Identifying and Mitigating Instability in Embeddings of the Degenerate Core

TL;DR

This paper investigates the stability of graph embeddings in the degenerate core during node removal, identifies instability patterns, and introduces STABLE, an algorithm that enhances stability without sacrificing link prediction accuracy.

Contribution

It uncovers instability patterns in degenerate core embeddings and proposes STABLE, a method to improve stability while maintaining high link prediction performance.

Findings

Identified three patterns of instability in core embeddings.

Quantified change points in embedding stability using regression.

STABLE improves embedding stability without losing link prediction accuracy.

Abstract

Are the embeddings of a graph's degenerate core stable? What happens to the embeddings of nodes in the degenerate core as we systematically remove periphery nodes (by repeated peeling off $k$-cores)? We discover three patterns w.r.t. instability in degenerate-core embeddings across a variety of popular graph embedding algorithms and datasets. We use regression to quantify the change point in graph embedding stability. Furthermore, we present the STABLE algorithm, which takes an existing graph embedding algorithm and makes it stable. We show the effectiveness of STABLE in terms of making the degenerate-core embedding stable and still producing state-of-the-art link prediction performance.