High-dimensional disjoint factor analysis with its EM algorithm version

• Published in: Japanese journal of statistics and data science Vol. 4; no. 1; pp. 427 - 448
• Main Authors: Cai, Jingyu, Adachi, Kohei
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.07.2021
• Subjects: Chemistry and Earth Sciences; Computer Science; Economics; Finance; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Medicine; Original Paper; Physics; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; High-dimensional data; Variable clustering; EM algorithm; Disjoint factor analysis
• ISSN: 2520-8756; 2520-8764
• DOI: 10.1007/s42081-021-00119-x

Vichi (Advances in Data Analysis and Classification, 11:563–591, 2017) proposed disjoint factor analysis (DFA), which is a factor analysis procedure subject to the constraint that variables are mutually disjoint. That is, in the DFA solution, each variable loads only a single factor among multiple ones. It implies that the variables are clustered into exclusive groups. Such variable clustering is considered useful for high-dimensional data with variables much more than observations. However, the feasibility of DFA for high-dimensional data has not been considered in Vichi (2017). Thus, one purpose of this paper is to show the feasibility and usefulness of DFA for high-dimensional data. Another purpose is to propose a new computational procedure for DFA, in which an EM algorithm is used. This procedure is called EM-DFA in particular, which can serve the same original purpose as in Vichi (2017) but more efficiently. Numerical studies demonstrate that both DFA and EM-DFA can cluster variables fairly well, with EM-DFA more computationally efficient.