Perceptron capacity revisited: classification ability for correlated patterns

Takashi Shinzato; Yoshiyuki Kabashima

doi:10.1088/1751-8113/41/32/324013

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arXiv · 0712.4050

Perceptron capacity revisited: classification ability for correlated patterns

Takashi Shinzato·Yoshiyuki Kabashima

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Abstract

In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes are developed based on the replica method and Thouless-Anderson-Palmer (TAP) approach by utilizing an integral formula concerning random rectangular matrices. The validity and relevance of the developed methodologies are shown for one known result and two example problems. A message-passing algorithm to perform the TAP scheme is also presented.

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Takashi Shinzato, Yoshiyuki Kabashima. 2007-12-25. Perceptron capacity revisited: classification ability for correlated patterns. https://doi.org/10.1088/1751-8113/41/32/324013

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