Overlapping Matrix Pattern Visualization: A Hypergraph Approach

In this work, we study a visual data mining problem: Given a set of discovered overlapping submatrices of interest, how can we order the rows and columns of the data matrix to best display these submatrices and their relationships? We find this problem can be converted to the hypergraph ordering problem, which generalizes the traditional minimal linear arrangement (or graph ordering) problem and then we are able to prove the NP-hardness of this problem. We propose a novel iterative algorithm which utilize the existing graph ordering algorithm to solve the optimal visualization problem. This algorithm can always converge to a local minimum. The detailed experimental evaluation using a set of publicly available transactional datasets demonstrates the effectiveness and efficiency of the proposed algorithm.