?p-norm multiple kernel learning with low-rank kernels
Kernel-based learning algorithms are well-known to poorly scale to large-scale applications. For such large tasks, a common solution is to use low-rank kernel approximation. Several algorithms and theoretical analyses have already been proposed in the literature, for low-rank Support Vector Machine or low-rank Kernel Ridge Regression but not for multiple kernel learning. The proposed method bridges this gap by addressing the problem of scaling ?p-norm ? p - norm multiple kernel for large learning tasks using low-rank kernel approximations. Our contributions stand on proposing a novel optimization problem, which takes advantage of the low-rank kernel approximations and on introducing a proximal gradient algorithm for solving that optimization problem. We also provide partial theoretical results on the impact of the low-rank approximations over the kernel combination weights. Experimental evidences show that the proposed approach scales better than the SMO-MKL algorithm for tasks involving about several hundred thousands of examples. Experimental comparisons with interior point methods also prove the efficiency of the algorithm we propose.
multiple kernel learning kernels low-rank approximation svm