Robust optimal graph clustering

Most graph-based clustering methods separate the graph construction and clustering into two independent processes. The manually pre-constructed graph may not be suitable for the subsequent clustering. Moreover, as real world data generally contains noises and outliers, the similarity graph directly learned from them will be unreliable and further impair the subsequent clustering performance. To tackle the problems, in this paper, we propose a novel clustering framework where a robust graph is learned with noise removal, and simultaneously, with desirable clustering structure. To this end, we first learn a discriminative representation of data samples via sparse reconstruction. Then, a robust graph is automatically constructed with adaptive neighbors to each data sample. Simultaneously, a reasonable rank constraint is imposed on the Laplacian matrix of similarity graph to pursue the ideal clustering structure, where the number of connected components in the learned graph is exactly equal to the number of clusters. We finally derive an alternate optimization algorithm guaranteed with convergence to solve the formulated unified learning framework to achieve better prediction accuracy. Experiments on both synthetic and real datasets demonstrate the superior performance of the proposed method compared with several state-of-the-art clustering techniques.