Algorithms for Projection-Pursuit Robust Principal Component Analysis

By Christophe Croux, Peter Filzmoser, M. R. Oliveira. 2007

258 citations recorded by the source corpus.

Principal Component Analysis (PCA) is very sensitive in presence of outliers. One of the most appealing robust methods for principal component analysis uses the Projection-Pursuit principle. Here, one projects the data on a lower-dimensional space such that a robust measure of variance of the projected data will be maximized. The Projection-Pursuit based method for principal component analysis has recently been introduced in the field of chemometrics, where the number of variables is typically large. In this paper, it is shown that the currently available algorithm for robust Projection-Pursuit PCA performs poor in presence of many variables. A new algorithm is proposed that is more suitable for the analysis of chemical data. Its performance is studied by means of simulation experiments and illustrated on some real datasets.

Subfields: Analytical Chemistry, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Analytical Chemistry

1. Peter J. Rousseeuw
2. Mia Hubert
3. Hamid Babamoradi
4. Å. Rinnan
5. Franciscus Winfried J van der Berg
6. Battista Biggio
7. Anthony D. Joseph
8. Fabio Roli

In Statistics and Probability

1. Mia Hubert
2. Peter J. Rousseeuw
3. Joel A. Tropp
4. Michael B. McCoy
5. Å. Rinnan
6. Franciscus Winfried J van der Berg
7. Hamid Babamoradi
8. Gilad Lerman

Citations in the corpus

• Adversarial Feature Selection Against Evasion Attacks (2016, background): “An example is given in [10], [26], where the authors have exploited a robust version of the principal component analysis (originally proposed in [64]) to reduce the influence of poisoning attacks in the training data, yielding a more secure network traffic anomaly detector.”
• Robust Computation of Linear Models by Convex Relaxation (2012, result): “], and it has been explored by many other authors [1,18,43,49,75].”
• Pattern Recognition Systems under Attack: Design Issues and Research Challenges (2014, unknown): “, robust principal component analysis [66, 29]).”
• An Object-Oriented Framework for Robust Multivariate Analysis (2009, unknown): “To improve the performance of the algorithm for high dimensional data a new improved version was proposed by Croux et al. (2007).”
• 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.”
• Adversarial machine learning (2019, methodology): “as an efficient method for estimating directions that maximize the median absolute deviation (MAD) without under-estimating variance [15].”
• ANTIDOTE: understanding and defending against poisoning of anomaly detectors (2009, methodology): “Because PCA solely focuses on link tra.c covariance, we explore poi­soning schemes that add cha.”
• Bootstrap based confidence limits in principal component analysis: a case study (2013, methodology): “Another possible way to suppress the influence of outliers is to apply (computationally demanding) robust PCA [35,37–39], which is however outside the scope of this paper on bootstrap-based uncertainty estimation.”