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Sparse Versus Simple Structure Loadings

Published online by Cambridge University Press:  01 January 2025

Nickolay T. Trendafilov  and
Kohei Adachi
Nickolay T. Trendafilov*
Affiliation:
Open University
Kohei Adachi
Affiliation:
Osaka University
*
Correspondence should be sent to Nickolay T. Trendafilov, Department of Mathematics and Statistics, Open University, Walton Hall, Milton Keynes MK7 6AA, UK. Email: Nickolay.Trendafilov@open.ac.uk
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Abstract

The component loadings are interpreted by considering their magnitudes, which indicates how strongly each of the original variables relates to the corresponding principal component. The usual ad hoc practice in the interpretation process is to ignore the variables with small absolute loadings or set to zero loadings smaller than some threshold value. This, in fact, makes the component loadings sparse in an artificial and a subjective way. We propose a new alternative approach, which produces sparse loadings in an optimal way. The introduced approach is illustrated on two well-known data sets and compared to the existing rotation methods.

Keywords

principal component analysisfactor analysisorthogonal and oblique rotationssparseness-inducing constraintsLASSO constraintsprojected gradients
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 3 , September 2015 , pp. 776 - 790
Copyright
Copyright © 2014 The Psychometric Society

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