Community Detection by Principal Components Clustering Methods

TL;DR

This paper introduces two novel community detection methods, PCC and NPCC, based on principal component clustering under the DCSBM model, demonstrating their effectiveness and robustness on synthetic and real datasets.

Contribution

The paper proposes parameter-free PCC and NPCC methods for community detection, with theoretical consistency and improved performance over existing methods.

Findings

NPCC achieves perfect clustering in ideal DCSBM cases.

NPCC outperforms PCC and RSC in real-world datasets.

Refinements PCC+ and NPCC+ further improve detection accuracy.

Abstract

Based on the classical Degree Corrected Stochastic Blockmodel (DCSBM) model for network community detection problem, we propose two novel approaches: principal component clustering (PCC) and normalized principal component clustering (NPCC). Without any parameters to be estimated, the PCC method is simple to be implemented. Under mild conditions, we show that PCC yields consistent community detection. NPCC is designed based on the combination of the PCC and the RSC method (Qin & Rohe 2013). Population analysis for NPCC shows that NPCC returns perfect clustering for the ideal case under DCSBM. PCC and NPCC is illustrated through synthetic and real-world datasets. Numerical results show that NPCC provides a significant improvement compare with PCC and RSC. Moreover, NPCC inherits nice properties of PCC and RSC such that NPCC is insensitive to the number of eigenvectors to be clustered and the choosing of the tuning parameter. When dealing with two weak signal networks Simmons and Caltech, by considering one more eigenvectors for clustering, we provide two refinements PCC+ and NPCC+ of PCC and NPCC, respectively. Both two refinements algorithms provide improvement performances compared with their original algorithms. Especially, NPCC+ provides satisfactory performances on Simmons and Caltech, with error rates of 121/1137 and 96/590, respectively.