Computational advances in sparse L1-norm principal-component analysis of multi-dimensional data

Abstract

We consider the problem of extracting a sparse Li-norm principal component from a data matrix X ∊ R^D×N of N observation vectors of dimension D. Recently, an optimal algorithm was presented in the literature for the computation of sparse L1-norm principal components with complexity O(N^S) where S is the desired sparsity. In this paper, we present an efficient suboptimal algorithm of complexity O(N²(N + D)). Extensive numerical studies demonstrate the near-optimal performance of the proposed algorithm and its strong resistance to faulty measurements/outliers in the data matrix.