ROBPCA: A New Approach to Robust Principal Component Analysis

@article{Hubert2005ROBPCAAN,
  title={ROBPCA: A New Approach to Robust Principal Component Analysis},
  author={Mia Hubert and Peter Rousseeuw and Karlien Vanden Branden},
  journal={Technometrics},
  year={2005},
  volume={47},
  pages={64 - 79}
}
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… Expand
View on Taylor & Francis
stat.osu.edu
838 Citations
Highly Influential Citations
61
Background Citations
122
Methods Citations
232
Results Citations
3

838 Citations

Citation Type

Citation Type

Robust PCA and classification in biosciences
TLDR
A robust PCA (ROBPCA) method is proposed that combines projection-pursuit ideas with robust estimation of low-dimensional data and shows that this combination of robust methods leads to better classifications than classical PCA and quadratic discriminant analysis. Expand
Chapter 34 The New Measure of Robust Principal Component Analysis
Principal Component Analysis (PCA) is a technique to transform the original set of variables into a smaller set of linear combinations that account for most of the original set variance. The data… Expand
The New Measure of Robust Principal Component Analysis
Principal Component Analysis (PCA) is a technique to transform the original set of variables into a smaller set of linear combinations that account for most of the original set variance. The data… Expand
S-Estimators for Functional Principal Component Analysis
Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in… Expand
Robust principal component analysis via ES-algorithm
Abstract In this paper, a new method for robust principal component analysis (PCA) is proposed. PCA is a widely used tool for dimension reduction without substantial loss of information. However, the… Expand
Robust Sparse Principal Component Analysis
TLDR
The method is applied on several real data examples, and diagnostic plots for detecting outliers and for selecting the degree of sparsity are provided, and an algorithm to compute the sparse and robust principal components is proposed. Expand
The Robust Principal Component Using Minimum Vector Variance
Component Analysis (PCA) is a technique to transform the original set of variables into a smaller set of linear combinations that account for most of the original set variance. The data reduction… Expand
Sparse Principal Component Analysis Based on Least Trimmed Squares
TLDR
A robust sparsePCA method is proposed to handle potential outliers in the data based on the least trimmed squares PCA method which provides robust but non-sparse PC estimates and the computation time is reduced to a great extent. Expand
Algorithms for Projection-Pursuit Robust Principal Component Analysis
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,… Expand
Robust and Sparse Kernel PCA and Its Outlier Map
TLDR
A two-stage algorithm was proposed: a robust distance was computed to identify the uncontaminated data set, followed by estimating the best-fit ellipsoid to these data for an informative and concise representation, and a kernel PCA outlier map was proposed to display and classify the outliers. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 45 REFERENCES
Robust PCA and classification in biosciences
TLDR
A robust PCA (ROBPCA) method is proposed that combines projection-pursuit ideas with robust estimation of low-dimensional data and shows that this combination of robust methods leads to better classifications than classical PCA and quadratic discriminant analysis. Expand
A fast method for robust principal components with applications to chemometrics
When faced with high-dimensional data, one often uses principal component analysis (PCA) for dimension reduction. Classical PCA constructs a set of uncorrelated variables, which correspond to… Expand
Fast cross-validation in robust PCA
One of the main issues in Principal Component Analysis (PCA) is the selection of the number of principal components. To determine this number, the Predicted Residual Error Sum of Squares (PRESS)… Expand
High breakdown estimators for principal components: the projection-pursuit approach revisited
Li and Chen (J. Amer. Statist. Assoc. 80 (1985) 759) proposed a method for principal components using projection-pursuit techniques. In classical principal components one searches for directions with… Expand
A robust PCR method for high‐dimensional regressors
We consider the multivariate calibration model which assumes that the concentrations of several constituents of a sample are linearly related to its spectrum. Principal component regression (PCR) is… Expand
Fast and robust discriminant analysis
TLDR
Robust discriminant rules are obtained by inserting robust estimates of location and scatter into generalized maximum likelihood rules at normal distributions and the highly robust MCD estimator is used as it can be computed very fast for large data sets. Expand
Robust methods for partial least squares regression
Partial least squares regression (PLSR) is a linear regression technique developed to deal with high‐dimensional regressors and one or several response variables. In this paper we introduce… Expand
A fast algorithm for the minimum covariance determinant estimator
The minimum covariance determinant (MCD) method of Rousseeuw is a highly robust estimator of multivariate location and scatter. Its objective is to find h observations (out of n) whose covariance… Expand
The kernel PCA algorithms for wide data. Part I: Theory and algorithms
Four classic PCA algorithms: NIPALS, the power method (POWER), singular value decomposition (SVD) and eigenvalue decomposition (EVD) are modified into their kernel version to analyse wide data sets.… Expand
LIBRA: a MATLAB library for robust analysis
TLDR
A MATLAB library of robust statistical methods used by chemometricians, statisticians, chemists, and engineers is introduced and many graphical tools to detect and classify the outliers are provided. Expand
...
1
2
3
4
5
...