Chapter6Architectureand Eguilibria6.3 Synaptic convergence to centroids:AvQAlgorithmsUnsupervised CompetitiveLearning (UCL)mi(t+1)=mi(t)+c[x(t)-mi(t)]6-146-15mi(t+l)=mi(t)ifi+j(cidefines a slowly deceasing sequence of learning coefficientFor instance,ci =0.1 1-,for10,000samplesx(t)10,000Supervised CompetitiveLearning (SCL)6-16mi(t +1)= mi(t) + ciri(x(t)[x(t)-mi(t)][mi(t)+ci[x(t)-mi(t))ifxEDj6-17mi(t)-ci[x(t)-mi(t)lifx@D)2002.12.4
2002.12.4 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
Chapter6Architectureand Eguilibria6.3 Synaptic convergence to centroids:AvQAlgorithmsDifferential CompetitiveLearning (DCL)mi(t+1)=mi(t)+ciAS(y(t)[x(t)-mi(t)) 6-186-19mi(t+l)=mi(t)ifi±jAS(y,(t+ 1) denotes the time change of the jth neuron's competitivesignal .In practice we only use the sign of (6-20)AS(y,(t+1)=S(y(t+1)-S(y(t))6-20Stochastic Equilibrium and ConvergenceCompetitive synaptic vector coverge to decsion-class centrolsMay coverge to locally mixima2002.12.4
2002.12.4 Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algorithms Differential Competitive Learning (DCL) ( 1) ( ) 6 19 ( 1) ( ) ( ( ))[ ( ) ( )] 6 18 + = − + = + − − m t m t if i j m t m t c S y t x t m t i i j j t j j j S (y (t +1)) j j denotes the time change of the jth neuron’s competitive signal . In practice we only use the sign of (6-20) Sj(yj (t +1)) = Sj(yj(t +1)) − Sj(yj(t)) 6− 20 Stochastic Equilibrium and Convergence Competitive synaptic vector coverge to decsion-class centrols. May coverge to locally mixima