On clusterings: Good, bad and spectral

  • Authors:
  • Ravi Kannan;Santosh Vempala;Adrian Vetta

  • Affiliations:
  • Yale University, New Haven, Connecticut, CT;M.I.T., Cambridge, Massachusetts, MA;M.I.T., Cambridge, Massachusetts, MA

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2004

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Abstract

We motivate and develop a natural bicriteria measure for assessing the quality of a clustering that avoids the drawbacks of existing measures. A simple recursive heuristic is shown to have poly-logarithmic worst-case guarantees under the new measure. The main result of the article is the analysis of a popular spectral algorithm. One variant of spectral clustering turns out to have effective worst-case guarantees; another finds a "good" clustering, if one exists.