Total Variation Graph Neural Networks

• URL: http://arxiv.org/abs/2211.06218v2
• Date: Thu, 27 Apr 2023 20:29:12 GMT
• Title: Total Variation Graph Neural Networks
• Authors: Jonas Berg Hansen and Filippo Maria Bianchi
• Abstract summary: Recently proposed Graph Neural Networks (GNNs) are trained with an unsupervised minimum cut objective. We propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut.
• Score: 5.571369922847262
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the $\ell_1$ distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

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