Multiple graph semi-supervised clustering with automatic calculation of graph associations

Abstract

Multiple graph clustering is an important tool in data integration and data mining for graph-based data. The prediction and classification accuracy can be significantly improved by integrating information from multiple sources and data sets. The aim of multiple graph clustering is to partition objects into several clusters such that clusters in each graph are well-separated and clusters across different graphs are consistent. Existing methods assume that the degrees of association among different graphs are the same. However, some graphs may be strongly or weakly associated with the other graphs due to high or low correlation of their associated cluster structures. When their cluster structures are (or are not) similar, their degree of association should be high (or low). Accurate clustering results can be obtained by integrating such association information in multiple graphs. The main aim of this paper is to study multiple graph semi-supervised clustering by considering a large amount of multiple graph data and a small amount of labeled data. We propose a constrained optimization problem that can determine cluster structures and degrees of association simultaneously in multiple graph clustering. In our formulation, we make use of orthogonality for cluster structure indicator and cosine correlation for degree of association. With orthogonality constraint in the clustering process, we develop a gradient flow method to solve the resulting optimization problem. And the convergence of the proposed iterative method is also shown. Numerical examples including synthetic data and real data sets with few known labels are tested, and are presented to show the efficiency and effectiveness of our proposed method compared with the testing methods in the literature.