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Nonnegative Lagrangian Relaxation of K-Means and Spectral Clustering

  • Chris Ding
  • Xiaofeng He
  • Horst D. Simon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3720)

Abstract

We show that K-means and spectral clustering objective functions can be written as a trace of quadratic forms. Instead of relaxation by eigenvectors, we propose a novel relaxation maintaining the nonnegativity of the cluster indicators and thus give the cluster posterior probabilities, therefore resolving cluster assignment difficulty in spectral relaxation. We derive a multiplicative updating algorithm to solve the nonnegative relaxation problem. The method is briefly extended to semi-supervised classification and semi-supervised clustering.

Keywords

Bipartite Graph Spectral Cluster Nonnegative Matrix Factorization Spectral Relaxation Simultaneous Cluster 
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 2005

Authors and Affiliations

  • Chris Ding
    • 1
  • Xiaofeng He
    • 1
  • Horst D. Simon
    • 1
  1. 1.Lawrence Berkeley National LaboratoryBerkeleyUSA.

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