Twin Mahalanobis distance-based support vector machines for pattern recognition

Authors:
Xinjun Peng;Dong Xu
Affiliations:
Department of Mathematics, Shanghai Normal University, 200234, PR China and Scientific Computing Key Laboratory of Shanghai Universities, 200234, PR China;Department of Mathematics, Shanghai Normal University, 200234, PR China and Scientific Computing Key Laboratory of Shanghai Universities, 200234, PR China
Venue:
Information Sciences: an International Journal
Year:
2012

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Abstract

Twin support vector machines (TSVMs) achieve fast training speed and good performance for data classification. However, TSVMs do not take full advantage of the statistical information in data, such as the covariance of each class of data. This paper proposes a new twin Mahalanobis distance-based support vector machine (TMSVM) classifier, in which two Mahalanobis distance-based kernels are constructed according to the covariance matrices of two classes of data for optimizing the nonparallel hyperplanes. TMSVMs have a special case of TSVMs when the covariance matrices in a reproducing kernel Hilbert space are degenerated to the identity ones. TMSVMs are suitable for many real problems, especially for the case that the covariance matrices of two classes of data are obviously different. The experimental results on several artificial and benchmark datasets indicate that TMSVMs not only possess fast learning speed, but also obtain better generalization than TSVMs and other methods.