High-dimensional disjoint factor analysis with its EM algorithm version

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.