Francis Bach, Michael Jordan
Spectral clustering refers to a class of techniques which rely on the eigen- structure of a similarity matrix to partition points into disjoint clusters with points in the same cluster having high similarity and points in dif- ferent clusters having low similarity. In this paper, we derive a new cost function for spectral clustering based on a measure of error between a given partition and a solution of the spectral relaxation of a minimum normalized cut problem. Minimizing this cost function with respect to the partition leads to a new spectral clustering algorithm. Minimizing with respect to the similarity matrix leads to an algorithm for learning the similarity matrix. We develop a tractable approximation of our cost function that is based on the power method of computing eigenvectors.