QP Representable Mahalanobis Ellipsoidal Learning Machine for Imbalanced Data Classification

In this paper, we propose a convex quadratic programming represent able Minimum Mahalanobis Enclosing Ellipsoid (QP-MMEE) for generally imbalanced dataset classification. This algorithm is modified from the previously MMEE algorithm (see paper [X.K. Wei, Y.H. Li, Y. Feng, and G.B. Huang, "Minimum Mahalanobis enclosing ellipsoid machine for pattern classification, " In Proceeding of the 3th International Conference on Intelligent Computing (ICIC\´07), CCIS 2, 2007, pp.1176-1185.]) Following the idea of MMEE, this method also tries to seek a hyper-ellipsoid to enclose almost all examples from one class but excludes almost all examples from the other class at the same time. We formulate the MMEE method as a convex quadratic programming problem. To further enhance its performance, a robust version of QP-MMEE is also proposed. We validate the proposed method using real world UCI benchmark datasets.