Trendafilov, Nickolay T. and Unkel, Steffen
(2011).
| DOI (Digital Object Identifier) Link: | http://dx.doi.org/10.1198/jcgs.2011.09211 |
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| Google Scholar: | Look up in Google Scholar |
Abstract
A new approach for exploratory factor analysis (EFA) of data matrices with more variables p than observations n is presented. First, the classic EFA model (n > p) is considered as a specific data matrix decomposition with fixed unknown matrix parameters. Then, it is generalized to a new model, called for short GEFA, which covers both cases of data, with either n > p or p ≥ n. An alternating least squares algorithm GEFALS is proposed for simultaneous estimation of all GEFA model parameters. As principal component analysis (PCA), GEFALS is based on singular value decomposition, which makes GEFA an attractive alternative to PCA for descriptive data analysis and dimensionality reduction. The existence and uniqueness of the GEFA parameters estimations is studied and the convergence properties of GEFALS are established. Finally, the new approach is illustrated with Thurstone's 26-variable box data and real high-dimensional data, while the performance of GEFALS - with simulation experiment.
| Item Type: | Journal Article |
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| Copyright Holders: | 2011 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America |
| ISSN: | 1537-2715 |
| Keywords: | factor analysis; p > n; Procrustes problem; singular value decomposition |
| Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |
| Related URLs: |
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| Item ID: | 29120 |
| Depositing User: | Sara Griffin |
| Date Deposited: | 18 Jul 2011 09:08 |
| Last Modified: | 03 Dec 2012 12:05 |
| URI: | http://oro.open.ac.uk/id/eprint/29120 |
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