Learning the optimal kernel for Fisher discriminant analysis via second order cone programming |
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Authors: | Reshma Khemchandani Jayadeva Suresh Chandra |
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Institution: | 1. Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India;2. IBM India Research Lab, Block-C, Institutional Area Vasant Kunj, New Delhi 110070, India |
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Abstract: | Kernel Fisher discriminant analysis (KFDA) is a popular classification technique which requires the user to predefine an appropriate kernel. Since the performance of KFDA depends on the choice of the kernel, the problem of kernel selection becomes very important. In this paper we treat the kernel selection problem as an optimization problem over the convex set of finitely many basic kernels, and formulate it as a second order cone programming (SOCP) problem. This formulation seems to be promising because the resulting SOCP can be efficiently solved by employing interior point methods. The efficacy of the optimal kernel, selected from a given convex set of basic kernels, is demonstrated on UCI machine learning benchmark datasets. |
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Keywords: | Fisher discriminant analysis Kernel methods Machine learning Kernel optimization Support vector machines Convex optimization Second order cone programming Semidefinite programming |
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