Neural Comput - Multiple spectral kernel learning and a gaussian complexity computation.

Tópicos

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Resumo

Multiple kernel learning (MKL) partially solves the kernel selection problem in support vector machines and similar classifiers by minimizing the empirical risk over a subset of the linear combination of given kernel matrices. For large sample sets, the size of the kernel matrices becomes a numerical issue. In many cases, the kernel matrix is of low-efficient rank. However, the low-rank property is not efficiently utilized in MKL algorithms. Here, we suggest multiple spectral kernel learning that efficiently uses the low-rank property by finding a kernel matrix from a set of Gram matrices of a few eigenvectors from all given kernel matrices, called a spectral kernel set. We provide a new bound for the gaussian complexity of the proposed kernel set, which depends on both the geometry of the kernel set and the number of Gram matrices. This characterization of the complexity implies that in an MKL setting, adding more kernels may not monotonically increase the complexity, while previous bounds show otherwise.

Resumo Limpo

multipl kernel learn mkl partial solv kernel select problem support vector machin similar classifi minim empir risk subset linear combin given kernel matric larg sampl set size kernel matric becom numer issu mani case kernel matrix loweffici rank howev lowrank properti effici util mkl algorithm suggest multipl spectral kernel learn effici use lowrank properti find kernel matrix set gram matric eigenvector given kernel matric call spectral kernel set provid new bound gaussian complex propos kernel set depend geometri kernel set number gram matric character complex impli mkl set ad kernel may monoton increas complex previous bound show otherwis

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