Sparse variable noisy PCA using l0 penalty

Sparse principal component analysis combines the idea of sparsity with principal component analysis (PCA). There are two kinds of sparse PCA; sparse loading PCA (slPCA) which keeps all the variables but zeroes out some of their loadings; and sparse variable PCA (svPCA) which removes whole variables by simultaneously zeroing out all the loadings on some variables. In this paper we propose a model based svPCA method based on the l₀ penalty. We compare the detection performance of the proposed method with other subset selection method using a simulated data set. Additionally, we apply the method on a real high dimensional functional magnetic resonance imaging (fMRI) data set.