CONVERGENCE THEOREMS FOR THE KOHONEN FEATURE MAPPING ALGORITHMS WITH VLRPS

The convergence of the Kohonen feature mapping algorithm with vanishin g learning rate parameters (VLRPs) is considered, which includes the s imple competitive learning algorithm as a special case. A few examples show that the learning fails to converge to ''global minima,'' in gen eral. Then, we present a novel approach which enables us to find out a new family of VLRPs such that the corresponding learning algorithm co nverges to the set of ''global minima'' with probability one. The new VLRPs is a generalization of the well-known rate parameters used in th e simulated annealing. A numerical example is also included to confirm our theoretical approach. We believe that this discovery is of import ance for a large class of learning algorithms in neural networks and s tatistics.