Global and Local Structure Learning for Sparse Tensor Completion
Dawon Ahn, Evangelos E. Papalexakis
TL;DR
The paper tackles tensor completion by addressing limitations of standard CP decomposition, which does not explicitly model inter-dimensional relations and often relies on costly prior knowledge. It introduces TGL, a framework that augments CP factor matrices with graph neural networks to learn global and local structures per mode; relation matrices are derived from cosine similarities and refined through KNN graphs, with factor updates guided by a joint reconstruction loss $\mathcal{L}$ and GNN-based updates $\mathbf{H}^{(l+1)}=\sigma(\hat{\mathbf{R}}\mathbf{H}^{(l)}\mathbf{W}^{(l)})$. Empirical results on Yelp and BBC-News show TGL achieving competitive accuracy, typically second-best behind the best baselines, and comparable to state-of-the-art methods like CoSTCo while avoiding reliance on predefined inter-dimensional priors. This work demonstrates that integrating CP decomposition with GNN-driven local/global structure learning can effectively complete sparse tensors and offer a-priori knowledge-free modeling, with potential for reduced redundancy in learned graphs in future work.
Abstract
How can we accurately complete tensors by learning relationships of dimensions along each mode? Tensor completion, a widely studied problem, is to predict missing entries in incomplete tensors. Tensor decomposition methods, fundamental tensor analysis tools, have been actively developed to solve tensor completion tasks. However, standard tensor decomposition models have not been designed to learn relationships of dimensions along each mode, which limits to accurate tensor completion. Also, previously developed tensor decomposition models have required prior knowledge between relations within dimensions to model the relations, expensive to obtain. This paper proposes TGL (Tensor Decomposition Learning Global and Local Structures) to accurately predict missing entries in tensors. TGL reconstructs a tensor with factor matrices which learn local structures with GNN without prior knowledges. Extensive experiments are conducted to evaluate TGL with baselines and datasets.