Summer School on

Sparsity in Image and Signal Analysis

At Hólar, Iceland, August 16 - 20, 2010 (both days included)

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.

Summer School on Sparsity in Image and Signal Analysis, Hólar, Iceland