# Sparsest factor analysis for clustering variables: a matrix decomposition approach

Adachi, Kohei and Trendafilov, Nickolay T. (2018). Sparsest factor analysis for clustering variables: a matrix decomposition approach. Advances in Data Analysis and Classification, 12(3) pp. 559–585.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1007/s11634-017-0284-z Look up in Google Scholar

## Abstract

We propose a new procedure for sparse factor analysis (FA) such that each variable loads only one common factor. Thus, the loading matrix has a single nonzero element in each row and zeros elsewhere. Such a loading matrix is the sparsest possible for certain number of variables and common factors. For this reason, the proposed method is named sparsest FA (SSFA). It may also be called FA-based variable clustering, since the variables loading the same common factor can be classified into a cluster. In SSFA, all model parts of FA (common factors, their correlations, loadings, unique factors, and unique variances) are treated as fixed unknown parameter matrices and their least squares function is minimized through specific data matrix decomposition. A useful feature of the algorithm is that the matrix of common factor scores is re-parameterized using QR decomposition in order to efficiently estimate factor correlations. A simulation study shows that the proposed procedure can exactly identify the true sparsest models. Real data examples demonstrate the usefulness of the variable clustering performed by SSFA.

Item Type: Journal Item 2017 Springer-Verlag 1862-5355 exploratory factor analysis; sparsest loadings; matrix decomposition factor analysis; variable clustering; QR re-parameterization Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and StatisticsFaculty of Science, Technology, Engineering and Mathematics (STEM) 49278 Nickolay Trendafilov 02 May 2017 15:25 21 Jul 2019 04:52 http://oro.open.ac.uk/id/eprint/49278    