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Fast Spectral Clustering of Data Using Sequential Matrix Compression

  • Bo Chen
  • Bin Gao
  • Tie-Yan Liu
  • Yu-Fu Chen
  • Wei-Ying Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4212)

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.

Keywords

Iteration Step Spectral Cluster Stable Point Laplacian Matrix Spectral Cluster Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bo Chen
    • 1
  • Bin Gao
    • 2
  • Tie-Yan Liu
    • 3
  • Yu-Fu Chen
    • 1
  • Wei-Ying Ma
    • 3
  1. 1.Department of mathematicsGraduate School of Chinese Academic of ScienceBeijingP.R. China
  2. 2.LMAM, School of Mathematical SciencesPeking UniversityBeijingP.R. China
  3. 3.Microsoft Research AsiaBeijingP.R. China

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