Fast spectral clustering of data using sequential matrix compression

Authors:
Bo Chen;Bin Gao;Tie-Yan Liu;Yu-Fu Chen;Wei-Ying Ma
Affiliations:
Department of mathematics, Graduate School of Chinese Academic of Science, Beijing, P.R. China;LMAM, School of Mathematical Sciences, Peking University, Beijing, P.R. China;Microsoft Research Asia, Beijing, P.R. China;Department of mathematics, Graduate School of Chinese Academic of Science, Beijing, P.R. China;Microsoft Research Asia, Beijing, P.R. China
Venue:
ECML'06 Proceedings of the 17th European conference on Machine Learning
Year:
2006

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Abstract

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.