Institutional Repository
Technical University of Crete
Technical University of Crete
EN
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EL
| URI | http://purl.tuc.gr/dl/dias/326A05A2-8523-4A97-9B95-F5FDEAADC5D3 | - |
| Identifier | https://doi.org/10.1109/TSP.2014.2338077 | - |
| Language | en | - |
| Extent | 12 | en |
| Title | Optimal algorithms for L1 -subspace signal processing | en |
| Creator | Markopoulos Panagiotis | en |
| Creator | Μαρκοπουλος Παναγιωτης | el |
| Creator | Karystinos Georgios | en |
| Creator | Καρυστινος Γεωργιος | el |
| Creator | Pados, D.A | en |
| Publisher | Institute of Electrical and Electronics Engineers | en |
| Description | Δημοσίευση σε επιστημονικό περιοδικό | el |
| Content Summary | We describe ways to define and calculate L1-norm signal subspaces that are less sensitive to outlying data than L2-calculated subspaces. We start with the computation of the L1 maximum-projection principal component of a data matrix containing N signal samples of dimension D. We show that while the general problem is formally NP-hard in asymptotically large N, D, the case of engineering interest of fixed dimension D and asymptotically large sample size N is not. In particular, for the case where the sample size is less than the fixed dimension , we present in explicit form an optimal algorithm of computational cost 2N. For the case N ≥ D, we present an optimal algorithm of complexity O(ND). We generalize to multiple L1-max-projection components and present an explicit optimal L1 subspace calculation algorithm of complexity O(NDK-K+1) where K is the desired number of L1 principal components (subspace rank). We conclude with illustrations of L1-subspace signal processing in the fields of data dimensionality reduction, direction-of-arrival estimation, and image | en |
| Type of Item | Peer-Reviewed Journal Publication | en |
| Type of Item | Δημοσίευση σε Περιοδικό με Κριτές | el |
| License | http://creativecommons.org/licenses/by/4.0/ | en |
| Date of Item | 2015-10-23 | - |
| Date of Publication | 2014 | - |
| Subject | $L_{1}$ norm | en |
| Subject | $L_{2}$ norm | en |
| Subject | dimensionality reduction | en |
| Subject | direction-of-arrival estimation | en |
| Subject | eigendecomposition | en |
| Subject | erroneous data | en |
| Subject | faulty measurements | en |
| Subject | machine learning | en |
| Subject | outlier resistance | en |
| Subject | subspace signal processing | en |
| Bibliographic Citation | P. P. Markopoulos, G. N. Karystinos, and D. A. Pados, "Optimal algorithms for L1 -subspace signal processing," IEEE Transactions on Signal Processing, vol. 62, no. 19, pp. 5046 - 5058, Oct. 2014. doi: 10.1109/TSP.2014.2338077 | en |
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