Fast computation of the L1-principal component of real-valued data

Abstract

Recently, Markopoulos et al. [1], [2] presented an optimal algorithm that computes the L1 maximum-projection principal component of any set of N real-valued data vectors of dimension D with complexity polynomial in N, O(ND). Still, moderate to high values of the data dimension D and/or data record size N may render the optimal algorithm unsuitable for practical implementation due to its exponential in D complexity. In this paper, we present for the first time in the literature a fast greedy single-bit-flipping conditionally optimal iterative algorithm for the computation of the L1 principal component with complexity O(N3). Detailed numerical studies are carried out demonstrating the effectiveness of the developed algorithm with applications to the general field of data dimensionality reduction and direction-of-arrival estimation.