Discrete Optimal Graph Clustering

Graph-based clustering is one of the major clustering methods. Most of it works in three separate steps: 1) similarity graph construction; 2) clustering label relaxing; and 3) label discretization with k-means (KM). Such common practice has three disadvantages: 1) the predefined similarity graph is often fixed and may not be optimal for the subsequent clustering; 2) the relaxing process of cluster labels may cause significant information loss; and 3) label discretization may deviate from the real clustering result since KM is sensitive to the initialization of cluster centroids. To tackle these problems, in this paper, we propose an effective discrete optimal graph clustering framework. A structured similarity graph that is theoretically optimal for clustering performance is adaptively learned with a guidance of reasonable rank constraints. Besides, to avoid the information loss, we explicitly enforce a discrete transformation on the intermediate continuous label, which derives a tractable optimization problem with a discrete solution. Furthermore, to compensate for the unreliability of the learned labels and enhance the clustering accuracy, we design an adaptive robust module that learns the prediction function for the unseen data based on the learned discrete cluster labels. Finally, an iterative optimization strategy guaranteed with convergence is developed to directly solve the clustering results. Extensive experiments conducted on both real and synthetic datasets demonstrate the superiority of our proposed methods compared with several state-of-the-art clustering approaches.

I. Introduction

Clustering is one of the fundamental techniques in machine learning. It has been widely applied to various research fields, such as gene expression [1], face analysis [2], image annotation [3], and recommendation [4], [5]. In past decades, many clustering approaches have been developed, such as -means (KM) [6], spectral clustering (SC) [7]–[11], spectral embedded clustering [12], and normalized cut [13].