Principle component analysis: Robust versions

Modern problems of optimization, estimation, signal and image processing, pattern recognition, etc., deal with huge-dimensional data; this necessitates elaboration of efficient methods of processing such data. The idea of building low-dimensional approximations to huge data arrays is in the heart of the modern data analysis.One of the most appealing methods of compact data representation is the statistical method referred to as the principal component analysis; however, it is sensitive to uncertainties in the available data and to the presence of outliers. In this paper, robust versions of the principle component analysis approach are proposed along with numerical methods for their implementation.

[1]  Olcay Arslan,et al.  Convergence behavior of an iterative reweighting algorithm to compute multivariate M-estimates for location and scatter , 2004 .

[2]  C. Croux,et al.  Principal Component Analysis Based on Robust Estimators of the Covariance or Correlation Matrix: Influence Functions and Efficiencies , 2000 .

[3]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[4]  Frank Plastria,et al.  Asymmetric distances, semidirected networks and majority in Fermat–Weber problems , 2009, Ann. Oper. Res..

[5]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[6]  G. Shevlyakov,et al.  Robustness in Data Analysis: Criteria and Methods , 2001 .

[7]  M. Shirosaki.  Another proof of the defect relation for moving targets , 1991 .

[8]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[9]  Yakov Z. Tsypkin,et al.  Robust identification , 1980, Autom..

[10]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[11]  G. Box.  NON-NORMALITY AND TESTS ON VARIANCES , 1953 .

[12]  Yi Ma,et al.  Robust principal component analysis? , 2009, JACM.

[13]  I. Jolliffe.  Principal Component Analysis , 2002 .

[14]  Xiaodong Li,et al.  Stable Principal Component Pursuit , 2010, 2010 IEEE International Symposium on Information Theory.