Abstract
As the backbone of many real-world complex systems, networks interact with others in nontrivial ways from time to time. It is a challenging problem to detect subgraphs that have dependencies on each other across multiple networks. Instead of devising a method for a specific scenario, we propose a generic framework to discover subgraphs in multiple interdependent networks, which generalizes the classical subgraph detection problem in a single network and can be applied to more practical applications. Specifically, we propose the Graph Block-structured Gradient Hard Thresholding Pursuit (GB-GHTP) framework to optimize interdependent networks with block-structured constraints, which enjoys 1) a theoretical guarantee and 2) a nearly linear time complexity on the network size. It is demonstrated how our framework can be applied to three practical applications: 1) evolving anomalous subgraph detection in dynamic networks, 2) anomalous subgraph detection in networks of networks, and 3) connected dense subgraph detection in dual networks. We evaluate our framework on large-scale datasets with comprehensive experiments, which validate our framework's effectiveness and efficiency.
Highlights
A graph1 G = (V, E) refers to a set of entities, denoted as nodes V, along with some connections between node pairs, represented by edges E
We focus on subgraph detection in attributed networks, in which nodes in a graph are associated with
We explore possible solutions for graph block-structured optimization by leveraging sparse optimization theories and approximate projections for graph-structured sparsity, aiming to provide a generic framework for subgraph detection problems in interdependent networks with tractable computation as well as provable theoretical guarantees
Summary
To the best of our knowledge, most related studies on subgraph detection in interdependent networks focus on a specific application and lack generality They are heuristic-driven without any theoretical guarantee. We explore possible solutions for graph block-structured optimization by leveraging sparse optimization theories and approximate projections for graph-structured sparsity, aiming to provide a generic framework for subgraph detection problems in interdependent networks with tractable computation as well as provable theoretical guarantees. We propose a novel generic framework, named Graph Block-structured Gradient Hard Thresholding Pursuit (GB-GHTP), for the graph block-structured optimization problem, which is efficient and useful for approximately solving a broad of class of subgraph detection problems in interdependent networks in nearly linear time on the network size.
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