Multi-class Discriminant Kernel Learning via Convex Programming

Regularized kernel discriminant analysis (RKDA) performs linear discriminant analysis in the feature space via the kernel trick. Its performance depends on the selection of kernels. In this paper, we consider the problem of multiple kernel learning (MKL) for RKDA, in which the optimal kernel matrix is obtained as a linear combination of pre-specified kernel matrices. We show that the kernel learning problem in RKDA can be formulated as convex programs. First, we show that this problem can be formulated as a semidefinite program (SDP). Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a convex quadratically constrained quadratic programming (QCQP) formulation for kernel learning in RKDA. A semi-infinite linear programming (SILP) formulation is derived to further improve the efficiency. We extend these formulations to the multi-class case based on a key result established in this paper. That is, the multi-class RKDA kernel ...

• Type: Journal
• Year: 2008
• Where: JMLR
• Authors: Jieping Ye, Shuiwang Ji, Jianhui Chen
• Keywords: Discriminant Analysis, JMLR 2008, Kernel Discriminant Analysis, Optimal Kernel Matrix