# Offline and online coupled tensor factorization with knowledge graph

## TL;DR

This paper introduces new methods to analyze irregular data tensors by combining dynamic and static information from knowledge graphs in both offline and online settings.

## Contribution

KG-CTF and OKG-CTF are novel coupled tensor factorization methods that integrate knowledge graph tensors with irregular temporal tensors.

## Key findings

- KG-CTF reduces error rates by up to 1.64× compared to existing PARAFAC2 methods.
- OKG-CTF achieves up to 5.7× faster running times compared to existing streaming approaches.

## Abstract

How can we accurately decompose a temporal irregular tensor along while incorporating a related knowledge graph tensor in both offline and online streaming settings? PARAFAC2 decomposition is widely applied to the analysis of irregular tensors consisting of matrices with varying row sizes. In both offline and online streaming scenarios, existing PARAFAC2 methods primarily focus on capturing dynamic features that evolve over time, since data irregularities often arise from temporal variations. However, these methods tend to overlook static features, such as knowledge-based information, which remain unchanged over time.

In this paper, we propose KG-CTF (Knowledge Graph-based Coupled Tensor Factorization) and OKG-CTF (Online Knowledge Graph-based Coupled Tensor Factorization), two coupled tensor factorization methods designed to effectively capture both dynamic and static features within an irregular tensor in offline and online streaming settings, respectively. To integrate knowledge graph tensors as static features, KG-CTF and OKG-CTF couple an irregular temporal tensor with a knowledge graph tensor by sharing a common axis. Additionally, both methods employ relational regularization to preserve the structural dependencies among the factor matrices of the knowledge graph tensor. To further enhance convergence speed, we utilize momentum-based update strategies for factor matrices. Through extensive experiments, we demonstrate that KG-CTF reduces error rates by up to 1.64× compared to existing PARAFAC2 methods. Furthermore, OKG-CTF achieves up to 5.7× faster running times compared to existing streaming approaches for each newly arriving tensor.