A0924
Title: Sparse PCA with multiple components
Authors: Jean Pauphilet - London Business School (United Kingdom) [presenting]
Ryan Cory-Wright - Imperial College (United Kingdom)
Abstract: Sparse principal component analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves finding directions (or PCs) that are jointly sparse and mutually orthogonal. Most existing works address sparse PCA (via methods such as iteratively computing one sparse PC and deflating the covariance matrix) that do not guarantee the orthogonality, let alone the optimality, of the resulting solution. Several optimization approaches are presented (semidefinite, combinatorial, and non-convex) to derive both upper bounds (on the maximum amount of variance explainable) and feasible solutions (i.e., sparse orthogonal PCs). Numerically, the algorithms match (and sometimes surpass) the best performing methods in terms of fraction of variance explained and systematically return PCs that are sparse and orthogonal. In contrast, it is found that existing methods like deflation return solutions that violate the orthogonality constraints, even when the data is generated according to sparse orthogonal PCs.
