Learning with Permutably Homogeneous Multiple-Valued Multiple-Threshold Perceptrons |
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| Authors: | Ngom Alioune Reischer Corina Simovici Dan A. Stojmenović Ivan |
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| Affiliation: | (1) Computer Science Department, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, P7B 5E1, Canada;(2) Department of Mathematics and Computer Science, University of Quebec at Trois-Rivieres, Trois-Rivieres, Quebec, G9A 5H7, Canada;(3) Department of Mathematics and Computer Science, University of Massachusetts at Boston, Boston, Massachusetts 02125, USA;(4) Department of Computer Science, School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario, K1N 9B4, Canada |
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| Abstract: | The (n,k,s)-perceptrons partition the input space V  Rn into s+1 regions using s parallel hyperplanes. Their learning abilities are examined in this research paper. The previously studied homogeneous (n,k,k–1)-perceptron learning algorithm is generalized to the permutably homogeneous (n,k,s)-perceptron learning algorithm with guaranteed convergence property. We also introduce a high capacity learning method that learns any permutably homogeneously separable k-valued function given as input. |
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| Keywords: | learning multiple-valued multiple-threshold functions multilinear separability partial order set perceptrons |
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