Journal
JOURNAL OF GLOBAL OPTIMIZATION
Volume 16, Issue 1, Pages 23-32Publisher
KLUWER ACADEMIC PUBL
DOI: 10.1023/A:1008324625522
Keywords
clustering; k-mean; linear regression
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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 m(1) given points in the space. The plane is generated by an eigenvector corresponding to a smallest eigenvalue of an n x n simple matrix derived from the m(1) 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.
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