Sparse variable PCA using a steepest descent on a Grassman manifold

Recently there has developed considerable interest in using sparseness with PCA. Almost all previous methods concentrate on zeroing out some loadings. Here we develop a new approach which zeros out whole variables automatically. We formulate a vector l₁ penalized PCA criterion and optimize it by steepest descent along geodesic on a Grassman manifold. This ensures that each step obeys PCA orthogonality as well as an invariance property of the criterion. We show in simulations that it outperforms a previous svPCA algorithm and apply it to a real high dimensional functional Magnetic Resonance Imaging (fMRI) data.