Fast Spectral Clustering via the Nyström Method

We propose and analyze a fast spectral clustering algorithm with computational complexity linear in the number of data points that is directly applicable to large-scale datasets. The algorithm combines two powerful techniques in machine learning: spectral clustering algorithms and Nyström methods commonly used to obtain good quality low rank approximations of large matrices. The proposed algorithm applies the Nyström approximation to the graph Laplacian to perform clustering. We provide theoretical analysis of the performance of the algorithm and show the error bound it achieves and we discuss the conditions under which the algorithm performance is comparable to spectral clustering with the original graph Laplacian. We also present empirical results.