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-Artificial Neural Network- Chapter 9 Self Organization Map(SOM)

-Artificial Neural Network- Chapter 9 Self Organization Map(SOM). 朝陽科技大學 資訊管理系 李麗華 教授. Introduction. It’s proposed by Kohonen in 1980. SOM is an unsupervised two layered network that can organize a topological map from a random starting point.

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-Artificial Neural Network- Chapter 9 Self Organization Map(SOM)

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  1. -Artificial Neural Network- Chapter 9 Self Organization Map(SOM) 朝陽科技大學 資訊管理系 李麗華 教授

  2. Introduction • It’s proposed by Kohonen in 1980. • SOM is an unsupervised two layered network that can organize a topological map from a random starting point. SOM is also called Kohnen’s self organizating feature map. The resulting map shows the natural relationships among the patterns that are given to the network. • The application is good for clustering analysis.

  3. k Yk1 Ykj Yk2 Ykj Yjk （Xij,Yij） j Y11 Y12 Y1k W1jk Wijk X2 X1 Network Structure • One input layer • One competitive layer which is usually a 2-Dim grid Input layer：f(x)：x Output layer：competitive layer with topological map relationship Weights ：randomly assigned

  4. Concept of Neighborhood Center：the winning node C is the center. Distance： R Factor（鄰近係數）： RFj：f（ rj,R）=e(- rj /R) e(-rj/R)→ 1 when rj= ∮ e(-rj/R)→ ∮ when rj= ∞ e(-rj/R)→ 0.368 when rj = R The longer the distance, the smaller the neighborhood area. R Factor Adjustment：Rn=R-rate  Rn-1 , R-rate<1.0 • N is the node is output N to C • rj is the distance from N to C • R：the radius of the neighborhood • rj ：distance from N to C

  5. Learning • Setup network • Randomly assign weights to W • Set the coordinate value of the output layer N（x,y） • Input a training vector X • Compute the winning node • Update weight △W with R factor • ηn=η-rate ηn-1 Rn=R-rate ηn-1 • Repeat from 4 to 7 until converge

  6. Reuse the network • Setup the network • Read the weight matrix • Set the coordriate value of the output layer N（x,y） • Read input vector • Compute the winning node • Output the clustering result Y.

  7. 1 j=j*&k=k* if φ others Computation process 1. Setup network X1~Xn（Input Vector） Njk （Output） 2. Compute winning node 3. Yjh =

  8. △Wijk=η（Xi － Wijk ）．RFjk When rjk= Wijk=△Wijk+Wijk 6. ηn=η-rate‧ηn-1 Rn= R-rate‧Rn-1 Computation process (cont.) 4. Update Weights 5. Repeat 1-4 for all input 7. Repeat until converge

  9. 1 7 8 2 3 5 10 -1 1 4 6 9 -1 1 Example • Let there be one 2-Dim clustering problem. • The vector space include 5 different clusters and each has 2 sample sets.

  10. RFjk= net22 1 Wi10 Wi02 Wi20 Wi11 -1 1 Wi12 Wi01 Wi22 Wi21 Wi00 -1 Solution Setup an 2X9 network Randomly assign weights Let R=2.0 η=1.0 代入第一個pattern[-0.9, -0.8] • net00=[(-0.9+0.2)2+(-0.8+0.8) 2]=0.49 • net01=[(-0.9-0.2) 2+(-0.8+0.4) 2]=1.37 • net02=[(-0.9+0.3) 2+(-0.8-0.6) 2]=2.32 • net10=[(-0.9+0.4) 2+(-0.8-0.6) 2]=1.71 • net11=[(-0.9+0.3) 2+(-0.8-0.2) 2]=1.36 • net12=[(-0.9+0.6) 2+(-0.8+0.2) 2]=0.45 • net20=[(-0.9+0.7) 2+(-0.8-0.2) 2]=1.04 • net21=[(-0.9-0.8) 2+(-0.8+0.6) 2]=2.93 • net22=[(-0.9+0.8) 2+(-0.8+0.6) 2]=0.05 【MIN】 Winning Node

  11. -0.17 1 Wi10 Wi02 Wi20 Wi11 -1 1 Wi12 Wi01 Wi22 Wi21 Wi00 -1 Solution (cont.) Update weight j*=2 k*=2 r00= RF00=0.243 RF01= r01= r02 = RF22= 1 r22= W00=η‧(X1-W00)‧ RF00 1.0 × （-0.9+0.2）×（0.243）=－0.17

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