Batch self-organizing map algorithm: A theoretical study of self-organization of a 1-D network under quantization effects

In this paper, we examine necessary and sufficient conditions that ensure self-organization of the batch variant of the self-organizing map algorithm for 1-D networks and for quantized weights and inputs. 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 and show the existence of metastable states of the Markov chain.