6.3 Synaptic convergence to centroids:AVQ Algorithms The Stochastic unsupervised competitive learning law: m;=S,y儿x-m,]+nj We want to show that at equilibrium m=x or E(m)=x As discussed in Chapter 4:S (x) The linear stochastic competitive learning law: m,=1o,(xx-m,]+n) The linear supervised competitive learning law: ri,=r(x)Ip (x)[x-mjl+n ,(x)=1p,(x)-∑1(x) 2003.11.19 82003.11.19 8 6.3 Synaptic convergence to centroids: AVQ Algorithms The Stochastic unsupervised competitive learning law: ( )[ ] m S y x m n j j j j j = − + We want to show that at equilibrium or E( ) m x m x j j j j = = ( ) j j D As discussed in Chapter 4: S I x  The linear stochastic competitive learning law: ( )[ ] j j D j j m = − + I x x m n The linear supervised competitive learning law: ( )[ ] ( ) ( ) ( ) ( ) j j i j j D j j j D D i j r I x x m n r I x I x m x x  = − + = −