Abstract
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.
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Wei, X., Li, Y., Feng, Y., Huang, G. (2007). Solving Mahalanobis Ellipsoidal Learning Machine Via Second Order Cone Programming. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques. ICIC 2007. Communications in Computer and Information Science, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74282-1_133
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DOI: https://doi.org/10.1007/978-3-540-74282-1_133
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74281-4
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