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A Guide for Sparse PCA: Model Comparison and Applications
- Source :
- Psychometrika, Psychometrika, 86. Springer
- Publication Year :
- 2021
- Publisher :
- Springer US, 2021.
-
Abstract
- PCA is a popular tool for exploring and summarizing multivariate data, especially those consisting of many variables. PCA, however, is often not simple to interpret, as the components are a linear combination of the variables. To address this issue, numerous methods have been proposed to sparsify the nonzero coefficients in the components, including rotation-thresholding methods and, more recently, PCA methods subject to sparsity inducing penalties or constraints. Here, we offer guidelines on how to choose among the different sparse PCA methods. Current literature misses clear guidance on the properties and performance of the different sparse PCA methods, often relying on the misconception that the equivalence of the formulations for ordinary PCA also holds for sparse PCA. To guide potential users of sparse PCA methods, we first discuss several popular sparse PCA methods in terms of where the sparseness is imposed on the loadings or on the weights, assumed model, and optimization criterion used to impose sparseness. Second, using an extensive simulation study, we assess each of these methods by means of performance measures such as squared relative error, misidentification rate, and percentage of explained variance for several data generating models and conditions for the population model. Finally, two examples using empirical data are considered. Supplementary Information The online version contains supplementary material available at 10.1007/s11336-021-09773-2.
- Subjects :
- Multivariate statistics
Psychometrics
Computer science
dimension reduction
01 natural sciences
sparse principal components analysis
010104 statistics & probability
03 medical and health sciences
Approximation error
high dimension-low sample size
Computer Simulation
0101 mathematics
Linear combination
Equivalence (measure theory)
General Psychology
030304 developmental biology
0303 health sciences
Principal Component Analysis
business.industry
Applied Mathematics
Dimensionality reduction
Sparse PCA
exploratory data analysis
Pattern recognition
Explained variation
regularization
Exploratory data analysis
Application Reviews and Case Studies
Artificial intelligence
business
Algorithms
Subjects
Details
- Language :
- English
- ISSN :
- 18600980 and 00333123
- Volume :
- 86
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Psychometrika
- Accession number :
- edsair.doi.dedup.....a4a2b364ec89b68208792b2abcae864e