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From Separating to Proximal Plane Classifiers: A Review

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Clusters, Orders, and Trees: Methods and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 92))

Abstract

A review of parallel and proximal plane classifiers is proposed. We discuss separating plane classifier introduced in support vector machines and we describe different proposals to obtain two proximal planes representing the two classes in the binary classification case. In details, we deal with proximal SVM classification by means of a generalized eigenvalues problem. Furthermore, some regularization techniques are analyzed in order to solve the singularity of the matrices. For the same purpose, proximal support vector machine using local information is handled. In addition, a brief description of twin support vector machines and nonparallel plane proximal classifier is reported.

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Acknowledgements

Authors would like to thank Dr. Panos Pardalos for the fruitful discussions and advice. This work has been partially funded by Italian Flagship project Interomics and by the Italian Ministry of Education, University and Research grant PON_00619.

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Authors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, High Performance Computing and Networking Institute, National Research Council, Naples, Italy

    Maria Brigida Ferraro

  2. High Performance Computing and Networking Institute, National Research Council, Naples, Italy

    Mario Rosario Guarracino

Authors
  1. Maria Brigida Ferraro
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  2. Mario Rosario Guarracino
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Corresponding author

Correspondence to Maria Brigida Ferraro .

Editor information

Editors and Affiliations

  1. Department of Higher Mathematics, National Research University Higher School of Economics, Moscow, Russia

    Fuad Aleskerov

  2. Department of Operations, University of Groningen, Groningen, The Netherlands

    Boris Goldengorin

  3. Department of Industrial and Systems Eng, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

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Ferraro, M.B., Guarracino, M.R. (2014). From Separating to Proximal Plane Classifiers: A Review. In: Aleskerov, F., Goldengorin, B., Pardalos, P. (eds) Clusters, Orders, and Trees: Methods and Applications. Springer Optimization and Its Applications, vol 92. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0742-7_10

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