# Scalable Label Propagation for Multi-relational Learning on the Tensor Product of Graphs

## TL;DR

This paper introduces LowrankTLP, a scalable tensor-based label propagation method for multi-relational learning on knowledge graphs, demonstrating improved accuracy and efficiency in tasks like hyperlink prediction and graph alignment.

## Contribution

It generalizes label propagation to normalized tensor product graphs and proposes a low-rank, scalable algorithm for multi-relational learning tasks.

## Key findings

- Accelerates label propagation on large tensor graphs to under half an hour.
- Effectively predicts hyperlinks and aligns multiple graphs across diverse applications.
- Achieves better scalability and accuracy compared to existing methods.

## Abstract

Multi-relational learning on knowledge graphs infers high-order relations among the entities across the graphs. This learning task can be solved by label propagation on the tensor product of the knowledge graphs to learn the high-order relations as a tensor. In this paper, we generalize a widely used label propagation model to the normalized tensor product graph, and propose an optimization formulation and a scalable Low-rank Tensor-based Label Propagation algorithm (LowrankTLP) to infer multi-relations for two learning tasks, hyperlink prediction and multiple graph alignment. The optimization formulation minimizes the upper bound of the noisy tensor estimation error for multiple graph alignment, by learning with a subset of the eigen-pairs in the spectrum of the normalized tensor product graph. We also provide a data-dependent transductive Rademacher bound for binary hyperlink prediction. We accelerate LowrankTLP with parallel tensor computation which enables label propagation on a tensor product of 100 graphs each of size 1000 in less than half hour in the simulation. LowrankTLP was also applied to predicting the author-paper-venue hyperlinks in publication records, alignment of segmented regions across up to 26 CT-scan images and alignment of protein-protein interaction networks across multiple species. The experiments demonstrate that LowrankTLP indeed well approximates the original label propagation with better scalability and accuracy.