Magnús Örn Úlfarsson
Sparse Principal Component Analysis
Principal component analysis (PCA) is a standard data analysis tool used in all branches of science and engineering. Sparse PCA combines PCA with the idea of sparseness and has been shown to be useful for large data sets arising for example in microarray data analysis and medical imaging. The are two kind of sparse PCA: sparse loading PCA (slPCA) and sparse variable PCA (svPCA). slPCA keeps all variables but zeroes out some of their loadings, but svPCA removes some variables completely by simultaneously zeroing out all their loadings. In this talk we will introduce a vector l1 penalized likelihood approach to svPCA. A formulation based on a optimization on a Grassmann manifold and a Stiefel manifold will be covered. The algorithm will be demonstrated on functional magnetic resonance imaging (fMRI) data.