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

Yina Han

doi:10.1109/TNNLS.2017.2785329

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

2018-10-01

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DOI：10.1109/TNNLS.2017.2785329

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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 l(p)-norm MKL framework with tunable variable p(p >= 1) to support controlled intrinsic sparsity. Unfortunately, this 1-D vector l(p)-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 l(p)-MKL to the 2-D matrix (r, p) norms (1 <= r, p < infinity). 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 l(p)-MKL in various scenarios.

Keywords:

Generalization bound

matrix regularization

multiple kernel learning (MKL)

support vector machine (SVM)

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

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