A Hierarchical Network Simplification Via Non-Negative Matrix Factorization

Author(s)

Dias, Markus Diego ; Mansour, Moussa R. ; Dias, Fabio ; Petronetto, Fabiano ; Silva, Claudio T. ; Nonato, L. Gustavo ; IEEE

• Document type: Journal article
• Source: 2017 30TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI); v. N/A, p. 8-pg., 2017-01-01.

Abstract

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 preserving 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. (AU)

• FAPESP's process: 14/12815-1 - Mathematical morphology in graphs: methods and applications in data visualization
• Grantee: Fábio Augusto Salve Dias
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 16/04190-7 - Visualizing and Analyzing Urban Data: Mathematical and Computational Aspects
• Grantee: Luis Gustavo Nonato
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 11/22749-8 - Challenges in exploratory visualization of multidimensional data: paradigms, scalability and applications
• Grantee: Luis Gustavo Nonato
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry
• Grantee: Francisco Louzada Neto
• Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC
• FAPESP's process: 16/04391-2 - Mathematical morphology operators for the visual analytics of urban data
• Grantee: Fábio Augusto Salve Dias
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor