Scalable Label Propagation for Multi-relational Learning on Tensor Product Graph

Label propagation on the tensor product of multiple graphs can infer multi-relations among the entities across the graphs by learning labels in a tensor. However, the tensor formulation is only empirically scalable up to three graphs due to the exponential complexity of computing tensors. In this paper, we propose an optimization formulation and a scalable Lowrank Tensor-based Label Propagation algorithm (LowrankTLP). The optimization formulation minimizes the rank-k approximation error for computing the closed-form solution of label propagation on a tensor product graph with efficient tensor computations used in LowrankTLP. LowrankTLP takes either a sparse tensor of known multi-relations or pairwise relations between each pair of graphs as the input to infer unknown multi-relations by semi-supervised learning on the tensor product graph. We also accelerate LowrankTLP with parallel tensor computation which enabled label propagation on a tensor product of 100 graphs of size 1000 within 150 seconds in simulation. LowrankTLP was also successfully applied to multi-relational learning for predicting author-paper-venue in publication records, alignment of several protein-protein interaction networks across species and alignment of segmented regions across up to 7 CT scan images. The experiments prove that LowrankTLP indeed well approximates the original label propagation with high scalability. Source code: https://github.com/kuanglab/LowrankTLP