Advances and Applications in Statistics
Volume 46, Issue 1, Pages 37 - 55
(July 2015) http://dx.doi.org/10.17654/ADASJul2015_037_055 |
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GEOMETRIC ERGODICITY OF THE NORMALIZED PERCEPTRON ALGORITHM FOR THE CLASSIFICATION OF NON-SEPARABLE GAUSSIAN INPUT VECTORS
Rieken S. Venema
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Abstract: In this paper, we study the asymptotic behavior of the normalized weight sequence of a single-layer perceptron. If the perceptron is used for the classification of two infinite populations that cannot be linearly separated, then the weights do not converge but under certain conditions approach a steady state. Assuming that the input vectors are two-dimensional and normally distributed, we will show that the normalized perceptron weight process is geometrically ergodic. |
Keywords and phrases: single-layer perceptron, non-separable classifications, normalized perceptron algorithm, Markov chains, geometrically ergodic. |
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