Reduced-rank L1-norm Principal-Component Analysis with performance guaranteesReduced-rank L1-norm Principal-Component Analysis with performance guarantees Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2023-03-062021enStandard 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.http://creativecommons.org/licenses/by/4.0/IEEE Transactions on Signal Processing69240-255 Kamrani Hossein Asli Alireza Zolghadr Markopoulos Panagiotis Μαρκοπουλος Παναγιωτης Langberg Michael Pados Dimitris A. Karystinos Georgios Καρυστινος Γεωργιος Institute of Electrical and Electronics Engineers Faulty data L1-norm Matrix analysis PCA Outliers