AffNet: Designing Multi-Headed Affinity and Adaptive Thresholding for Unsupervised Homophily Estimation

Abstract

The message-passing (MP) framework contributes to the profound success of the graph neural networks (GNNs). MP predominantly operates on homophilic graphs where the adjacent nodes are highly likely to have identical class labels. However, for heterophilic graphs containing adjacent nodes frequently with different class labels, numerous sophisticated algorithms have been proposed. A prior idea about the homophily of a graph helps choose the algorithm to be used. The estimation of homophily relies on the node labels which, practically, are often unavailable. Hence, we remain clueless about which GNNs should be applied to the input dataset. To mitigate the issue, we propose a novel and efficient method to measure the homophily without having prior information on the node labels. Our method employs trainable affinity vectors equipped with nodes apart from the pre-existing node features. The affinity vector of a node represents the feature vector that the node expects in a suitable neighbor. We measure affinity scores between nodes as the similarity between the affinity of one node to the features of another node. In this connection, we define a unique homophily measure based on the affinity scores of nodes with themselves. Extending the concept, the multi-headed affinity (MHA) vectors are designed to represent a diverse set of choices the nodes have to connect to other neighbors. Furthermore, we design an adaptive strategy to apply learned thresholds by going beyond the prevailing ones that use fixed thresholds. The estimated affinity scores are subsequently considered as the probability scores determining the existence of edges. In this context, we propose a robust architecture AffNet that can be used to simultaneously estimate homophily in an unsupervised setting, solve the link prediction task and build recommendation systems. Applying our framework to several standard and large-scale datasets, we obtain impressive performances compared with the various state-of-the-art methods.