Clusterability Analysis and Incremental Sampling for Nyström Extension Based Spectral Clustering

To alleviate the memory and computational burdens of spectral clustering for large scale problems, some kind of low-rank matrix approximation is usually employed. Nyström method is an efficient technique to generate low rank matrix approximation and its most important aspect is sampling. The matrix approximation errors of several sampling schemes have been theoretically analyzed for a number of learning tasks. However, the impact of matrix approximation error on the clustering performance of spectral clustering has not been studied. In this paper, we firstly analyze the performance of Nyström method in terms of cluster ability, thus answer the impact of matrix approximation error on the clustering performance of spectral clustering. Our analysis immediately suggests an incremental sampling scheme for the Nyström method based spectral clustering. Experimental results show that the proposed incremental sampling scheme outperforms existing sampling schemes on various clustering tasks and image segmentation applications, and its efficiency is comparable with existing sampling schemes.