document: Learning subspace kernels for classification Kernel methods have been applied successfully in many data mining tasks . Subspace kernel learning was recently proposed to discover an effective low-dimensional subspace of a kernel feature space for improved classification . In this paper , we propose to construct a subspace kernel using the Hilbert-Schmidt Independence Criterion ( HSIC ) . We show that the optimal subspace kernel can be obtained efficiently by solving an eigenvalue problem . One limitation of the existing subspace kernel learning formulations is that the kernel learning and classification are independent and the subspace kernel may not be optimally adapted for classification . To overcome this limitation , we propose a joint optimization framework , in which we learn the subspace kernel and subsequent classifiers simultaneously . In addition , we propose a novel learning formulation that extracts an uncorrelated subspace kernel to reduce the redundant information in a subspace kernel . Following the idea from multiple kernel learning , we extend the proposed formulations to the case when multiple kernels are available and need to be combined . We show that the integration of subspace kernels can be formulated as a semidefinite program ( SDP ) which is computationally expensive . To improve the efficiency of the SDP formulation , we propose an equivalent semi-infinite linear program ( SILP ) formulation which can be solved efficiently by the column generation technique . Experimental results on a collection of benchmark data sets demonstrate the effectiveness of the proposed algorithms .
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