Spectral relaxation for k-rneans clustering

  • Hongyuan Zha
  • , Xiaofeng He
  • , Chris Ding
  • , Horst Simon
  • , Ming Gu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

114 Scopus citations

Abstract

The popular K-rneans clustering partitions a data set by minimizing a surn-of-squares cost function. A coordinate descend method is then used to find local minima. In this paper we show that the minimization can be reformulated as a trace maximization problem associated with the Gram matrix of the data vectors. Furthermore, we show that a relaxed version of the trace maximization problem possesses global optimal solutions which can be obtained by computing a partial eigendecomposition of the Gram matrix, and the cluster assignment for each data vectors can be found by computing a pivoted QR decomposition of the eigenvector matrix. As a by-product we also derive a lower bound for the minimum of the surn-of-squares cost function.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 14 - Proceedings of the 2001 Conference, NIPS 2001
PublisherNeural information processing systems foundation
ISBN (Print)0262042088, 9780262042086
StatePublished - 2002
Externally publishedYes
Event15th Annual Neural Information Processing Systems Conference, NIPS 2001 - Vancouver, BC, Canada
Duration: 3 Dec 20018 Dec 2001

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258

Conference

Conference15th Annual Neural Information Processing Systems Conference, NIPS 2001
Country/TerritoryCanada
CityVancouver, BC
Period3/12/018/12/01

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