Clustering of noised and heterogeneous multi-view data with graph learning and projection decomposition

Abstract

Complex systems in society and nature cannot be effectively modeled and represented by a single perspective, resulting in the so-called multi-view data, which provide an absolutely excellent chance to explore the fundamental mechanisms of systems. In comparison with single-view clustering, multi-view clustering simultaneously considers the intrinsic property within the same view and the relations across various views. Current methods for multi-view are criticized for the undesirable result because they fail to resolve the heterogeneity, consistency, and diversity of various views. To address these issues, we propose Consistency and Diversity Preserving with Projection Decomposition for multi-view clustering (aka CDP2D), in which the shared and specific projection matrices are automatically learned. Specifically, CDP2D constructs a graph for each view, transforming the multi-view clustering issue into multi-layer network clustering. Then, CDP2D separates the projection matrix of self-representation into common and specific parts with low-rank constraint: the former part characterizes the consistency of various views, and the latter part characterizes the specificity of each view. To ensure the diversity of various views, CDP2D minimizes the similarity among the view-specific parts, which is formulated as trace optimization. All these procedures are integrated into an overall objective function, and the optimization rules are derived. The extensive experimental results on 10 datasets indicate that CDP2D observably outperforms 12 state-of-the-art algorithms in terms of various measurements, implying that it is promising for analyzing multi-view data with projection matrix decomposition.