EE 381V Project : A Survey on Sparse PCA

Principal Component Analysis (PCA) is a frequently used tool to analyse, visualize and reduce the dimensionality of data occurring in a variety of fields in science and engineering. Given a data matrix X ∈ Rn×p (where n is the number of points and p is the dimensionality), PCA finds a set of d(≪ p) orthonormal vectors V = {v1, v2, . . . , vd} in R such that the span(V ) explains the maximum amount of variance in the data (or equivalently, the projection of the data onto span(V ) is maximized). This can be cast as a sequence of optimization problems, as follows :