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 $\approx$ $\textbf{99.96}\%$.

翻译：本文提出了一种新颖的方法——$\textit{知识持久性}$（$\mathcal{KP}$），用于加速知识图谱（KG）补全方法的评估。当前基于排名的评估方法的计算复杂度与KG规模呈二次关系，导致评估时间过长，进而产生高碳排放。$\mathcal{KP}$通过拓扑数据分析的视角（具体应用持久同调）表征KG补全方法的拓扑结构，从而解决这一问题。持久同调的特性使$\mathcal{KP}$能够仅通过分析部分数据评估KG补全的质量。在标准数据集上的实验结果表明，所提出的度量指标与排名指标（Hits@N、MR、MRR）具有高度相关性。性能评估显示，$\mathcal{KP}$在计算上高效：在某些情况下，一种KG补全方法的评估时间（验证+测试）从18小时（使用Hits@10）缩短至27秒（使用$\mathcal{KP}$），平均而言（跨方法与数据）评估时间（验证+测试）减少了约$\textbf{99.96}\%$。