Tensor Convolutional Network for Higher-Order Interaction Prediction in Sparse Tensors
Jun-Gi Jang, Jingrui He, Andrew Margenot, Hanghang Tong
TL;DR
This work tackles top-$k$ higher-order interaction prediction in sparse tensors, where many entities have few observed relations, by integrating a relation-aware Tensor-originated Graph Convolutional Network (TCN) with existing tensor factorization (TF) methods. The approach constructs a tensor-originated hypergraph from observed interactions, derives a clique-expanded graph, and propagates through a linear GCN-like scheme to produce richer latent vectors that feed into TF predictors. Key contributions include the tensor-originated hypergraph and clique-expanded graph construction, a simple yet effective relation-aware encoder, and demonstrated plug-in compatibility with multiple TF models, yielding substantial performance gains on real-world datasets, especially in highly sparse, higher-order settings. The findings indicate that TCN significantly enhances top-$k$ HOIP in sparse tensors, offering practical improvements for recommendation systems, temporal graphs, and knowledge-graph completion, with scalable avenues for future work toward trillion-scale data.
Abstract
Many real-world data, such as recommendation data and temporal graphs, can be represented as incomplete sparse tensors where most entries are unobserved. For such sparse tensors, identifying the top-k higher-order interactions that are most likely to occur among unobserved ones is crucial. Tensor factorization (TF) has gained significant attention in various tensor-based applications, serving as an effective method for finding these top-k potential interactions. However, existing TF methods primarily focus on effectively fusing latent vectors of entities, which limits their expressiveness. Since most entities in sparse tensors have only a few interactions, their latent representations are often insufficiently trained. In this paper, we propose TCN, an accurate and compatible tensor convolutional network that integrates seamlessly with existing TF methods for predicting higher-order interactions. We design a highly effective encoder to generate expressive latent vectors of entities. To achieve this, we propose to (1) construct a graph structure derived from a sparse tensor and (2) develop a relation-aware encoder, TCN, that learns latent representations of entities by leveraging the graph structure. Since TCN complements traditional TF methods, we seamlessly integrate TCN with existing TF methods, enhancing the performance of predicting top-k interactions. Extensive experiments show that TCN integrated with a TF method outperforms competitors, including TF methods and a hyperedge prediction method. Moreover, TCN is broadly compatible with various TF methods and GNNs (Graph Neural Networks), making it a versatile solution.