Special invited paper: The SCORE normalization, especially for heterogeneous network and text data

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.

Subject clustering by IF-PCA and several recent methods

“…The PCA clustering approach has many modern variants, including, but not limited to, Spectral-Gem ( Lee et al, 2010b ) and SCORE ( Jin, 2015 ; Ke and Jin, 2023 ). In this paper, we consider Spectral-Gem but skip the discussion on SCORE (SCORE was motivated by unsupervised learning in network and text data and shown to be effective on those types of data; it is unclear whether SCORE is also effective for genetic and genomic data).…”