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Proceedings Paper

L1-norm principal-component analysis in L2-norm-reduced-rank data subspaces
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Paper 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.

Paper Details

Date Published: 5 May 2017
PDF: 10 pages
Proc. SPIE 10211, Compressive Sensing VI: From Diverse Modalities to Big Data Analytics, 1021104 (5 May 2017); doi: 10.1117/12.2263733
Show Author Affiliations
Panos P. Markopoulos, Rochester Institute of Technology (United States)
Dimitris A. Pados, Univ. at Buffalo (United States)
George N. Karystinos, Technical Univ. of Crete (Greece)
Michael Langberg, Univ. at Buffalo (United States)

Published in SPIE Proceedings Vol. 10211:
Compressive Sensing VI: From Diverse Modalities to Big Data Analytics
Fauzia Ahmad, Editor(s)

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