Incremental and Adaptive L1-Norm Principal Component Analysis: Novel Algorithms and Applications

L1-norm Principal-Component Analysis (L1-PCA) is known to attain remarkable resistance against faulty/corrupted points among the processed data. However, computing L1-PCA of “big data” with large number of measurements and/or dimensions may be computationally impractical. This work proposes new algorithmic solutions for incremental and adaptive L1-PCA. The first algorithm computes L1-PCA incrementally, processing one measurement at a time, with very low computational and memory requirements; thus, it is appropriate for big data and big streaming data applications. The second algorithm combines the merits of the first one with additional ability to track changes in the nominal signal subspace by revising the computed L1-PCA as new measurements arrive, demonstrating both robustness against outliers and adaptivity to signal-subspace changes. The proposed algorithms are evaluated in an array of experimental studies on subspace estimation, video surveillance (foreground/background separation), image conditioning, and direction-of-arrival (DoA) estimation