Inverse Graph Identification: Can We Identify Node Labels Given Graph Labels?

TL;DR

This paper introduces the novel problem of Inverse Graph Identification (IGI), focusing on identifying nodes from graph labels, and proposes a Gaussian Mixture Graph Convolutional Network (GMGCN) with hierarchical graph assistance to address it.

Contribution

The paper defines IGI as a new problem, formalizes its variants, and proposes GMGCN with a consensus loss, demonstrating its effectiveness through extensive experiments.

Findings

GMGCN outperforms baseline methods on benchmark datasets.

The hierarchical graph structure improves node classification accuracy.

The proposed approach effectively addresses the inverse graph identification problem.

Abstract

Graph Identification (GI) has long been researched in graph learning and is essential in certain applications (e.g. social community detection). Specifically, GI requires to predict the label/score of a target graph given its collection of node features and edge connections. While this task is common, more complex cases arise in practice---we are supposed to do the inverse thing by, for example, grouping similar users in a social network given the labels of different communities. This triggers an interesting thought: can we identify nodes given the labels of the graphs they belong to? Therefore, this paper defines a novel problem dubbed Inverse Graph Identification (IGI), as opposed to GI. Upon a formal discussion of the variants of IGI, we choose a particular case study of node clustering by making use of the graph labels and node features, with an assistance of a hierarchical graph that further characterizes the connections between different graphs. To address this task, we propose Gaussian Mixture Graph Convolutional Network (GMGCN), a simple yet effective method that makes the node-level message passing process using Graph Attention Network (GAT) under the protocol of GI and then infers the category of each node via a Gaussian Mixture Layer (GML). The training of GMGCN is further boosted by a proposed consensus loss to take advantage of the structure of the hierarchical graph. Extensive experiments are conducted to test the rationality of the formulation of IGI. We verify the superiority of the proposed method compared to other baselines on several benchmarks we have built up. We will release our codes along with the benchmark data to facilitate more research attention to the IGI problem.