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Reduced-rank L1-norm Principal-Component Analysis with performance guarantees

Kamrani Hossein, Asli Alireza Zolghadr, Markopoulos Panagiotis, Langberg Michael, Pados Dimitris A., Karystinos Georgios

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URIhttp://purl.tuc.gr/dl/dias/D364CA99-C7DD-4326-A237-65839F1851AB-
Identifierhttps://doi.org/10.1109/TSP.2020.3039599-
Identifierhttps://ieeexplore.ieee.org/document/9266768-
Languageen-
Extent16 pagesen
TitleReduced-rank L1-norm Principal-Component Analysis with performance guaranteesen
CreatorKamrani Hosseinen
CreatorAsli Alireza Zolghadren
CreatorMarkopoulos Panagiotisen
CreatorΜαρκοπουλος Παναγιωτηςel
CreatorLangberg Michaelen
CreatorPados Dimitris A.en
CreatorKarystinos Georgiosen
CreatorΚαρυστινος Γεωργιοςel
PublisherInstitute of Electrical and Electronics Engineersen
Content SummaryStandard 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 ItemPeer-Reviewed Journal Publicationen
Type of ItemΔημοσίευση σε Περιοδικό με Κριτέςel
Licensehttp://creativecommons.org/licenses/by/4.0/en
Date of Item2023-03-06-
Date of Publication2021-
SubjectFaulty dataen
SubjectL1-normen
SubjectMatrix analysisen
SubjectPCAen
SubjectOutliersen
Bibliographic CitationH. 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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