Dynamic networks clustering via mirror distance

TL;DR

This paper introduces DNCMD, a novel clustering algorithm for dynamic networks based on mirror distances, with theoretical guarantees and applications to brain connectomes and trade networks.

Contribution

The paper develops DNCMD, a new clustering method for dynamic networks using mirror distances, with proven exact recovery guarantees under various models.

Findings

DNCMD achieves exact recovery of network evolution patterns in simulations.

DNCMD successfully analyzes Drosophila connectome data.

DNCMD reveals temporal patterns in trade networks.

Abstract

The classification of different patterns of network evolution, for example in brain connectomes or social networks, is a key problem in network inference and modern data science. Building on the notion of a network's Euclidean mirror, which captures its evolution as a curve in Euclidean space, we develop the Dynamic Network Clustering through Mirror Distance (DNCMD), an algorithm for clustering dynamic networks based on a distance measure between their associated mirrors. We provide theoretical guarantees for DNCMD to achieve exact recovery of distinct evolutionary patterns for latent position random networks both when underlying vertex features change deterministically and when they follow a stochastic process. We validate our theoretical results through numerical simulations and demonstrate the application of DNCMD to understand edge functions in Drosophila larval connectome data, as well as to analyze temporal patterns in dynamic trade networks.