First passage time analysis of topologically correct feature maps in discrete Kohonen networks

In this paper we consider Kohonen networks with quantized weights and analyze the influence of temporal correlation of input patterns on the time required to configure topologically correct feature maps. We formulate the configuration time as the first passage time to an absorbing state, which represents all topologically correct feature maps. Based on the Markov chain formulation, we derive the mean, the variance and the probability distribution of the configuration time. From numerical results it turned out that the positive correlation of input sequence tends to slow down the configuration time.