title: A Pure L1-norm Principal Component Analysis.
abstract: TheL1norm has been applied in numerous variations of principal component analysis (PCA).L1-norm PCA is an attractive alternative to traditionalL2-based PCA because it can impart robustness in the presence of outliers and is indicated for models where standard Gaussian assumptions about the noise may not apply. Of all the previously-proposed PCA schemes that recast PCA as an optimization problem involving theL1norm, none provide globally optimal solutions in polynomial time. This paper proposes anL1-norm PCA procedure based on the efficient calculation of the optimal solution of theL1-norm best-fit hyperplane problem. We present a procedure calledL1-PCA* based on the application of this idea that fits data to subspaces of successively smaller dimension. The procedure is implemented and tested on a diverse problem suite. Our tests show thatL1-PCA* is the indicated procedure in the presence of unbalanced outlier contamination.
authors: Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284.
authors: Jp
authors: J
authors: Brooks
authors: Jh
authors: J
authors: Dulá
authors: El
authors: E
authors: Boone
keywords: L1 regression; linear programming; principal component analysis
references: Neural Comput. 2008 Feb;20(2):555-72
references: 18045015
references: IEEE Trans Pattern Anal Mach Intell. 2008 Sep;30(9):1672-80
references: 18617723
references: Appl Math Lett. 2012 Jan 1;26(1):51-56
references: 23024460