k-Plane Clustering

  • Authors:
  • P. S. Bradley;O. L. Mangasarian

  • Affiliations:
  • Microsoft Research, Redmond, WA 98052, USA and Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA E-mail: bradley@microsoft.com, olvi@cs.wisc.ed ...;Microsoft Research, Redmond, WA 98052, USA and Computer Sciences Department, University of Wisconsin, Madison, WI 53706, USA E-mail: bradley@microsoft.com, olvi@cs.wisc.ed ...

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2000

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Abstract

A finite new algorithm is proposed for clustering m given points in n-dimensional real space into k clusters by generating k planes that constitute a local solution to the nonconvex problem of minimizing the sum of squares of the 2-norm distances between each point and a nearest plane. The key to the algorithm lies in a formulation that generates a plane in n-dimensional space that minimizes the sum of the squares of the 2-norm distances to each of m1 given points in the space. The plane is generated by an eigenvector corresponding to a smallest eigenvalue of an n × n simple matrix derived from the m1 points. The algorithm was tested on the publicly available Wisconsin Breast Prognosis Cancer database to generate well separated patient survival curves. In contrast, the k-mean algorithm did not generate such well-separated survival curves.