Can Persistent Homology provide an efficient alternative for Evaluation of Knowledge Graph Completion Methods?

TL;DR

This paper introduces Knowledge Persistence, a topological data analysis-based method using persistent homology, to evaluate knowledge graph completion efficiently, significantly reducing evaluation time while maintaining high correlation with traditional metrics.

Contribution

The paper presents a novel, topology-based evaluation metric for knowledge graph completion that drastically reduces computational time compared to traditional ranking methods.

Findings

High correlation with standard metrics like Hits@N, MR, MRR

Evaluation time reduced by approximately 99.96%

Evaluation time decreased from 18 hours to 27 seconds in some cases

Abstract

In this paper we present a novel method, $\textit{Knowledge Persistence}$ ($\mathcal{KP}$), for faster evaluation of Knowledge Graph (KG) completion approaches. Current ranking-based evaluation is quadratic in the size of the KG, leading to long evaluation times and consequently a high carbon footprint. $\mathcal{KP}$ addresses this by representing the topology of the KG completion methods through the lens of topological data analysis, concretely using persistent homology. The characteristics of persistent homology allow $\mathcal{KP}$ to evaluate the quality of the KG completion looking only at a fraction of the data. Experimental results on standard datasets show that the proposed metric is highly correlated with ranking metrics (Hits@N, MR, MRR). Performance evaluation shows that $\mathcal{KP}$ is computationally efficient: In some cases, the evaluation time (validation+test) of a KG completion method has been reduced from 18 hours (using Hits@10) to 27 seconds (using $\mathcal{KP}$), and on average (across methods & data) reduces the evaluation time (validation+test) by $\approx$ $\textbf{99.96}\%$.