6.3 Synaptic convergence to centroids: AvQ algorithms The stochastic unsupervised competitive learning law m;=S,V,I We want to show that at equilibrium m, =x, or E(m, ) =x As discussed in Chapter 4: S,lD (x) The linear stochastic competitive learning law x)X-m,:|+n The linear supervised competitive learning law m=r(xI(x[x-m, ]+n Dur ∑(x) 2003.11.192003.11.19 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  = − + = −