Convergence theorems for the kohonen feature mapping algorithms with VLRPs

✍ Scribed by J.F. Feng; B. Tirozzi

• Book ID: 104352906
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 1018 KB
• Volume: 33
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(96)00236-2

✦ Synopsis

The convergence of the Kohonen feature mapping algorithm with vanishing learning rate parameters (VLRPs) is considered, which includes the simple competitive learning algorithm as a special case. A few examples show that the learning fails to converge to "global minima," in general. Then, we present a novel approach which enables us to find out a new family of VLRPs such that the corresponding learning algorithm converges to the set of "global minima" with probability one. The new VLRPs is a generalization of the well-known rate parameters used in the simulated annealing. A numerical example is also included to confirm our theoretical approach. We believe that this discovery is of importance for a large class of learning algorithms in neural networks and statistics.