2012/02/14 by Nima Reyhani, Hideitsu Hino, Reyhani, Nima +3 · 1 citation
Computer Science · Engineering · Mathematics · #Face and Expression Recognition #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1202.3761
Kernel methods are successful approaches for different machine learning\nproblems. This success is mainly rooted in using feature maps and kernel\nmatrices. Some methods rely on the eigenvalues/eigenvectors of the kernel\nmatrix, while for other methods the spectral information can be used to\nestimate the excess risk. An important question remains on how close the sample\neigenvalues/eigenvectors are to the population values. In this paper, we\nimprove earlier results on concentration bounds for eigenvalues of general\nkernel matrices. For distance and inner product kernel functions, e.g. radial\nbasis functions, we provide new concentration bounds, which are characterized\nby the eigenvalues of the sample covariance matrix. Meanwhile, the obstacles\nfor sharper bounds are accounted for and partially addressed. As a case study,\nwe derive a concentration inequality for sample kernel target-alignment.\n