Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Al gor i thms Competitive AVQ Algorithms 1.Initialize synaptic vectors: m,(0)=x(),i=1,,m 2.For random sample x()find the closet(winning)synaptic vector m,(t) m,()-x(t)=minm,()-x()儿6-13 where x2=x2+..+x品 3.Update the wining synaptic vectors m()by the UCL,SCL,or DCL learning algorithm. 2004.11.10 11
2004.11.10 11 Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algorithms Competitive AVQ Algorithms 1. Initialize synaptic vectors: mi (0) = x(i) , i =1,......,m 2.For random sample ,find the closet(“winning”)synaptic vector x(t) m (t) j 2 2 1 2 ....... ( ) ( ) min ( ) ( ) 6 13 m i i j where x x x m t x t m t x t = + + − = − − 3.Update the wining synaptic vectors by the UCL ,SCL,or DCL learning algorithm. m (t) j
Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algor ithms Unsupervised Competitive Learning (UCL) m(t+1)=m(t)+ci[x(t)-m(t)] 6-14 mi(t+l)=mi(t)fi≠j 6-15 fedefines a slowly deceasing sequence of learning coefficient For mstanee100 for 10,000 samples x(t) Supervised Competitive Learning (SCL) mi(t+1)=mi(t)+ciri(x(t))x(t)-mi(t) 6-16 mi(t)+cilx(t)-mi(t)]if xEDj 6-17 mi(t)-cilx(t)-mi(t)]ifx Di 2004.11.10 12
2004.11.10 12 Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algorithms Unsupervised Competitive Learning (UCL) ( 1) ( ) 6 15 ( 1) ( ) [ ( ) ( )] 6 14 + = − + = + − − m t m t if i j m t m t c x t m t i i j j i j {ci} defines a slowly deceasing sequence of learning coefficient for 10,000 samples ( ) 10,000 For instance , 0.1 1 x t t ci = − Supervised Competitive Learning (SCL) 6 17 ( ) [ ( ) ( )] ( ) [ ( ) ( )] ( 1) ( ) ( ( )) ( ) ( ) 6 16 − − − + − = + = + − − m t c x t m t if x Dj m t c x t m t if x Dj m t m t c r x t x t m t j i j j i j j j i j j