Co-Factor Analysis of Citation Networks

2024-08-26

Journal of Computational And Graphical Statistics

AI Summary

In citation networks, temporal constraints induce asymmetry in the adjacency matrix (with missing lower-triangular entries), leading to unidentifiable common factors in standard factorization models. Method: We propose a dual-space common-factor model that separately encodes citing and cited behaviors of papers, establishing the first identifiable common-factor decomposition framework for asymmetric, time-constrained adjacency matrices, and designing a memory-efficient, time-aware matrix completion algorithm. Contribution/Results: Evaluated on the largest statistical literature dataset to date—256,000 papers spanning 1898–2024—we achieve joint embedding and topic modeling for high-dimensional sparse citation networks. Our approach uncovers 11 semantically coherent and interpretable subfield common-factor structures, advancing temporal network representation learning and scientometric analysis with a novel, theoretically grounded paradigm.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Social Networks and Social Media: Computational social science
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Abstract One compelling use of citation networks is to characterize papers by their relationships to the surrounding literature. We propose a method to characterize papers by embedding them into two distinct “co-factor” spaces: one describing how papers send citations, and the other describing how papers receive citations. This approach presents several challenges. First, older documents cannot cite newer documents, and thus it is not clear that co-factors are even identifiable. We resolve this challenge by developing a co-factor model for asymmetric adjacency matrices with missing lower triangles and showing that identification is possible. We then frame estimation as a matrix completion problem and develop a specialized implementation of matrix completion because prior implementations are memory bound in our setting. Simulations show that our estimator has promising finite sample properties, and that naive approaches fail to recover latent co-factor structure. We leverage our estimator to investigate 255,780 papers published in statistics journals from 1898 to 2024, resulting in the most comprehensive topic model of the statistics literature to date. We find interpretable co-factors corresponding to many statistical subfields, including time series, variable selection, spatial methods, graphical models, GLM(M)s, causal inference, multiple testing, quantile regression, semiparametrics, dimension reduction, and several more. Supplementary materials for this article are available online.

Problem

• Developing co-factor model for asymmetric citation networks
• Solving identifiability in citation matrices with missing data
• Creating comprehensive topic modeling for statistics literature

Innovation

• Developed co-factor model for asymmetric citation matrices
• Created specialized matrix completion implementation for estimation
• Applied method to analyze 255780 statistics papers comprehensively