Fast Spectral Clustering of Data with Sequential Matrix Compression

Spectral clustering has attracted much research interest in recent years since it can yield impressively good clustering results. Traditional spectral clustering algorithms first solve an eigenvalue decomposition problem to get the low-dimensional embedding of the data points, and then apply some heuristic methods such as k-means to get the desired clusters. However, eigenvalue decomposition is very time-consuming, making the overall complexity of spectral clustering very high, and thus preventing spectral clustering from being widely applied in large-scale problems. To tackle this problem, different from traditional algorithms, we propose a very fast and scalable spectral clustering algorithm called the sequential matrix compression (SMC) method. In this algorithm, we scale down the computational complexity of spectral clustering by sequentially reducing the dimension of the Laplacian matrix in the iteration steps with very little loss of accuracy. Experiments showed the feasibility and efficiency of the proposed algorithm.