Spectral and Semidefinite Relaxation of the CLUHSIC Algorithm

CLUHSIC is a recent clustering framework that unifies the geometric, spectral and statistical views of clustering. In this paper, we show that the recently proposed discriminative view of clustering, which includes the DIFFRAC and DisKmeans algorithms, can also be unified under the CLUHSIC framework. Moreover, CLUHSIC involves integer programming and one has to resort to heuristics such as iterative local optimization. In this paper, we propose two relaxations that are much more disciplined. The first one uses spectral techniques while the second one is based on semidefinite programming (SDP). Experimental results on a number of structured clustering tasks show that the proposed method significantly outperforms existing optimization methods for CLUHSIC. Moreover, it can also be used in semi-supervised classification. Experiments on real-world protein subcellular localization data sets clearly demonstrate the ability of CLUHSIC in incorporating structural and evolutionary information.