Some Options for L1-subspace Signal Processing
Conference: ISWCS 2013 - The Tenth International Symposium on Wireless Communication Systems
08/27/2013 - 08/30/2013 at Ilmenau, Deutschland
Proceedings: ISWCS 2013
Pages: 5Language: englishTyp: PDF
Personal VDE Members are entitled to a 10% discount on this title
Authors:
Markopoulos, Panos P.; Pados, Dimitris A. (Electrical Engineering Dept., State University of New York at Buffalo, Buffalo, NY 14260, USA)
Karystinos, George N. (Electronic and Computer Engineering Dept., Technical University of Crete, Chania, 73100, Greece)
Abstract:
We describe ways to define and calculate L1-norm signal subspaces which are less sensitive to outlying data than L2-calculated subspaces. We focus on the computation of the L1 maximum-projection principal component of a data matrix containing N signal samples of dimension D and conclude that the general problem is formally NP-hard in asymptotically large N, D. We prove, however, that the case of engineering interest of fixed dimension D and asymptotically large sample support N is not and we present an optimal algorithm of complexity O(N(exp D)). We generalize to multiple L1-max-projection components and present an explicit optimal L1 subspace calculation algorithm in the form of matrix nuclear-norm evaluations. We conclude with illustrations of L1-subspace signal processing in the fields of data dimensionality reduction and direction-of-arrival estimation.