Spectral clustering via adaptive layer aggregation for multi-layer networks

TL;DR

This paper introduces adaptive spectral clustering methods for multi-layer networks that optimize layer aggregation to improve community detection, especially in challenging regimes where traditional methods fail.

Contribution

It develops a novel convex layer aggregation approach based on asymptotic spectral analysis, enhancing community detection accuracy in multi-layer networks.

Findings

The proposed methods estimate the optimal layer aggregation minimizing mis-clustering errors.

Gaussian mixture models outperform k-means in spectral clustering for these methods.

Numerical results show the new approach is highly competitive with existing techniques.

Abstract

One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches based on effective convex layer aggregations. Our aggregation methods are strongly motivated by a delicate asymptotic analysis of the spectral embedding of weighted adjacency matrices and the downstream $k$-means clustering, in a challenging regime where community detection consistency is impossible. In fact, the methods are shown to estimate the optimal convex aggregation, which minimizes the mis-clustering error under some specialized multi-layer network models. Our analysis further suggests that clustering using Gaussian mixture models is generally superior to the commonly used $k$-means in spectral clustering. Extensive numerical studies demonstrate that our adaptive aggregation techniques, together with Gaussian mixture model clustering, make the new spectral clustering remarkably competitive compared to several popularly used methods.