Projection Sparse Principal Component Analysis: an efficient least squares method

We propose a new sparse principal component analysis (SPCA) method in which the solutions are obtained by projecting the full cardinality principal components onto subsets of variables. The resulting components are guaranteed to explain a given proportion of variance. The computation of these solutions is very efficient. The proposed method compares well with the optimal least squares sparse components. We show that other SPCA methods fail to identify the best sparse approximations of the principal components and explain less variance than our solutions. We illustrate and compare our method with the analysis of a real dataset containing socioeconomic data and the computational results for nine datasets of increasing dimension with up to 16,000 variables.