  Sparse Principal Components Analysis aims to find principal components with
few non-zero loadings. We derive such sparse solutions by adding a genuine
sparsity requirement to the original Principal Components Analysis (PCA)
objective function. This approach differs from others because it preserves
PCA's original optimality: \uns\ of the components and Least Squares
approximation of the data. To identify the best subset of non-zero loadings we
propose a Branch-and-Bound search and an iterative elimination algorithm. This
last algorithm finds sparse solutions with large loadings and can be run
without specifying the cardinality of the loadings and the number of components
to compute in advance. We give thorough comparisons with the existing Sparse
PCA methods and several examples on real datasets.
