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Semi-sparse PCA

Published online by Cambridge University Press:  01 January 2025

Lars Eldén  and
Nickolay Trendafilov Open the ORCID record for Nickolay Trendafilov [Opens in a new window]
Lars Eldén
Affiliation:
Linköping University
Nickolay Trendafilov*
Affiliation:
The Open University
*
Correspondence should bemade to Nickolay Trendafilov, School of Mathematics and Statistics, The Open University, Milton Keynes, UK. Email:[email protected]
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Abstract

It is well known that the classical exploratory factor analysis (EFA) of data with more observations than variables has several types of indeterminacy. We study the factor indeterminacy and show some new aspects of this problem by considering EFA as a specific data matrix decomposition. We adopt a new approach to the EFA estimation and achieve a new characterization of the factor indeterminacy problem. A new alternative model is proposed, which gives determinate factors and can be seen as a semi-sparse principal component analysis (PCA). An alternating algorithm is developed, where in each step a Procrustes problem is solved. It is demonstrated that the new model/algorithm can act as a specific sparse PCA and as a low-rank-plus-sparse matrix decomposition. Numerical examples with several large data sets illustrate the versatility of the new model, and the performance and behaviour of its algorithmic implementation.

Keywords

alternative factor analysismatrix decompositionsleast squaresStiefel manifoldsparse PCArobust PCA
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 1 , 15 March 2019 , pp. 164 - 185
Copyright
Copyright © 2018 The Psychometric Society

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