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Technical University of Crete
Technical University of Crete
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| URI | http://purl.tuc.gr/dl/dias/D364CA99-C7DD-4326-A237-65839F1851AB | - |
| Identifier | https://doi.org/10.1109/TSP.2020.3039599 | - |
| Identifier | https://ieeexplore.ieee.org/document/9266768 | - |
| Language | en | - |
| Extent | 16 pages | en |
| Title | Reduced-rank L1-norm Principal-Component Analysis with performance guarantees | en |
| Creator | Kamrani Hossein | en |
| Creator | Asli Alireza Zolghadr | en |
| Creator | Markopoulos Panagiotis | en |
| Creator | Μαρκοπουλος Παναγιωτης | el |
| Creator | Langberg Michael | en |
| Creator | Pados Dimitris A. | en |
| Creator | Karystinos Georgios | en |
| Creator | Καρυστινος Γεωργιος | el |
| Publisher | Institute of Electrical and Electronics Engineers | en |
| Content Summary | Standard Principal-Component Analysis (PCA) is known to be sensitive to outliers among the processed data. On the other hand, L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data [1]. Exact calculation of the K L1-norm Principal Components (L1-PCs) of a rank-r datamatrix X ∈ℝ D×N costs O(N (r-1)K+1 ) [1], [2]. In this work, we present reduced-rank L1-PCA (RR L1-PCA): a hybrid approach that approximates the K L1-PCs of X by the L1-PCs of its L2-norm-based rank-d approximation (d ≤ r), calculable exactly with reduced complexity O(N (d-1)K+1 ). The proposed method combines the denoising capabilities and low computation cost of standard PCA with the outlier-resistance of L1-PCA. RR L1-PCA is accompanied by formal performance guarantees as well as thorough numerical studies that corroborate its computational and corruption resistance merits. | 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 | 2023-03-06 | - |
| Date of Publication | 2021 | - |
| Subject | Faulty data | en |
| Subject | L1-norm | en |
| Subject | Matrix analysis | en |
| Subject | PCA | en |
| Subject | Outliers | en |
| Bibliographic Citation | H. Kamrani, A. Z. Asli, P. P. Markopoulos, M. Langberg, D. A. Pados and G. N. Karystinos, "Reduced-rank L1-norm Principal-Component Analysis with performance guarantees," IEEE Trans. Signal Process., vol. 69, pp. 240-255, 2021, doi: 10.1109/TSP.2020.3039599. | en |
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