A novel Kernel Clustering with Quasi-Monte Carlo Random Feature Map

Abstract

Conventional kernel clustering approaches are helpful in extracting the essential non-linear data structure, but the high computational complexity makes them unavailability to large data sets. To overcome this limitation, many attentions have been paid on Random Fourier feature (RFF) map based kernel clustering algorithms. However, as the RFF map cannot achieve sufficiently precise approximation to the kernel, the clustering performance of RFF map based kernel clustering algorithms are not superior enough. On the basis of the above issues, this paper puts forward a novel Quasi-Monte Carlo feature (QMCF) map based kernel fuzzy clustering method, which is named QMCF-FCM. In this method, low-rank random features are yielded and fuzzy c-means is executed by leveraging Quasi-Monte Carlo sequences in this feature space. Experiments on a synthetic data set show that the QMCF map achieves more accurate approximation to the kernel than the RFF map and the proposed method obtains better clustering results than RFF map based kernel clustering method.