Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algor ithms AVQ centroid theorem: if a competitive AVQ system converges,it converge to the centroid of the sampled decision class. Prob(mij=xj)=1 at equilibrium 6-21 Proof.Suppose the jth neuronin Fy wins the actitve competition. Suppose the jth synaptic vector mi codesfor decisionclass Di Suppose the synaptic vector has reachedequilibrium mj=0 6-22 2004.11.10 142004.11.10 14 Chapter 6 Architecture and Equilibria 6.3 Synaptic convergence to centroids:AVQ Algorithms AVQ centroid theorem: if a competitive AVQ system converges,it converge to the centroid of the sampled decision class. ) 1 6 21 ^ Prob(mj = x j = at equilibrium − Proof. Suppose the jth neuron in Fy wins the actitve competition. Suppose the jth synaptic vector codes for decision class mj Dj = 0 6 − 22 • m j Suppose the synaptic vector has reached equilibrium