Self-organization of the batch Kohonen network under quantization effects

Abstract

In this work, we investigate the effect of quantized weights and inputs on the self-organizing properties of the batch variant of Kohonen's self-organizing map algorithm. In particular, we examine necessary and sufficient conditions that ensure self-organization of the batch SOM algorithm for one-dimensional (1D) networks mapping a quantized 1D input space. Using Markov chain formalism, it is shown that the existing analysis for the original algorithm can be extended to also include the more general batch variant. Finally, simulations verify the theoretical results, relate the speed of weight ordering to the distribution of the inputs, extend the results to the 2D case, and show the existence of metastable states of the Markov chain.

Keywords:

• self-organizing maps
• batch SOM algorithm
• Markov chains
• quantization effects
• discrete SOM weights

2010 AMS Subject Classifications :

• 60J10
• 60J20

ACM Computing Classification System :

• C.1.3
• I.1.3
• I.2.6