Conceptos Básicos
The authors propose a new spectral clustering method called Mixed-SLIM for detecting mixed memberships in networks under the degree-corrected mixed membership model. They provide theoretical bounds for the estimation error of the proposed algorithm and its regularized version.
Resumen
The content discusses the problem of mixed membership community detection in networks. It introduces the degree-corrected mixed membership (DCMM) model, which allows nodes to belong to multiple communities and have varying degrees within the same community.
The authors propose a new spectral clustering method called Mixed-SLIM, which extends the symmetric Laplacian inverse matrix (SLIM) approach to the mixed membership setting. The key steps of Mixed-SLIM are:
Compute the symmetric Laplacian inverse matrix ̂M based on the adjacency matrix.
Extract the leading K eigenvectors of ̂M and normalize the rows to obtain ̂X*.
Apply K-medians clustering on the rows of ̂X* to find the cluster centers.
Project the rows of ̂X* onto the spans of the cluster centers to obtain the final membership matrix ̂Π.
The authors provide theoretical analysis, showing the consistency of the regularized version Mixed-SLIMτ under the DCMM model.
Numerical experiments on synthetic and real-world datasets demonstrate that the Mixed-SLIM methods outperform state-of-the-art approaches for both community detection and mixed membership community detection problems.