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Kernel classification using a linear programming approach

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Abstract

A support vector machine (SVM) classifier corresponds in its most basic form to a quadratic programming problem. Various linear variations of support vector classification have been investigated such as minimizing the L1-norm of the weight-vector instead of the L2-norm. In this paper we introduce a classifier where we minimize the boundary (lower envelope) of the epigraph that is generated over a set of functions, which can be interpreted as a measure of distance or slack from the origin. The resulting classifier appears to provide a generalization performance similar to SVMs while displaying a more advantageous computational complexity. The discussed formulation can also be extended to allow for cases with imbalanced data.

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Acknowledgements

Theodore Trafalis work has been conducted at the National Research Institute University Higher School of Economics and has been supported by the RSF grant n. 14-41-00039.

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Authors and Affiliations

  1. School of Electrical and Computer Engineering, University of Oklahoma, 110 W. Boyd, Norman, OK, 73019, USA

    Alexander M. Malyscheff

  2. School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd, Norman, OK, 73019, USA

    Theodore B. Trafalis

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  1. Alexander M. Malyscheff
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  2. Theodore B. Trafalis
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Correspondence to Alexander M. Malyscheff.

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Malyscheff, A.M., Trafalis, T.B. Kernel classification using a linear programming approach. Ann Math Artif Intell 88, 39–51 (2020). https://doi.org/10.1007/s10472-019-09642-w

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  • DOI: https://doi.org/10.1007/s10472-019-09642-w

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