Consistency of regularized spectral clustering in degree-corrected mixed membership model

TL;DR

This paper introduces a novel spectral clustering method called Mixed-RSC for community detection in networks modeled by the degree-corrected mixed membership (DCMM) model, providing theoretical guarantees and optimal regularization parameter choice.

Contribution

It is the first to develop a spectral clustering algorithm for mixed membership community detection under DCMM using regularized Laplacian matrices, with proven consistency and error bounds.

Findings

Algorithm is asymptotically consistent under mild conditions.

Provides the theoretical optimal regularization parameter.

Demonstrates superior performance on simulated and real-world networks.

Abstract

Community detection in network analysis is an attractive research area recently. Here, under the degree-corrected mixed membership (DCMM) model, we propose an efficient approach called mixed regularized spectral clustering (Mixed-RSC for short) based on the regularized Laplacian matrix. Mixed-RSC is designed based on an ideal cone structure of the variant for the eigen-decomposition of the population regularized Laplacian matrix. We show that the algorithm is asymptotically consistent under mild conditions by providing error bounds for the inferred membership vector of each node. As a byproduct of our bound, we provide the theoretical optimal choice for the regularization parameter {\tau}. To demonstrate the performance of our method, we apply it with previous benchmark methods on both simulated and real-world networks. To our knowledge, this is the first work to design spectral clustering algorithm for mixed membership community detection problem under DCMM model based on the application of regularized Laplacian matrix.