Some Options for L1-Subspace Signal Processing
| Autor: | Markopoulos, Panos P., Karystinos, George N., Pados, Dimitris A. |
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| Rok vydání: | 2013 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: In Proceedings Tenth Intern. Symposium on Wireless Communication Systems (ISWCS '13), Ilmenau, Germany, Aug. 27-30, 2013 (The 2013 ISWCS Best Paper Award in Physical Layer Comm. and Signal Processing); 5 pages; 3 figures |
| Databáze: | arXiv |
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