  Graph based clustering is one of the major clustering methods. Most of it
work in three separate steps: similarity graph construction, clustering label
relaxing and label discretization with k-means. 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. 3) label discretization may
deviate from the real clustering result since k-means is sensitive to the
initialization of cluster centroids. To tackle these problems, in this paper,
we propose an effective discrete optimal graph clustering (DOGC) framework. A
structured similarity graph that is theoretically optimal for clustering
performance is adaptively learned with a guidance of reasonable rank
constraint. Besides, to avoid the information loss, we explicitly enforce a
discrete transformation on the intermediate continuous label, which derives a
tractable optimization problem with discrete solution. Further, to compensate
the unreliability of the learned labels and enhance the clustering accuracy, we
design an adaptive robust module that learns 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.
