5 May 2017 L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces
Author Affiliations +
Abstract
Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data.1 On the other hand, it has been recently shown that 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.2, 3 Exact calculation of the K L1-norm Principal Components (L1-PCs) of a rank-r data matrix X∈ RD×N costs O(2NK), in the general case, and O(N(r-1)K+1) when r is fixed with respect to N.2, 3 In this work, we examine approximating the K L1-PCs of X by the K L1-PCs of its L2-norm-based rank-d approximation (K≤d≤r), calculable exactly with reduced complexity O(N(d-1)K+1). Reduced-rank L1-PCA aims at leveraging both the low computational cost of standard PCA and the outlier-resistance of L1-PCA. Our novel approximation guarantees and experiments on dimensionality reduction show that, for appropriately chosen d, reduced-rank L1-PCA performs almost identical to L1-PCA.
Conference Presentation
© (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Panos P. Markopoulos, Panos P. Markopoulos, Dimitris A. Pados, Dimitris A. Pados, George N. Karystinos, George N. Karystinos, Michael Langberg, Michael Langberg, } "L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces", Proc. SPIE 10211, Compressive Sensing VI: From Diverse Modalities to Big Data Analytics, 1021104 (5 May 2017); doi: 10.1117/12.2263733; https://doi.org/10.1117/12.2263733
PROCEEDINGS
10 PAGES + PRESENTATION

SHARE
Back to Top