ROBPCA: A New Approach to Robust Principal Component Analysis. We introduce a new method for robust principal component analysis (PCA). Classical PCA is based on the empirical covariance matrix of the data and hence is highly sensitive to outlying observations. Two robust approaches have been developed to date. The first approach is based on the eigenvectors of a robust scatter matrix such as the minimum covariance determinant or an S-estimator and is limited to relatively low-dimensional data. The second approach is based on projection pursuit and can handle high-dimensional data. Here we propose the ROBPCA approach, which combines projection pursuit ideas with robust scatter matrix estimation. ROBPCA yields more accurate estimates at noncontaminated datasets and more robust estimates at contaminated data. ROBPCA can be computed rapidly, and is able to detect exact-fit situations. As a by-product, ROBPCA produces a diagnostic plot that displays and classifies the outliers. We apply the algorithm to several datasets from chemometrics and engineering.

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  1. Alrawashdeh, Mufda Jameel; Radwan, Taha Radwan; Abunawas, Kalid Abunawas: Performance of linear discriminant analysis using different robust methods (2018)
  2. Wilcox, Rand: Modern statistics for the social and behavioral sciences. A practical introduction (2017)
  3. Greco, Luca; Farcomeni, Alessio: A plug-in approach to sparse and robust principal component analysis (2016)
  4. Heylen, Joke; van Mechelen, Iven; Verduyn, Philippe; Ceulemans, Eva: KSC-N: clustering of hierarchical time profile data (2016)
  5. Schmitt, Eric; Vakili, Kaveh: The FastHCS algorithm for robust PCA (2016)
  6. Fusco, Elisa: Enhancing non-compensatory composite indicators: a directional proposal (2015)
  7. Hubert, Mia; Rousseeuw, Peter; Segaert, Pieter: Rejoinder to `Multivariate functional outlier detection’ (2015)
  8. Harris, Paul; Brunsdon, Chris; Charlton, Martin; Juggins, Steve; Clarke, Annemarie: Multivariate spatial outlier detection using robust geographically weighted methods (2014)
  9. Hubert, M.; Rousseeuw, P.; Vakili, K.: Shape bias of robust covariance estimators: an empirical study (2014)
  10. Lim, Yaeji; Park, Yeonjoo; Oh, Hee-Seok: Robust principal component analysis via ES-algorithm (2014)
  11. Xanthopoulos, Petros; Guarracino, Mario R.; Pardalos, Panos M.: Robust generalized eigenvalue classifier with ellipsoidal uncertainty (2014)
  12. Liang, Zhiyu; Lee, Yoonkyung: Eigen-analysis of nonlinear PCA with polynomial kernels (2013)
  13. Morris, Katherine; McNicholas, Paul D.; Scrucca, Luca: Dimension reduction for model-based clustering via mixtures of multivariate $t$-distributions (2013)
  14. Todorov, Valentin; Filzmoser, Peter: Comparing classical and robust sparse PCA (2013)
  15. Turkmen, Asuman; Billor, Nedret: Partial least squares classification for high dimensional data using the PCOUT algorithm (2013)
  16. Boudt, Kris; Cornelissen, Jonathan; Croux, Christophe: The Gaussian rank correlation estimator: robustness properties (2012)
  17. Sawant, Pallavi; Billor, Nedret; Shin, Hyejin: Functional outlier detection with robust functional principal component analysis (2012)
  18. Todorov, Valentin; Templ, Matthias; Filzmoser, Peter: Detection of multivariate outliers in business survey data with incomplete information (2011) ioport
  19. Debruyne, Michiel; Hubert, Mia; Van Horebeek, Johan: Detecting influential observations in kernel PCA (2010)
  20. Debruyne, Michiel; Verdonck, Tim: Robust kernel principal component analysis and classification (2010)

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