Architecture for Visualization Using Teacher Information based on SOM

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1 THE INSTITUTE OF ELECTRONICS, INFORMATION AND COMMUNICATION ENGINEERS TECHNICAL REPORT OF IEICE NTT (SOM) SOM 2 Architecture for Visualization Using Teacher Information based on SOM Empirical Studies on Visualizing Time Series of Medical Data Ken-ichi FUKUI, Kazumi SAITO, Masahiro KIMURA, and Masayuki NUMAO The Institute of Scientific and Industrial Research, Osaka University 8-1 Mihogaoka, Ibaraki, Osaka, NTT Communication Science Laboratories 2-4 Hikaridai, Seika, Kyoto Department of Electronics and Informatics, Ryukoku University 1-5 Yokotani,Seta Oe-cho, Otsu, Shiga, {k-fukui,numao}@sanken.osaka-u.ac.jp, saito@cslab.kecl.ntt.co.jp, kimura@rins.ryukoku.ac.jp Abstract In this paper, we propose an architecture for visualization that constructs the map suggesting the cluster in a sequence that involves in classification by utilizing the teacher information for the display method of the map, while making the best use of the characteristics of Self-Organizing Maps (SOM) that are to create clusters and to arrange the similar clusters near within the low dimensional map. This proposal method consists of 2 learning phases, firstly the sequence of the winner neurons are obtained by SOM, secondly connectivity weights are obtained by perceptron, finally the map is visualized by reversing the obtained weights into the map. In the experiments using time series of real-world medial data, we evaluate the visualization and classification performance by comparing the display method by the ratio of classes. Key words Data Self-Organizing Maps, Teacher Information, Perceptron, Visual Data Mining, Time Series, Medical 1

2 1. 2. Kohonen SOM(Self-Organizing Maps) 2. 1 SOM [1] Kohonen SOM(Self-Organizing SOM Maps) SOM (unsupervised) N V x n = (x n,1,, x n,v ), (n = 1,, N) SOM 2 ( ) ( 2 3 ) m j SOM m new j = m j + h c(x),j [x m j]. (1) [2] Sammon s Mapping [3] c(x) = arg min x m i. (2) h c(x),j c(x) (2) h c(x),j SOM h c(x),j = α exp ( r j r c(x) 2 ). (3) 2σ 2 SOM Kohonen LVQ-SOM [1] [4][6] r j 2 j α σ SOM [9] M M E SOM = h i,j x n m j 2. (4) SOM M SOM ( ) C i c(x) = i SOM 2. 2 SBSOM SOM [7] SOM [6], [8] SOM Seqence-Based SOM(SBSOM) [8]. SOM SBSOM 2 SBSOM SBSOM (x n, t n) (m j, s j ) t n s j ( ) c(x) = arg min δ(t n, s j ) x n m j. (5) j { 1 if t n = s j, δ(t n, s j) = (6) otherise. i i=1 x n C i j=1 2

3 GOT IFN ( ) 1 ( ) 2 Weight Decay 1 [1] β Weight Decay SBSOM SOM S3. w j K SOM k k n(k) k ) : r = 1,, k} K k=1 {(x (k) n(r), t(k) n(r) n(k) = N S1. r, k (x (k) n(r), t(k) n(r) ) (SB)SOM 3. 1 (1 ) C S2. GOT,GPT,TP,ALB,T- BIL,D-BIL,I-BIL,TTT,ZTT,CHE,T-CHO 11 k i( ) (i = 1,, M) 1 2 GOT { 1/n(k) if r c(x (k) n(r) y k,j = ) C j, ( ) IFN (7) otherwise w = (w 1,, w M ) (IFN) ẑ k = w y k z k = IFN { 1, 1}, (k = 1,, K) K M E pct = (z k ẑ k ) 2 + β wj 2. (8) k=1 j=

4 normalized 5.5 interpolated Original Data : 3% 2.5 IFN IFN HCV-RNA 1 1-fold cross validation 3 IFN (55 ) ( % IFN ( ) % 64.29% (8) β β = SOM ( ) [11] fold cross validation (3) 3. 4 SBSOM(15 52 ) ( ) (ILP) [11] ( )/( ) (4) 67.2% 2 (5) IFN SOM ( ) (MDL) [12] 3 C PCR 73.3% 4

4 ( ) 5 6 8 6 4 2 Ratio Perceptron 1 2 3 4 5 6 7 8 9

5 4 ( ) Ratio Perceptron ) ( ) ( ) 4. SOM SOM ( ) ( ) 6 ( 5

6 3 ( ) ( ) ( ) (Maximum Entropy Method) [1] T. Kohonen: Self-Organizing Maps, Springer-Verlag, Heidelberg (1995). [2] J. B. Kruskal and M. Wish: Multidimensional scaling, Number 7-11 in Paper Series on Quantitative Applications in the Social Sciences (1978). [3] J. Sammon: A nonlinear mapping for data structure analysis, IEEE Transactions on Computers, c-18, pp (1969). [4] R. Hecht-Nielsen: Counterpropagaton networks, IEEE Frist international Conference on Neural Networks, pp (1987). [5] B. Fritzke: Growing cell structures: A selforganizing networks for unsupervised and supervised learning, Neural Networks, 7, pp (1994). [6],,, som, Technical Report NC23142, (24). [7] T. Kohonen, S. Kaski, K. Lagus, J. Salojrvi, J. Honkela, V. Paatero and A. Saarela: Self organization of a massive document collection, IEEE Transaction on Neural Networks, 11(3), pp (2). [8] K. Fukui, K. Saito, M. Kimura and M. Numao: Sbsom: Self-organizing map for visualizing structure in the time series of hot topics, Proc. Joint Workshop of Vietnamese Society of AI, SIGKBS-JSAI, ICS-IPSJ, and IEICE-SIGAI on Active Mining, pp (24). [9] T. Kohonen: Comparison of som point densities based on different criteria, Neural Computation, 11, pp (1999). [1] S. Hanson and L. Pratt: Comparing biases for minimal network construction with back-propagation, Advances in Neural Information Processing Systems 1, pp (1989). [11] Ilp, (25). [12],,, SIG-KBS-A45-5, pp (25). 6

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