article · Neural Computation · 2013

Multiple Spectral Kernel Learning and a Gaussian Complexity Computation

Cited by 2Abstract and details only

Abstract

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.

Cite this paper

APA 7

Reyhani, N. (2013). Multiple Spectral Kernel Learning and a Gaussian Complexity Computation. Neural Computation, 25(7), 1926–1951. https://doi.org/10.1162/neco_a_00457

MLA 9

Reyhani, Nima. “Multiple Spectral Kernel Learning and a Gaussian Complexity Computation.” Neural Computation, vol. 25, no. 7, 2013, pp. 1926–51, https://doi.org/10.1162/neco_a_00457.

Chicago

Reyhani, Nima. 2013. “Multiple Spectral Kernel Learning and a Gaussian Complexity Computation.” Neural Computation 25 (7): 1926–51. https://doi.org/10.1162/neco_a_00457.

Harvard

Reyhani, N. (2013) ‘Multiple Spectral Kernel Learning and a Gaussian Complexity Computation’, Neural Computation, 25(7), pp. 1926–1951. Available at: https://doi.org/10.1162/neco_a_00457.

BibTeX

@article{reyhani2013multiple,
  title = {{Multiple Spectral Kernel Learning and a Gaussian Complexity Computation}},
  author = {Reyhani, Nima},
  journal = {Neural Computation},
  volume = {25},
  number = {7},
  pages = {1926--1951},
  year = {2013},
  doi = {10.1162/neco_a_00457}
}

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