PHLP: Sole Persistent Homology for Link Prediction - Interpretable Feature Extraction

TL;DR

This paper introduces PHLP, a novel topological data analysis method using persistent homology for link prediction that enhances interpretability and improves existing GNN-based models without relying on neural networks.

Contribution

PHLP is the first approach applying persistent homology to link prediction independently of neural networks, offering interpretable features and performance improvements.

Findings

PHLP performs comparably to state-of-the-art models on benchmark datasets.

Incorporating PHLP outputs improves GNN-based model performance.

PHLP provides interpretable topological features for link prediction.

Abstract

Link prediction (LP), inferring the connectivity between nodes, is a significant research area in graph data, where a link represents essential information on relationships between nodes. Although graph neural network (GNN)-based models have achieved high performance in LP, understanding why they perform well is challenging because most comprise complex neural networks. We employ persistent homology (PH), a topological data analysis method that helps analyze the topological information of graphs, to interpret the features used for prediction. We propose a novel method that employs PH for LP (PHLP) focusing on how the presence or absence of target links influences the overall topology. The PHLP utilizes the angle hop subgraph and new node labeling called degree double radius node labeling (Degree DRNL), distinguishing the information of graphs better than DRNL. Using only a classifier, PHLP performs similarly to state-of-the-art (SOTA) models on most benchmark datasets. Incorporating the outputs calculated using PHLP into the existing GNN-based SOTA models improves performance across all benchmark datasets. To the best of our knowledge, PHLP is the first method of applying PH to LP without GNNs. The proposed approach, employing PH while not relying on neural networks, enables the identification of crucial factors for improving performance.