Algorithms based on spectral graph cut objectives such as normalized cuts, ratio cuts and ratio association have become popular in recent years because they are widely applicable and simple to implement via standard eigenvector computations. Despite strong performance for a number of clustering tasks, spectral graph cut algorithms still suffer from several limitations: first, they require the number of clusters to be known in advance, but this information is often unknown a priori; second, they tend to produce clusters with uniform sizes. In some cases, the true clusters exhibit a known size distribution; in image segmentation, for instance, human-segmented images tend to yield segment sizes that follow a power-law distribution. In this paper, we propose a general framework of power-law graph cut algorithms that produce clusters whose sizes are power-law distributed, and also does not fix the number of clusters upfront. To achieve our goals, we treat the Pitman-Yor exchangeable partition probability function (EPPF) as a regularizer to graph cut objectives. Because the resulting objectives cannot be solved by relaxing via eigenvectors, we derive a simple iterative algorithm to locally optimize the objectives. Moreover, we show that our proposed algorithm can be viewed as performing MAP inference on a particular Pitman-Yor mixture model. Our experiments on various data sets show the effectiveness of our algorithms.

Spectral clustering enjoys its success in both data clustering and semisupervised 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.

Spectral clustering enjoys its success in both data clustering and semisupervised 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.

Spectral clustering enjoys its success in both data clustering and semisupervised 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. Inthis paper, we present a new spectral clustering algorithm, named "Soft Cut". It improves the normalized cut algorithm by introducing softmembership, 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.