Adaptive Spectral Rotation via Joint Cluster and Pairwise Structure

Density structure and pairwise structure serve as two different but complementary perspectives for clustering. Either side of road is frequently visited and explored by multiple clustering methods. However, there are seldom approaches, which could mutually exploit both structures for clustering. To address this problem, in this paper, we develop a novel adaptive joint clustering algorithm, which combines unsupervised discrete orthogonal least squares discriminant analysis (DOLSDA) and discrete spectral clustering (DSC) with adaptive neighbors and side information into a unified model. First, we extend supervised OLSDA to a discrete kernel clustering problem. To further achieve a clear pairwise structure, a new similarity with adaptive neighbors is then derived to establish sparse Laplacian matrix. In addition, side information could be incorporated to formulate clearer graph by modifying the proposed similarity. Based on the constructed graph, DSC is embedded with the discrete kernel OLSDA (DKOLSDA) clustering to exploit both cluster and pairwise data structures. Equipped with the proposed framework regarding quadratic weighted optimization, adaptive weight can be obtained automatically to leverage both unsupervised DKOLSDA and DSC. Since the unified problem is still discrete, we develop an increment scheme to achieve the optimal spectral rotation for the approximate solution to the predicted indicator.