Application of Random Matrix Theory to sociological data analysis

2017 Fiscal Year Final Research Report

• Project/Area Number: 26380658
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Sociology
• Research Institution: Ritsumeikan University
• Principal Investigator: NAKAI Miki 立命館大学, 産業社会学部, 教授 (00241282)
• Research Collaborator: Vernizzi Graziano Siena College, Department of Physics and Astronomy, Professor
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ランダム行列理論 / 共分散行列 / カテゴリカル・データ / 社会学データ / 欠損値データ

Outline of Final Research Achievements

During the 2014-2017 period, our research focused on applying mathematical techniques from Random Matrix Theory (RMT) to central problems in sociological data analysis. First, we developed a novel geometrical framework for correlation matrices of heterogeneous (i.e. categorical and continuous) sets of variables. Second, we applied RMT to the Principal Component Analysis of the SSM2005 dataset, within the geometrical framework. Third, we extended our analysis to the Missing Data problem, and developed a new method that maximizes the number of non-missing data entries after list-wise deletion. Finally, we produced algorithms in Matlab/Octave and R, and disseminated results at international conferences.

Free Research Field

社会学