论文标题
图形稀疏的相关信息原理
Principle of Relevant Information for Graph Sparsification
论文作者
论文摘要
图形稀疏旨在减少图形边缘的数量，同时保持其结构特性。在本文中，我们通过从相关信息原理（PRI）中汲取灵感来提出第一个一般有效的信息理论理论理论。为此，我们将PRI从标准标量随机变量设置扩展到结构化数据（即图形）。我们的图形目标是通过在图形laplacian上操作来实现的，这是通过用稀疏边缘选择向量$ \ mathbf {w} $表达子图的图形拉普拉斯式实现的。我们就图形PRI方法的有效性提供了理论和经验理由。我们还在一些特殊情况下分析了其分析解决方案。我们最终提出了三个代表性的现实世界应用，即图形稀疏，图形正规化的多任务学习和医学成像衍生的大脑网络分类，以证明我们对普遍的稀疏技术的有效性，多功能性和方法的可解释性。 Graph-pri代码可从https://github.com/sjyucnel/pri-graphs获得
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
