ATGC,ATGC [14], 1024, , (Hsall), Mmuall, (Cfaall), Ecoall, (Dmaall), (Osaall),HMM- S-SOM, U-matrix 33 68
70 33: HMM-S-SOM,,.. F-HMM-S-SOM,HMM U-matrix, ( 34), ( 35),,,,,,,,,, 69
71 34: F-HMM-S-SOM : U-matrix 35: F-HMM-S-SOM : U-matrix 70
72 5.2.2, ,,,,,,, 36,,,, U, D, S, U D,, F-HMM-S-SOM,F- HMM-S-SOM HMM, 37 4, U,S,D 3,Umatrix, 71
73 36: 72
74 37:,,. t t+1, HMM-S-SOM F-HMM-S-SOM , , S-HMM-SOM, F-S-HMM-SOM,, S-HMM-SOM,U-matrix,,F-S-HMM-SOM, 73
75 38: 74
76 39: 75
77 , U-matrix,,,, F-S-HMM-SOM 1.377,S-HMM-SOM 2.623,,., 40,, S-HMM-SOM 40,,,, F-S-HMM-SOM 40,,,,,,,,,,,,,,,,, 76
78 40: 77
79 ,, 41,,,, , ,,,,, 4,,,,,, 78
80 41: 79
81 図 42: 移動平均線との比較 80
82 図 43: 移動平均線との比較 81
83 : 82
84 6,,,,,,,,,,,,, 44, 1,2, SOM v j x i 1, (mask-vector)w i w i,, ,1,0 83
85 44:, 1, 0 1,1 2, 30 5,,,, 45: SOM,, 45, h a, 84
86 STEP 1: 1 x i = {x i0, x i1,..., x in }, h a = {h a0, h a1,..., h an } 2 w i = {w i0, w i1,..., w in } 1 STEP 2: i,l 1 [argmin] i {w ij (h aj v aj w ij x ij )} L 2 (34) j L = j w2 ij w i w i STEP 3: wi,, µ a µ a µ ai ω 46 46: 85
87 (35) m [argmin] m { 1 m m k=2 ( ω k ω m ) 2 } ϕ (35),ϕ 0.5 µ t ω k f(t) = k, f(t) m w new it = w old it + γ(1 w old it ) (36) m < f(t) w new it = w old it + γ(0 w old it ) (37),γ 0 < γ < 1, wi w i 1 0 h a STEP 4:, x new j = x old j + α(v a x old j ) (38) w new j = w old j + β(w i w old j ) (39) α,,0 < α < 1, β 0 < β < 1 86
88 STEP2STEP4,,, h a, 6.1, h a, 1 3,,, noise Mersenne Twister[15] 01 1x,y,z y = 3 x + noise z = noise 2x 0.5, x,y,z x,y,z 87
89 47: y = 3 x + noise z = noise (x 0.5) y = 2 x + noise z = noise (x > 0.5) 3x 0.5,x,z, x 0.5,y z y = 3 x + 2 noise z = noise (x 0.5) 88
90 48: 2 y = 2 z + noise + 2 x = noise (x > 0.5) ,, x y model z, x y 0.819, SOM 51 SOM, 8, 89
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102 1. Gen Niina, Kazuhiro Muramatsu, Hiroshi Dozono: Basic Study on the Classification of Time Series Data Using a Frequency Integrated Spherical Hidden Markov Self Organizing Map, Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.19 No.2, pp , Gen Niina, Kazuhiro Muramatsu, Hiroshi Dozono: Causal analysis of data using 2-layerd Spherical Self-Organizing Map, The 2015 International Conference on Computational Science and Computational Intelligence (CSCI 15), Las Vegas, USA, pp , Gen Niina, Kazuhiro Muramatsu, Hiroshi Dozono, Tatsuya Chuuto: The data analysis of stock market using a Frequency Integrated Spherical Hidden Markov Self Organizing Map, ICSIIT 2015, 4th International Conference on Soft Computing, Intelligent System and Information Technology, March 11-14, 2015 / Bari, Indonesia, pp , Gen Niina, Kazuhiro Muramatsu, Hiroshi Dozono: The Frequency Integrated Spherical Hidden Markov Self Organizing Map for Learning Time Series Data, ISIS2013, The International Symposium on Advanced Intelligent Systems, Daejeon, Korea, pp ,
103 4. Hiroshi Dozono, Gen Niina and Kazuhiro Muramatsu,: Mapping of DNA sequences using Hidden Markov Model Self-Organizing Maps, Proceedings of The 10th annual IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology, IEEE Press, Singapore, Hiroshi Dozono, Gen Niina and Yutaro Kaneko: Mapping the Groups of DNA Sequences using Hidden Markov Model Self Organizing Maps, The First BMIRC International Symposium on Frontiers in Computational Systems Biology and Bioengineering, Fukuoka, Japan, Gen Niina, Hiroshi Dozono: The Spherical Hidden Markov Self Organizing Map for Learning Time Series Data, 22nd International Conference on Artificial Neural Networks, Lausanne, Switzerland, pp , Part I, ,, :, 15,, , : DirectX SOM 19, ,, : 64,
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