Title: Implementation guidance of sparse principal component analysis on different methods and when to use them
Authors: Rosember Guerra-Urzola - Tilburg University (Netherlands) [presenting]
Katrijn Van Deun - Tilburg University (Netherlands)
Juan Vera Lizcano - Tilburg University (Netherlands)
Klaas Sijtsma - Tilburg University (Netherlands)
Abstract: Several sparse PCA methods have been introduced for reasons such as interpretability gains and improvement on statistical efficiency in the high-dimensional setting. Existing procedures for sparse PCA are based on different model formulations of PCA in combination with different optimization criteria and numerical techniques to obtain sparseness. The current sparse PCA literature misses clear guidance on the properties and performance of the different methods, often relying on the misconception that the equivalence of the formulations for ordinary PCA also holds in sparse PCA formulations. A guide on the implementation of sparse PCA is offered. First, we discuss several popular sparse PCA methods in terms of the assumed model, the optimization criterion used to impose sparseness, and the algorithmic procedure. Second, using extensive numerical experiments, we assess the performance of each of these methods on performance measures such as Mean Square Error, Percentage of explained variance, and Misidentification rate under several conditions for the population model. Our study highlights that the different sparse PCA methods may yield very different results. We offer some guiding rules in choosing among the different sparse PCA methods that are tailored to the aim of the PCA analysis and the characteristics of the data.