Local Intrinsic Dimensionality for Dynamic Graph Embeddings

TL;DR

This paper explores how local intrinsic dimensionality (LID), specifically NC-LID, can be adapted for dynamic graphs to evaluate and improve the quality of dynamic network embeddings, marking initial steps towards LID-aware methods.

Contribution

It introduces the adaptation of NC-LID for dynamic graphs and demonstrates its effectiveness as an indicator of embedding quality in real-world networks.

Findings

NC-LID correlates with embedding quality in dynamic networks.

NC-LID can identify nodes with poor temporal structure preservation.

First empirical evidence of LID's applicability to dynamic graph embeddings.

Abstract

The notion of local intrinsic dimensionality (LID) has important theoretical implications and practical applications in the fields of data mining and machine learning. Recent research efforts indicate that LID measures defined for graphs can improve graph representational learning methods based on random walks. In this paper, we discuss how NC-LID, a LID measure designed for static graphs, can be adapted for dynamic networks. Focusing on dynnode2vec as the most representative dynamic graph embedding method based on random walks, we examine correlations between NC-LID and the intrinsic quality of 10 real-world dynamic network embeddings. The obtained results show that NC-LID can be used as a good indicator of nodes whose embedding vectors do not tend to preserve temporal graph structure well. Thus, our empirical findings constitute the first step towards LID-aware dynamic graph embedding methods.