Principle of Relevant Information for Graph Sparsification

• URL: http://arxiv.org/abs/2206.00118v1
• Date: Tue, 31 May 2022 21:00:42 GMT
• Title: Principle of Relevant Information for Graph Sparsification
• Authors: Shujian Yu, Francesco Alesiani, Wenzhe Yin, Robert Jenssen, Jose C. Principe
• Abstract summary: Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. We propose the first general and effective information-theoretic formulation of graph sparsification, by taking inspiration from the Principle of Relevant Information (PRI) We present three representative real-world applications, namely graph sparsification, graph regularized multi-task learning, and medical imaging-derived brain network classification.
• Score: 27.54740921723433
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. In this paper, we propose the first general and effective information-theoretic formulation of graph sparsification, by taking inspiration from the Principle of Relevant Information (PRI). To this end, we extend the PRI from a standard scalar random variable setting to structured data (i.e., graphs). Our Graph-PRI objective is achieved by operating on the graph Laplacian, made possible by expressing the graph Laplacian of a subgraph in terms of a sparse edge selection vector $\mathbf{w}$. We provide both theoretical and empirical justifications on the validity of our Graph-PRI approach. We also analyze its analytical solutions in a few special cases. We finally present three representative real-world applications, namely graph sparsification, graph regularized multi-task learning, and medical imaging-derived brain network classification, to demonstrate the effectiveness, the versatility and the enhanced interpretability of our approach over prevalent sparsification techniques. Code of Graph-PRI is available at https://github.com/SJYuCNEL/PRI-Graphs

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