Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo

By Guoying Li, Zhonglian Chen. 1985

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Citations in the corpus

ANTIDOTE: understanding and defending against poisoning of anomaly detectors (2009, methodology): “Robust PCA algorithms instead use measures of dispersion based on the concept of robust projection pursuit (RPP) estimators [19].”
Sliced Inverse Regression for Dimension Reduction (1991, background): “Some robust versions of them may be preferable (see Donoho, Johnstone, Rousseeuw, and Stahe11985; Fill and Johnstone 1984;and Li and Chen 1985).”
Robust statistics for outlier detection (2011, methodology): “These methods maximize a robust measure of spread to obtain consecutive directions on which the data points are projected, see Refs 31–34.”
High breakdown estimators for principal components: the projection-pursuit approach revisited (2005, methodology): “The proof results immediately from arguments given by Li and Chen 1985, page 760.”
Robust methods for partial least squares regression (2003, background): “For such high-dimensional data sets, projection pursuit algorithms have been developed [12], [7].”
Sign and rank covariance matrices (2000, methodology): “For still another projection pursuit based approach see Huber (1981), Li and Chen (1985) and Croux and Ruiz-Gazen (1997).”
Robust functional principal components: A projection-pursuit approach (2011, methodology): “This approach was introduced by Li and Chen (1985), who proposed estimators based on maximizing (or minimizing) a robust scale.”
An Object-Oriented Framework for Robust Multivariate Analysis (2009, unknown): “Such a method was ﬁrst introduced by Li and Chen (1985) using an M estimator of scale S n as a projection index (PI) .”
Computational Statistics Handbook with MATLAB (2001, methodology): “These include projection pursuit probability density estimation [Friedman, Stuetzle, and Schroeder, 1984], projection pursuit regression [Friedman and Stuetzle, 1981], robust estimation [Li and Chen, 1985], and projection pursuit for pattern recognition [Flick, et al.”
Robust Computation of Linear Models by Convex Relaxation (2012, result): “], and it has been explored by many other authors [1,18,43,49,75].”
Inferences Based on a Skipped Correlation Coefficient (2004, unknown): “…Online/04/020131-13 © 2004 Taylor & Francis Ltd DOI: 10.1080/0266476032000148821 (1996), Rousseeuw & Leroy (1987), Rocke (1996), Hampel et al. (1986, chapter 5), Li & Chen (1985), Lupuhaä (1989), Stahel (1981), Donoho (1982), Marrona (1976), Mosteller & Tukey (1977, p. 211) and Wilcox (1997).”
Robust PCA via Outlier Pursuit (2010, background): “Algorithms with non-diminishing breakdown point, such as P rojection-Pursuit [25] are non-convex or even combinatorial, and hence computationally intracta ble (NP-hard) as the size of the problem scales.”
Behavior of Machine Learning Algorithms in Adversarial Environments (2010, methodology): “Robust PCA algorithms instead use measures of dispersion based on the concept of robust projection pursuit (RPP) estimators [Li and Chen, 1985].”