Methods of L1-estimation of a covariance matrix
Computational Statistics & Data Analysis - Special issue on statistical data analysis based on the L:0I1:0E norm and relate
Correspondence analysis with least absolute residuals
Computational Statistics & Data Analysis - Special issue on statistical data analysis based on the L:0I1:0E norm and relate
An algorithm for nonmetric discriminant analysis
Computational Statistics & Data Analysis
The Centroid Decomposition: Relationships between Discrete Variational Decompositions and SVDs
SIAM Journal on Matrix Analysis and Applications
Robust Q-mode principal component analysis in L1
Computational Statistics & Data Analysis
Editorial: Nonparametric and Robust Methods
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
Neurocomputing
A pure L1-norm principal component analysis
Computational Statistics & Data Analysis
Graph Partitioning by Correspondence Analysis and Taxicab Correspondence Analysis
Journal of Classification
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We develop a new method of robust principal component analysis based on the L"1-norm projection pursuit approach. The aim of the paper is threefold. First, we present the underlying mathematical theory and show that it is closely related to the old centroid method of calculating principal components. Second, we present three algorithms to perform the required calculations. Third, we use Benzecri's geometric relative measure of the influence of a point on a principal axis to define cutpoints for the identification of outliers, and iteratively use it to eliminate outliers and obtain robust L"1-norm projection pursuit principal components. Two examples of well-known data sets are provided.