A pure \(L_1\)-norm principal component analysis

DOI10.1016/j.csda.2012.11.007zbMath1349.62247OpenAlexW2068722138WikidataQ37103543 ScholiaQ37103543MaRDI QIDQ333698

José H. Dulá, Edward L. Boone, J. Paul Brooks

Publication date: 31 October 2016

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.csda.2012.11.007

zbMATH Keywords

linear programmingprincipal component analysis\(L_{1}\) regression

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Nonparametric robustness (62G35)

Related Items (13)

Robust \(\ell_1\) approaches to computing the geometric median and principal and independent components ⋮ Hankel tensor-based model and \(L_1\)-Tucker decomposition-based frequency recovery method for harmonic retrieval problem ⋮ Non-Negative Sparse Regression and Column Subset Selection with L1 Error ⋮ A survey of high dimension low sample size asymptotics ⋮ Reduced row echelon form and non-linear approximation for subspace segmentation and high-dimensional data clustering ⋮ Unnamed Item ⋮ Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning ⋮ Principal component analysis: a generalized Gini approach ⋮ Joint sparse principal component analysis ⋮ On the Complexity of Robust PCA and ℓ₁-Norm Low-Rank Matrix Approximation ⋮ Modal Principal Component Analysis ⋮ WILCOXON RANK BASED PRINCIPAL COMPONENT ANALYSIS ⋮ Optimization for L₁-Norm Error Fitting via Data Aggregation

Uses Software

• LAPACK
• R
• CPLEX
• pcaPP
• pcaL1

Cites Work

• Unnamed Item
• High breakdown estimators for principal components: the projection-pursuit approach revis\-ited
• L1-norm projection pursuit principal component analysis
• Methods of \(L_ 1\) estimation of a covariance matrix
• On orthogonal linear \(\ell_1\) approximation
• Median hyperplanes in normed spaces -- a survey
• Arbitrary-norm separating plane
• The \(L_1\)-norm best-fit hyperplane problem
• Principal component analysis.
• Optimal Estimation of Executive Compensation by Linear Programming
• On L1 and Chebyshev estimation
• Linear Programming Techniques for Regression Analysis
• Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo
• Stability of principal component analysis studied by the bootstrap method
• LAPACK Users' Guide
• Robust L1 Principal Component Analysis and Its Bayesian Variational Inference

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