Title: Maximum likelihood EM factor analysis of high-dimensional data with the sparsest constraint on loadings
Authors: Jingyu Cai - Osaka University (Japan) [presenting]
Kohei Adachi - Osaka University (Japan)
Abstract: The constrained factor analysis (FA) procedures have been proposed, in which each variable is constrained to load only one factor. Thus, the resulting loading matrix is the sparsest, in that it has a single nonzero element in each row and zeros elsewhere. Such procedures can be called sparsest FA. We propose a new sparsest FA procedure feasible for the high-dimensional data with the number of variables greater than that of observations. Such data have not been considered in the existing approaches. In the proposed procedure, the FA log-likelihood is maximized over loadings, factor correlations, and unique variances, with the loadings constrained to be the sparsest. This maximization is attained using a modified version of the EM algorithm for confirmatory FA. The original EM algorithm for FA is feasible to high-dimensional data and our modified version also has this property. The loadings being the sparsest facilitates their interpretation, in particular, for high-dimensional cases, as a great number of variables are classified exclusively into a few clusters on the basis of what factor is loaded by each variable. Such a benefit is illustrated with numerical examples.