Solving Mahalanobis Ellipsoidal Learning Machine Via Second Order Cone Programming

In this paper, we propose a Second Order Cone Programming representable Mahalanobis Ellipsoidal Learning Machine (SOCP-MELM) for One Class Classification (OCC). We propose to utilize the covariance matrix and thus the Mahalanobis distance to replace the Euclidean distance in standard Support Vector Data Description (SVDD). Consequently, we modify and rewrite the SVDD as a standard SOCP problem and then solve it directly in its primal form via interior point methods in polynomial time. By introducing a specified uncertainty model and using the chebyshev inequality, we propose a robust form of SOCP-MELM. Finally, we validate the proposed method using real world benchmark datasets.