document: Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming The kernel function plays a central role in kernel methods . In this paper , we consider the automated learning of the kernel matrix over a convex combination of pre-specified kernel matrices in Regularized Kernel Discriminant Analysis ( RKDA ) , which performs lineardiscriminant analysis in the feature space via the kernel trick . Previous studies have shown that this kernel learning problem can be formulated as a semidefinite program ( SDP ) , which is however computationally expensive , even with the recent advances in interior point methods . Based on the equivalence relationship between RKDA and least square problems in the binary-class case , we propose a Quadratically Constrained Quadratic Programming ( QCQP ) formulation for the kernel learning problem , which can be solved more efficiently than SDP . While most existing work on kernel learning deal with binary-class problems only , we show that our QCQP formulation can be extended naturally to the multi-class case . Experimental results on both binary-class and multi-class benchmarkdata sets show the efficacy of the proposed QCQP formulations .
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