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Cluster Structure of K-means Clustering via Principal Component Analysis

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Advances in Knowledge Discovery and Data Mining (PAKDD 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3056))

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Abstract

K-means clustering is a popular data clustering algorithm. Principal component analysis (PCA) is a widely used statistical technique for dimension reduction. Here we prove that principal components are the continuous solutions to the discrete cluster membership indicators for K-means clustering, with a clear simplex cluster structure. Our results prove that PCA-based dimension reductions are particularly effective for K-means clustering. New lower bounds for K-means objective function are derived, which is the total variance minus the eigenvalues of the data covariance matrix.

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References

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Author information

Authors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, US

    Chris Ding & Xiaofeng He

Authors
  1. Chris Ding
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  2. Xiaofeng He
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Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, Deakin University, VIC 3125, Australia

    Honghua Dai

  2. University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    Ramakrishnan Srikant

  3. Faculty of Engineering and Information Technology, Centre for Quantum Computation and Intelligent Systems, and Australian ACS National Committee for Artificial Intelligence, University of Technology, Sydney, Australia

    Chengqi Zhang

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© 2004 Springer-Verlag Berlin Heidelberg

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Ding, C., He, X. (2004). Cluster Structure of K-means Clustering via Principal Component Analysis. In: Dai, H., Srikant, R., Zhang, C. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2004. Lecture Notes in Computer Science(), vol 3056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24775-3_50

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  • DOI: https://doi.org/10.1007/978-3-540-24775-3_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22064-0

  • Online ISBN: 978-3-540-24775-3

  • eBook Packages: Springer Book Archive

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