Sparse Principal Component Analysis with Model order Reduction

Abstract

Principal Component Analysis (PCA) has become a standard tool for identification of the maximal variance in data. The directions of maximum variance provide very insightful information about the data in a lot of applications. By augmenting the PCA problem with a penalty term that promotes sparsity, we are able to obtain sparse vectors describing the direction of maximum variance in the data. A sparse vector becomes very useful in many applications like finance, where it has a direct impact on cost. An algorithm which computes principal component vector in in a reduced space by using model order reduction techniques and enforces sparsity in the full space is described in this work. We achieve computational savings by enforcing sparsity in different coordinates than those in which the principal components are computed. This is illustrated by applying the algorithm to synthetic data. The algorithm is also applied to the linearized Navier-Stokes equations for a plane channel flow.