Some Options for L1-Subspace Signal Processing

Panos P. Markopoulos; George N. Karystinos; Dimitris A. Pados

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arXiv · 1309.1194

Some Options for L1-Subspace Signal Processing

Panos P. Markopoulos·George N. Karystinos·Dimitris A. Pados

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Abstract

We describe ways to define and calculate $L_1$-norm signal subspaces which are less sensitive to outlying data than $L_2$-calculated subspaces. We focus on the computation of the $L_1$ 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 $O(N^D)$. We generalize to multiple $L_1$-max-projection components and present an explicit optimal $L_1$ subspace calculation algorithm in the form of matrix nuclear-norm evaluations. We conclude with illustrations of $L_1$-subspace signal processing in the fields of data dimensionality reduction and direction-of-arrival estimation.

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BibTeX RIS

Panos P. Markopoulos, George N. Karystinos, Dimitris A. Pados. 2013-09-04. Some Options for L1-Subspace Signal Processing. https://arxiv.org/abs/1309.1194

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