Institutional Repository
Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/326A05A2-8523-4A97-9B95-F5FDEAADC5D3 | ||
| Year | 2014 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| 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 https://doi.org/10.1109/TSP.2014.2338077 | ||
| Appears in Collections |
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
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