Clustering by Maximizing Sum-of-Squared Separation Distance

Maximizing the separating margin is crucial for the good generalization performance of Support Vector Machines (SVMs). Analogous to the definition of separation distance or separating margin in SVMs, we propose a definition on separation distance in clustering tasks when a hyperplane is used to separate clusters. For given training data and a given metric distance, by maximizing the proposed separation distance, our clustering algorithm constructs an “optimal” hyperplane that can be applied to unseen data in the future. The resulting hyperplane corresponds to a nonlinear decision boundary in the input feature space through an appropriate distance feature mapping. A graph-theoretic perspective of the proposed method is discussed. In particular, we show that, under certain conditions, the proposed clustering algorithm is equivalent to a spectral relaxed graph cut. Extensive experimental results are provided to validate the method.