Chebyshev Accelerated Spectral Clustering

ABSTRACTSpectral clustering is widely used in modern data analysis. Spectral clustering methods speed up the computation and keep useful information by reducing dimensionality. Recently, graph signal filtering (GSF) has been introduced to further speed up the dimensionality reduction process by avoiding solving eigenvectors. In this work, we first prove that the non-ideal filter not only affects the accuracy of GSF, but also the calculation speed. Then we further propose a modified Kernel Polynomial Method (KPM) to help GSF set the filter properly and effectively. We combine the main steps of KPM and GSF, and propose a novel spectral clustering method: Chebyshev Accelerated Spectral Clustering (CASC). In CASC, we take advantages of the excellent properties of Chebyshev polynomials: Compared with other spectral clustering methods using GSF, CASC spends negligible time on estimating the eigenvalues, and achieves the same accuracy with less computation. The experiments on artificial and real-world data prove that CASC is accurate and fast.