Journal of Global Optimization

, Volume 16, Issue 1, pp 23–32 | Cite as

k-Plane Clustering

  • P.S. Bradley
  • O.L. Mangasarian


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.

Clustering k-Mean Linear regression 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • P.S. Bradley
    • 1
    • 2
  • O.L. Mangasarian
    • 1
    • 2
  1. 1.Microsoft ResearchRedmondUSA
  2. 2.Computer Sciences DepartmentUniversity of WisconsinMadisonUSA

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