Functional principal component analysis (FPCA) is a popular approach in functional data analysis to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). Most existing FPCA approaches use a set of flexible basis functions such as B-spline basis to represent the FPCs, and control the smoothness...

PETER D. WENTZELL, DARREN T. ANDREWS, DAVID C. HAMILTON, KLAAS FABER AND BRUCE R. KOWALSKI 1 Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, Halifax, Nova Scotia B3H 4J3, Canada 2 Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia B3H 3J5, Canada 3 Center for Process Analytical Chemistry, University of Washingto...

High-dimensional Principal Component Analysis by Arash Ali Amini Doctor of Philosophy in Electrical Engineering University of California, Berkeley Associate Professor Martin Wainwright, Chair Advances in data acquisition and emergence of new sources of data, in recent years, have led to generation of massive datasets in many fields of science and engineering. These datasets are usually characte...

We present an extension of sparse PCA, or sparse dictionary learning, where the sparsity patterns of all dictionary elements are structured and constrained to belong to a prespecified set of shapes. This structured sparse PCA is based on a structured regularization recently introduced by [1]. While classical sparse priors only deal with cardinality, the regularization we use encodes higher-orde...