Anomaly and Change Detection in Graph Streams through Constant-Curvature Manifold Embeddings

TL;DR

This paper explores embedding attributed graph streams into constant-curvature manifolds to improve change and anomaly detection, demonstrating the potential benefits of non-Euclidean geometries over traditional Euclidean spaces.

Contribution

It introduces a novel approach of embedding graphs into hyper-spherical and hyperbolic manifolds for enhanced change detection in graph streams.

Findings

Curved manifold embeddings can better capture graph geometry.

Preliminary results show improved change detection performance.

Learning the manifold curvature adapts to application-specific graph structures.

Abstract

Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data representation possibly characterised by convenient geometric properties. Euclidean spaces are by far the most widely used embedding spaces, thanks to their well-understood structure and large availability of consolidated inference methods. However, recent research demonstrated that many types of complex data (e.g., those represented as graphs) are actually better described by non-Euclidean geometries. Here, we investigate how embedding graphs on constant-curvature manifolds (hyper-spherical and hyperbolic manifolds) impacts on the ability to detect changes in sequences of attributed graphs. The proposed methodology consists in embedding graphs into a geometric space and perform change detection there by means of conventional methods for numerical streams. The curvature of the space is a parameter that we learn to reproduce the geometry of the original application-dependent graph space. Preliminary experimental results show the potential capability of representing graphs by means of curved manifold, in particular for change and anomaly detection problems.