%A P. S. Bradley & O. L. mangasarian
%T k-Plane Clustering
%D August 1998
%R 98-08
%I COMPUTER SCIENCES DEPARTMENT, UNIVERSITY OF WISCONSIN
%C MADISON, WI
%X
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 $n\times n$
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.