Hubness-based Sampling Method for Nyström Spectral Clustering

Abstract

Nystrom method is widely used for spectral clustering to obtain low-rank approximations of a large matrix. Sampling is crucial to Nystrom method, since selecting the representative sample points that can reflect the data structure is important for obtaining good approximation results. To improve the performance of Nystrom based spectral clustering, in this paper, we propose a new sampling method by considering the hubness score of sample points. The data points with the high hubness scores, i.e., appearing frequently in the nearest neighbor lists of other data points, have high probabilities to be selected as the sample points. Taking advantage of the topological property of hubs (i.e., data points with high hubness score), the selected sampling points have close relationships with other data points, thus the proposed method is able to achieve scalable and accurate clustering results. We further design fast computation methods, i.e., local hubness approximated methods, to speed up the sampling process. Experimental results on both synthetic and real-world data sets show that the proposed method not only achieves good performance, but also outperforms other sampling methods for Nystrom based spectral clustering.