Advances and Applications in Discrete Mathematics
Volume 18, Issue 1, Pages 107 - 115
(January 2017) http://dx.doi.org/10.17654/AADMJan2017_107_115 |
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LINEAR-INTEGER SEPARATION OF BINARY PATTERNS BY LINEAR PROGRAMMING
José Luis MartÃnez Flores and Damián Gibaja
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Abstract: Pattern separation is a problem in which a condition is sought to distinguish between the elements of two disjoint sets of patterns that are usually represented as points in . The literature shows the importance of pattern separation in various applications, one example being that of artificial neural networks, where conditions under which two sets of patterns are linearly separable are desired. In addition, to previous work, the linear separability of patterns using linear programming has been characterized. This paper makes two important contributions. The first is a necessary and sufficient condition for linear-integer separation of n-dimensional binary patterns using linear programming. The second is the identification of a class of linear programming problems whose constraint matrix is not totally unimodular but nevertheless yield integer solutions. |
Keywords and phrases: pattern, separation, classification, neural networks. |
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