Fast Compressive Spectral Clustering

Compressive spectral clustering (CSC) efficiently leverages graph filter and random sampling techniques to speed up clustering process. However, we find that CSC algorithm suffers from two main problems: i) The direct use of the dichotomy and eigencount techniques for estimating laplacian matrix's k-th eigenvalue is expensive. ii) The computation of polynomial approximation repeats in each iteration for every cluster in the interpolation process, which occupies most of the computation time of CSC. To address these problems, we propose a new approach called FCSC for fast compressive spectral clustering. FCSC addresses the first problem by assuming that the eigenvalues approximately satisfy local uniform distribution, and addresses the second problem by recalculating the pairwise similarity between nodes with low-dimensional representation to reconstruct denoised laplacian matrix. The time complexity of reconstruction is linear with the number of non-zeros in laplacian matrix. As experimentally demonstrated on artificial and real-world datasets, our approach significantly reduces the computation time while preserving high clustering accuracy comparable to previous designs, verifying the effectiveness of FCSC.