Title
Sparse Principal Subspace Estimation
Speaker
Vince Vu, Carnegie Mellon University
Abstract
Principal components analysis (PCA) is an important and widely used technique for dimension reduction in the visualization and analysis of multivariate data. Its main idea is to capture the principal modes of variation of the data within a subspace spanned by the leading eigenvectors of a population covariance matrix. Unfortunately, it may not provide consistent estimates of the population eigenvectors when applied to high-dimensional data.
In this talk I introduce a new method, sparse principal subspace estimation, that is more suitable for the high-dimensional regime. The method builds on the main idea of PCA by imposing the following constraint: the principal subspace of variation is spanned mostly by a smaller number of variables. This sparsity constraint is reasonable when the signal of interest has sparse representation in some basis, and importantly, it can make estimation feasible and enhance interpretability in high-dimensions. I will discuss theoretical properties, algorithmic issues, and examples in data visualization and the analysis of neuroimaging data.