The SCORE normalization, especially for highly heterogeneous network and text data

TL;DR

This paper reviews the SCORE spectral normalization method for community detection in heterogeneous networks, highlighting its theoretical foundations, adaptations, and practical applications, demonstrating its effectiveness and optimality.

Contribution

It provides a comprehensive review of SCORE, including its theoretical basis, adaptations to mixed membership and topic modeling, and real data applications, emphasizing its optimal performance.

Findings

SCORE converts a simplicial cone to a simplex in the spectral domain.

It achieves exponential rates and sharp phase transitions in community detection.

SCORE attains optimal rates in mixed membership estimation and topic modeling.

Abstract

SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical 'ideology' underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex, and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling.