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

arXiv: https://arxiv.org/abs/2301.12929 · HTML: https://mlsanity.com/paper/2301.12929/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 68 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 29 of 29)

- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [Complex Embeddings for Simple Link Prediction](https://mlsanity.com/paper/1606.06357/) (2016)
- [RotatE: Knowledge Graph Embedding by Relational Rotation in Complex Space](https://mlsanity.com/paper/1902.10197/) (2019)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [KEPLER: A Unified Model for Knowledge Embedding and Pre-trained Language Representation](https://mlsanity.com/paper/1911.06136/) (2019)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [Sustainable AI: Environmental Implications, Challenges and Opportunities](https://mlsanity.com/paper/2111.00364/) (2021)
- [The Carbon Footprint of Machine Learning Training Will Plateau, Then Shrink](https://mlsanity.com/paper/2204.05149/) (2022)
- [A Novel Embedding Model for Knowledge Base Completion Based on Convolutional Neural Network](https://mlsanity.com/paper/1712.02121/) (2017)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [CoDEx: A Comprehensive Knowledge Graph Completion Benchmark](https://mlsanity.com/paper/2009.07810/) (2020)
- [Sliced Wasserstein Kernel for Persistence Diagrams](https://mlsanity.com/paper/1706.03358/) (2017)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [A Re-evaluation of Knowledge Graph Completion Methods](https://mlsanity.com/paper/1911.03903/) (2019)
- [Bringing Light Into the Dark: A Large-scale Evaluation of Knowledge Graph Embedding Models Under a Unified Framework](https://mlsanity.com/paper/2006.13365/) (2020)
- [Knowledge Base Completion: Baselines Strike Back](https://mlsanity.com/paper/1705.10744/) (2017)
- [Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections](https://mlsanity.com/paper/2106.15427/) (2021)
- [A Survey on Knowledge Graph Embeddings with Literals: Which model links better Literal-ly?](https://mlsanity.com/paper/1910.12507/) (2019)
- [Probability Calibration for Knowledge Graph Embedding Models](https://mlsanity.com/paper/1912.10000/) (2019)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Topological Data Analysis](https://mlsanity.com/paper/1609.08227/) (2016)
- [Efficient Non-Sampling Knowledge Graph Embedding](https://mlsanity.com/paper/2104.10796/) (2021)
- [Knowledge Base Completion: Baseline strikes back (Again)](https://mlsanity.com/paper/2005.00804/) (2020)
- [Highly Efficient Knowledge Graph Embedding Learning with Orthogonal Procrustes Analysis](https://mlsanity.com/paper/2104.04676/) (2021)
- [Pykg2vec: A Python Library for Knowledge Graph Embedding](https://mlsanity.com/paper/1906.04239/) (2019)
- [HopfE: Knowledge Graph Representation Learning using Inverse Hopf Fibrations](https://mlsanity.com/paper/2108.05774/) (2021)
- [Swift and Sure: Hardness-aware Contrastive Learning for Low-dimensional Knowledge Graph Embeddings](https://mlsanity.com/paper/2201.00565/) (2022)
- [Ranking vs. Classifying: Measuring Knowledge Base Completion Quality](https://mlsanity.com/paper/2102.06145/) (2021)
- [Topology Applied to Machine Learning: From Global to Local](https://mlsanity.com/paper/2103.05796/) (2021)

## Built on by (most cited first, 1 of 1)

- [Are We Wasting Time? A Fast, Accurate Performance Evaluation Framework for Knowledge Graph Link Predictors](https://mlsanity.com/paper/2402.00053/) (2024)

## Abstract (arXiv)

In this paper we present a novel method, textitKnowledge Persistence (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. 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 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 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 KP), and on average (across methods & data) reduces the evaluation time (validation+test) by ≈ 99.96%.