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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

Απλή Εγγραφή

URIhttp://purl.tuc.gr/dl/dias/D364CA99-C7DD-4326-A237-65839F1851AB-
Αναγνωριστικόhttps://doi.org/10.1109/TSP.2020.3039599-
Αναγνωριστικόhttps://ieeexplore.ieee.org/document/9266768-
Γλώσσαen-
Μέγεθος16 pagesen
ΤίτλοςReduced-rank L1-norm Principal-Component Analysis with performance guaranteesen
ΔημιουργόςKamrani Hosseinen
ΔημιουργόςAsli Alireza Zolghadren
ΔημιουργόςMarkopoulos Panagiotisen
ΔημιουργόςΜαρκοπουλος Παναγιωτηςel
ΔημιουργόςLangberg Michaelen
ΔημιουργόςPados Dimitris A.en
ΔημιουργόςKarystinos Georgiosen
ΔημιουργόςΚαρυστινος Γεωργιοςel
ΕκδότηςInstitute of Electrical and Electronics Engineersen
ΠερίληψηStandard 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
ΤύποςPeer-Reviewed Journal Publicationen
ΤύποςΔημοσίευση σε Περιοδικό με Κριτέςel
Άδεια Χρήσηςhttp://creativecommons.org/licenses/by/4.0/en
Ημερομηνία2023-03-06-
Ημερομηνία Δημοσίευσης2021-
Θεματική ΚατηγορίαFaulty dataen
Θεματική ΚατηγορίαL1-normen
Θεματική ΚατηγορίαMatrix analysisen
Θεματική ΚατηγορίαPCAen
Θεματική ΚατηγορίαOutliersen
Βιβλιογραφική ΑναφοράH. 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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