Matrix-Regularized Multiple Kernel Learning via (r,p) Norms

This paper examines a matrix-regularized multiple kernel learning (MKL) technique based on a notion of (r,p) norms. For the problem of learning a linear combination in the support vector machine-based framework, model complexity is typically controlled using various regularization strategies on the combined kernel weights. Recent research has developed a generalized ℓp-norm MKL framework with tunable variable p(p≥1) to support controlled intrinsic sparsity. Unfortunately, this ``1-D'' vector ℓp-norm hardly exploits potentially useful information on how the base kernels ``interact.'' To allow for higher order kernel-pair relationships, we extend the ``1-D'' vector ℓp-MKL to the ``2-D'' matrix (r,p) norms (1 ≤ r,p∞). We develop a new formulation and an efficient optimization strategy for (r,p)-MKL with guaranteed convergence. A theoretical analysis and experiments on seven UCI data sets shed light on the superiority of (r,p)-MKL over ℓp-MKL in various scenarios.