k-plane clustering

A finite new algorithm is proposed for clustering m given points in n-dimen sional 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 th e algorithm lies in a formulation that generates a plane in n-dimensional s pace 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 f rom the m(1) points. The algorithm was tested on the publicly available Wis consin Breast Prognosis Cancer database to generate well separated patient survival curves. In contrast, the k-mean algorithm did not generate such we ll-separated survival curves.