A Fast deflation Method for Sparse Principal Component Analysis via Subspace Projections

Given a data set, PCA aims at finding a sequence of orthogonal vectors that repr esent the directions of largest variance. By capturing these directions, the princ ipal components offer a way to compress the data with minimum information loss. However, principal components are usually linear combinations of all original features. That is, the weights in the linear combinations (known as loadings) are typically nonzero. I n this sense, it is difficult to give a good physical interpretation. During the past decade, various sparse principal component analysis (SPCA) approaches have been developed to improve the interpretabili ty of principal components. SPCA is an extension of PCA that aims at finding sparse loading vectors capturing the maximum amount of variance in the data. These SPCA methods ca n be categorized into two groups: block methods [16,20,22-24,32] and deflati on methods [5,7,25,28]. Block methods aims to find all sparse loadings together, whil e deflation methods compute one loading at a time.