Robust Structured Graph Clustering

Graph-based clustering methods have achieved remarkable performance by partitioning the data samples into disjoint groups with the similarity graph that characterizes the sample relations. Nevertheless, their learning scheme still suffers from two important problems: 1) the similarity graph directly constructed from the raw features may be unreliable as real-world data always involves adverse noises, outliers, and irrelevant information and 2) most graph-based clustering methods adopt two-step learning strategy that separates the similarity graph construction and clustering into two independent processes. Under such circumstance, the generated graph is unstructured and fixed. It may suffer from a low-quality clustering structure and thus lead to suboptimal clustering performance. To alleviate these limitations, in this article we propose a robust structured graph clustering (RSGC) model. We formulate a novel learning framework to simultaneously learn a robust structured similarity graph and perform clustering. Specifically, the structured graph with proper probabilistic neighborhood assignment is adaptively learned on a robust latent representation that resists the noises and outliers. Furthermore, an explicit rank constraint is imposed on the Laplacian matrix to structurize the graph such that the number of the connected components is exactly equal to the ground-truth cluster number. To solve the challenging objective formulation, we propose to first transform it into an equivalent one that can be tackled more easily. An iterative solution based on the augmented Lagrangian multiplier is then derived to solve the model. In RSGC, the discrete cluster labels can be directly obtained by partitioning the learned similarity graph without reliance on label discretization strategy as most graph-based clustering methods. Experiments on both synthetic and real data sets demonstrate the superiority of the proposed method compared with the state-of-the-art clustering techniques.

I. Introduction

Clustering divides the samples into disjoint groups such that the samples within the same group are highly similar to each other. As an unsupervised learning task, it has been widely applied in the research fields of machine learning, data mining, and computer vision [1]–[3]. For its important role, various clustering methods have been brought forward over the past decades, such as -means [4], support vector clustering [5], hierarchical clustering [6], multiview clustering [3], [7], and maximum margin clustering [8].