  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.
