k -means projective clustering

In many applications it is desirable to cluster high dimensional data along various subspaces, which we refer to as projective clustering. We propose a new objective function for projective clustering, taking into account the inherent trade-off between the dimension of a subspace and the induced clustering error. We then present an extension of the k-means clustering algorithm for projective clustering in arbitrary subspaces, and also propose techniques to avoid local minima. Unlike previous algorithms, ours can choose the dimension of each cluster independently and automatically. Furthermore, experimental results show that our algorithm is significantly more accurate than the previous approaches.