Nystrom Method for Approximating the GMM Kernel

Abstract: The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted to the (generalized) consistent weighted sampling (GCWS) to convert the GMM kernel to linear kernel. We call this approach as GMM-GCWS''. In the machine learning literature, there is a popular algorithm which we callRBF-RFF''. That is, one can use the random Fourier features'' (RFF) to convert theradial basis function'' (RBF) kernel to linear kernel. It was empirically shown in (Li, 2016) that RBF-RFF typically requires substantially more samples than GMM-GCWS in order to achieve comparable accuracies. The Nystrom method is a general tool for computing nonlinear kernels, which again converts nonlinear kernels into linear kernels. We apply the Nystrom method for approximating the GMM kernel, a strategy which we name as ``GMM-NYS''. In this study, our extensive experiments on a set of fairly large datasets confirm that GMM-NYS is also a strong competitor of RBF-RFF.