Hierarchical high-order co-clustering algorithm by maximizing modularity

The star-structured high-order heterogeneous data is ubiquitous, such data represent objects of a certain type, connected to other types of data, or the features, so that the overall data schema forms a star-structure of inter-relationships. In this paper, we study the problem of co-clustering of star-structured high-order heterogeneous data. We present a new solution, a Hierarchical High-order Co-clustering Algorithm by Maximizing Modularity, MHCoC, which iteratively optimizes the objective function based on modularity and finally converges to a unique clustering result. In contrast to the traditional co-clustering methods, MHCoC merges information of multiple feature spaces of high-order heterogeneous data. Moreover, MHCoC takes a top-down strategy to perform a greedy divisive procedure, generating a tree-like hierarchical clustering result that reveal the relationship between clusters. To illustrate the process in more detail, we design a toy example to describe how MHCoC selects the appropriate co-cluster and splits it. Extensive experiments on real-world datasets demonstrate the effectiveness of the proposed method.