Spectral Measures of Distortion for Change Detection in Dynamic Graphs

Luca Castelli Aleardi (1) , Semih Salihoglu , Gurprit Singh , Maks Ovsjanikov (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We propose a novel framework for detecting, quantifying and visualizing changes between two snapshots of a dynamic network. Unlike existing approaches, which can be sensitive to noise, and are often based on heuristics, we show how a theoretically-justified, inherently multi-scale notion of change, or distortion, can be defined and computed using spectral graph-theoretic tools. Our primary observation is that informative, robust and multi-scale measures of change can be obtained by computing a real-valued function (which we call the distortion function) on the nodes of the input graph, via the optimization of a pre-defined distortion energy in a provably optimal way. Based on extensive tests on a wide variety of networks, we demonstrate the ability of our approach to highlight the evolution of the network in an informative and multi-scale manner.

Domaines: Géométrie algorithmique [cs.CG]; Réseaux sociaux et d'information [cs.SI]

Luca Castelli Aleardi, Semih Salihoglu, Gurprit Singh, Maks Ovsjanikov. Spectral Measures of Distortion for Change Detection in Dynamic Graphs. 2018. ⟨hal-01864079v2⟩