A Self-Balanced Min-Cut Algorithm for Image Clustering

Many spectral clustering algorithms have been proposed and successfully applied to image data analysis such as content based image retrieval, image annotation, and image indexing. Conventional spectral clustering algorithms usually involve a two-stage process: eigendecomposition of similarity matrix and clustering assignments from eigenvectors by k-means or spectral rotation. However, the final clustering assignments obtained by the two-stage process may deviate from the assignments by directly optimize the original objective function. Moreover, most of these methods usually have very high computational complexities. In this paper, we propose a new min-cut algorithm for image clustering, which scales linearly to the data size. In the new method, a self-balanced min-cut model is proposed in which the Exclusive Lasso is implicitly introduced as a balance regularizer in order to produce balanced partition. We propose an iterative algorithm to solve the new model, which has a time complexity of O(n) where n is the number of samples. Theoretical analysis reveals that the new method can simultaneously minimize the graph cut and balance the partition across all clusters. A series of experiments were conducted on both synthetic and benchmark data sets and the experimental results show the superior performance of the new method.