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

Perceptron capacity revisited: classification ability for correlated patterns