A Hierarchical Network Simplification via Non-Negative Matrix Factorization

Visualization tools play an important part in assisting analysts in the understanding of networks and underlying phenomena. However these tasks can be hindered by visual clutter. Simplification/decimation schemes have been a main alternative in this context. Nevertheless, network simplification methods have not been properly evaluated w.r.t. their effectiveness in reducing complexity while reserving relevant structures and content. Moreover, most simplification techniques only consider information extracted from the topology of the network, altogether disregarding additional content. In this work we propose a novel methodology to network simplification that leverages topological information and additional content associated with network elements. The proposed methodology relies on non-negative matrix factorization (NMF) and graph matching, combined to generate a hierarchical representation of the network, grouping the most similar elements in each level of the hierarchy. Moreover, the matrix factorization is only performed at the beginning of the process, reducing the computational cost without compromising the quality of the simplification. The effectiveness of the proposed methodology is assessed through a comprehensive set of quantitative evaluations and comparisons, which shows that our approach outperforms existing simplification methods.