A Probabilistic Approach for Optimizing Spectral Clustering

Spectral clustering enjoys its success in both data clustering and semi-supervised learning. But, most spectral clustering algorithms cannot handle multi-class clustering problems directly. Additional strategies are needed to extend spectral clustering algorithms to multi-class clustering problems. Furthermore, most spectral clustering algorithms employ hard cluster membership, which is likely to be trapped by the local optimum. In this paper, we present a new spectral clustering algorithm, named "Soft Cut". It improves the normalized cut algorithm by introducing soft membership, and can be efficiently computed using a bound optimization algorithm. Our experiments with a variety of datasets have shown the promising performance of the proposed clustering algorithm.