Sparsifying the least-squares approach to PCA: comparison of lasso and cardinality constraint

Rosember Guerra-Urzola (), Niek C. Schipper (), Anya Tonne (), Klaas Sijtsma (), Juan C. Vera () and Katrijn Deun ()
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Rosember Guerra-Urzola: Tilburg University
Niek C. Schipper: Tilburg University
Klaas Sijtsma: Tilburg University
Juan C. Vera: Tilburg University
Katrijn Deun: Tilburg University

Advances in Data Analysis and Classification, 2023, vol. 17, issue 1, No 13, 269-286

Abstract: Abstract Sparse PCA methods are used to overcome the difficulty of interpreting the solution obtained from PCA. However, constraining PCA to obtain sparse solutions is an intractable problem, especially in a high-dimensional setting. Penalized methods are used to obtain sparse solutions due to their computational tractability. Nevertheless, recent developments permit efficiently obtaining good solutions of cardinality-constrained PCA problems allowing comparison between these approaches. Here, we conduct a comparison between a penalized PCA method with its cardinality-constrained counterpart for the least-squares formulation of PCA imposing sparseness on the component weights. We compare the penalized and cardinality-constrained methods through a simulation study that estimates the sparse structure’s recovery, mean absolute bias, mean variance, and mean squared error. Additionally, we use a high-dimensional data set to illustrate the methods in practice. Results suggest that using cardinality-constrained methods leads to better recovery of the sparse structure.

Keywords: Cardinality constraint; Sparse PCA; Penalized linear regression; 62H25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11634-022-00499-2

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