Removing or weighting outliers (7 papers)
1. Removing outliers (3 papers)
D. Geiger, R. Pereira, "The outlier process", IEEE Workshop on Neural Networks for Signal Processing", pages 61-69, 1991.
M. Black, A. Rangarajan, "On the unification of line processes, outlier rejection, and robust statistics with applications in early vision", International Journal on Computer Vision, Volume 25, No. 19, pages 57-92, 1996.
P. Filzmoser, R. Maronna, M. Werner, "Outlier identification in high dimensions", Technometrics, pages 1694-1711, 2008.
2. Weighting outliers (4 papers)
K. Gabriel, S. Zamir, "Lower rank approximation of matrices by least squares with any choice of weights", Technometrics, Volume 21, pages 489-498, 1979.
L. Delchambre, “Weighted principal component analysis: a weighted covariance eigen-decomposition approach”, Monthly Notices of the Royal Astronomical Society, pages 1-12, 2014.
Y. Deng, K. Hu, B. Li, Y. Zhang, "Robust Principal Component Analysis via Discriminant Sample Weight Learning", Preprint, 2024.
S. Wang, F. Nie, Z. Wang, R. Wang, X. Li, "Data Subdivision based Dual-Weighted Robust Principal Component Analysis", IEEE Transactions on Image Processing, Volume 34, pages 1271-1284, 2025.
Robust Estimation of Mean and Covariance (39 papers)
1. Affine-Equivariant M-Estimators of Scatter (12 papers) [Not robust to many outliers]
R. Maronna, "Robust M-Estimators of Multivariate Location and Scatter", The Annals of Statistics, Volume 4, pages 51-67, 1976.
N. Campell, "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimations", Applied Statistics, Volume 29, pages 231-237, 1980.
P. Huber, "Robust Statistics", Wiley, New York, 1981.
F. Ruymgaart, "A robust principal analysis", Journal of Multivariate Analysis", pages 485-497, 1981.
S. Devlin, R. Gnanadesikan, J. Kettenring, "Robust estimation of dispersion matrices and principal components", Journal of the American Statistical Association, Volume 76, pages 354-362, 1981.
G. Boente, "Asymptotic theory for robust principal components", Journal of Multivariate Analysis, Volume 21, pages 67-78, 1987.
M. Locantore, J. Marron, D. Simpson, N. Tripoli, J. Zhang, K. Cohen, “Robust principal components for functional data”, pages 1-28, 1999.
G. Draskovic, A. Breloy, F. Pascal, "On the asymptotics of Maronna’s robust PCA", Preprint, 2018.
H. Cevallos-Valdiviezo, S. Van Aels, "Fast computation of robust subspace estimators", Computational Statistics and Data Analysis, 2019.
P. Filzmoser, S. Hoppner, I. Ortner, S. Serneels, "Cellwise robust M-regression", Computational Statistics and Data Analysis, Volume 147, page 106944, 2020.
Y. Liu, "Robust sparse covariance-regularized regression for high-dimensional data with Casewise and Cellwise outlier", PhD Thesis, University of British Columbia, 2023.
M. Mayrhofer, U. Radojicic, P. Filzmoser, “Robust covariance estimation and explainable outlier detection for matrix-valued data”, Preprint, March 2024.
2. Positive-breakdown estimators (27 papers) [More robust, but limited to small to moderate dimensions]
2.1 Minimum Covariance Determinant (MCD) (6 papers)
V. Todorov, N. Neykov, P. Neytchev, "Stability of (high-breakdown point) robust principal components analysis", COMPSTAT 1994, Volume 10, pages 90-92, 1994.
P. Rousseeuw, K. Van Driessen, "A fast algorithm for the minimum covariance determinant estimator", Technometrics, Volume 41, pages 212–223, 1999.
R. Maronna, R. Martin, V. Yohai, "Robust Statistics: Theory and methods", Wiley Series in Probability and Statistics, 2006.
P. Huber, E. Ronchetti, "Robust Statistics", Wiley Series in Probability and Statistics, 2009.
M. Hubert, M. Debruyne, “Minimum Covariance Determinant”, Wiley Interdisciplinary Reviews: Computational Statistics, Wiley, 2010.
J. Raymaekers, P. Rousseeuw, "The Cellwise Minimum Covariance Determinant Estimator", Journal of the American Statistical Association, 2024.
2.2 Minimum Vector Variance (MVV) (1 paper)
D. Herwindiati, S. Isa, "The New Measure of Robust Principal Component Analysis", International Conference on Electronic Engineering and Computing Technology , February 2010.
2.3 S-Estimators (7 papers)
L. Davies, "Asymptotic Behavior of S-Estimators of Multivariate Location and Dispersion Matrices", The Annals of Statistics, Volume 15, pages 1269-1292, 1987.
P. Rousseeuw, A. Leroy, "Robust Regression and Outlier Detection", NewYork: Wiley, 1987.
R. Maronna, R. Martin, V. Yohai, "Robust Statistics: Theory and methods", Wiley Series in Probability and Statistics, 2006.
M. Salibian-Barrera, V. Yohai, "A fast algorithm for S-regression estimates", Journal of Computational and Graphical Statistics, Volume 15, pages 414–427, 2006.
G. Boente, M. Barrera, "S-estimators for functional principal component analysis", Technical Report, 2013.
O. Toka, M. Cetin, O. Arslan, “Robust regression estimation and variable selection when cellwise and casewise outliers are present”, Journal of Mathematics and Statistics, Volume 50, pages 289-30, 2021.
2.4 Minimum Volume Ellipsoid (MVE) estimator (2 papers)
R. Naga, G. Antille, "Stability of robust and non-robust principal component analysis", Computational Statistics and Data Analysis", Volume 10, pages 169-174, 1990.
R. Maronna, R. Martin, V. Yohai, "Robust Statistics: Theory and Methods", Wiley Series in Probability and Statistics, 2006.
2.5 Stahel-Donoho estimator (3 papers)
M. Debruyne, M. Hubert, “The Influence Function of Stahel-Donoho Type Methods for Robust PCA” , 2005.
R. Maronna, R. Martin, V. Yohai, "Robust Statistics: Theory and Methods", Wiley Series in Probability and Statistics, 2006.
S. Van Aelst, E. Vandervieren, G. Willems, “Stahel-Donoho Estimators with Cellwise Weights”, Journal of Statistical Computation and Simulation, Volume 81, pages 1-27, 2011.
2.6 Concentration Steps (CS) (1 paper)
P. Rousseeuw, K. Van Driessen, “An algorithm for positive-breakdown methods based on concentration steps”, Data Analysis: Scientific Modeling and Practical Application, Springer-Verlag, pages 335-346, 2000.
2.7 M-estimators (7 papers)
Geometric Median Subspace (GMS)
T. Zhang, G. Lerman, “A novel M-Estimator for robust PCA”, Journal of Machine Learning Research, 2014.
M. Coudron, G. Lerman, "On the sample complexity of robust PCA", Neural Information Processing Systems, NIPS 2012, 2012.
Extended Geometric Median Subspace (EGMS)
T. Zhang, G. Lerman, “A novel M-Estimator for robust PCA”, Journal of Machine Learning Research, 2014.
M. Coudron, G. Lerman, "On the sample complexity of robust PCA", Neural Information Processing Systems, NIPS 2012, 2012.
Fast Median Subspace (FMS)
G. Lerman, T. Maunu, “Fast, robust and nonconvex subspace recovery”, Information and Inference, 2017.
Density Power Divergence (DPD)
S. Roy, A. Basu, A. Ghosh, "Robust Principal Component Analysis using Density Power Divergence", Preprint, 2023.
Cauchy–Schwarz Divergence (CSD)
K. Nakao, A. Levada, “Entropic principal component analysis using Cauchy–Schwarz divergence”, Knowledge and Information Systems, Volume 65, Issue 12, pages 5375-5385, December 2023.
3. Spherical Geodesic Gradient Descent (SGGD) (1 paper)
T. Maunu, T. Zhang, G. Lerman, “A Well-Tempered Landscape for Non-convex Robust Subspace Recovery”, Journal of Machine Learning Research, Volume 20, pages 1-59, 2019.
4. RANSAC-type Estimator (1 paper)
T. Maunu, G. Lerman, “Robust Subspace Recovery with Adversarial Outliers”, Preprint, May 2019.
5. Orthogonalized Gnanadesikan-Kettenring (OGK) (1 paper)
R. Maronna, R. Zamar, "Robust estimates of location and dispersion for high dimensional data sets", Technometrics, Volume 43, pages 307-317, 2002.
6. Kronecker Spatio-Temporal Covariances (3 papers)
Kronecker PCA (KronPCA)
K. Greenewald, T. Tsiligkaridis, A. Hero, “Kronecker sum decompositions of space-time data", IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013, pages 65–68, 2013.
K. Greenewald, A. Hero, “Kronecker PCA based spatio-temporal modeling of video for dismount classification", SPIE, 2014.
Diagonally Loaded KronPCA (DL-KronPCA)
K. Greenewald, A. Hero, "Robust Kronecker Product PCA for Spatio-Temporal Covariance Estimation", IEEE Transactions on Image Processing, Volume 63, No. 23, pages 6368 - 6378, 2015.
Projection Pursuit Techniques (9 papers)
L. Ammann, "Robust singular value decompositions: A new approach to projection pursuit", Journal of the American Statistical Association, pages 505–514, 1993.
C. Croux, A. Ruiz-Gazen, "A Fast Algorithm for Robust Principal Components based on Projection Pursuit", COMPSTAT 1996, pages 211-217, 1996.
M. Hubert, P. Rousseeuw, S. Verboven, "A fast method for robust principal components with applications to chemometrics", 2001.
C. Croux, A. Ruiz-Gazen, "High breakdown estimators for principle components: the projection-pursuit approach revisited", Journal of Multivariate Analysis", Volume 95, pages 206-226, 2005.
C. Croux, P. Filzmoser, M. Oliveira, "Algorithms for projection-pursuit robust principal component analysis", Chemometrics and Intelligent Laboratory Systems", Volume 87, pages 218-225, 2007.
M. Hubert, P. Rousseeuw, S. Verboven, "A Fast Method for Robust Principal Components with Applications to Chemometrics", Chemometrics and Intelligent Laboratory Systems, Volume 60, pages 101-111, 2002.
L. Bali, G. Boente, D. Tyler, J. Wang, "Robust functional principal components: a projection-pursuit approach", Annals of Statistics, Volume 39, pages 2852-2882, 2011.
N. Kwak, "Principal component analysis based on l1-norm maximization", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 30, No. 9, pages 1672–1680, 2008.
M. McCoy, J. Tropp, "Two proposals for robust PCA using semidefinite programming", Electronic Journal of Statistics, pages 1123–1160, 2011.
Mixed techniques (6 papers)
ROBPCA [Row-wise outliers]
M. Hubert, P. Rousseeuw, K. Vanden Branden, "ROBPCA: A New Approach to Robust Principal Component Analysis", Technometrics, Volume 47, No. 1, pages 64-49, February 2005.
M. Hubert, P. Rousseeuw , S. Van Aelst, "High-breakdown robust multivariate methods", Statistical Science, Volume 23, pages 92-119, 2008.
M. Debruyne, M. Hubert, “The influence function of Stahel-Donoho type methods for robust PCA” , 2005.
K. Genel, H. Celik, “An Application of Robust Principal Component Analysis Methods for Anomaly Detection”, Turkish Journal of Science and Technology, Volume19 Issue 1, page 107, 2024
MROBPCA [Row-wise outliers] [missing data]
S. Serneels, "Principal component analysis for data containing outliers and missing elements", Computational Statistics and Data Analysis, Volume 52, pages 1712-1727, 2008.
MacroPCA [Cell-wise outliers][Row-wise outliers] [missing data]
M. Hubert, P. Rousseeuw, W. Van den Bossche,"MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers", Technometrics, Volume 61, No. 4, pages 459-473, 2019.
Robust Error Estimation (14 papers)
P. Verboon, W. Heiser, "Resistant lower-rank approximation of matrices by iterative majorization". Computational Statistics and Data Analysis, Volume 18, pages 457-467, 1994.
R. Maronna, V. Yohai, "Robust lower-rank approximation of data matrices with element-wise contamination", Technometrics, Volume 50, pages 295-304, 2008.
S. Brubaker, "Robust PCA and clustering in noisy mixtures", ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, pages 1078–1087, Philadelphia, USA, 2009.
H. Xu, C. Caramanis, S. Mannor, "Principal component analysis with contaminated data: The high dimensional case", COLT 2010, pages 490–502, 2010.
S. Wang, F. Nie, Z. Wang, R. Wang, X. Li, "Robust Principal Component Analysis via Joint Reconstruction and Projection", IEEE Transactions on Neural Networks and Learning Systems, 2022.
Y. Gao, T. Lin, J. Pan, F. Nie, Y. Xie, "Fuzzy Sparse Deviation Regularized Robust Principal Component Analysis", IEEE Transactions on Image Processing, Volume 31, pages 5645-5660, 2022.
Y. Gao, T. Lin, Y. Zhang, S. Luo, F. Nie, "Robust Principal Component Analysis based on Discriminant Information", IEEE Transactions on Knowledge and Data Engineering, Volume 35, No. 2, pages 1991-2003, February 2023.
Y. Gao, Y. Feng, Y. Xie, J. Pan, F. Nie, "Normalized Robust PCA With Adaptive Reconstruction Error Minimization", IEEE Transactions on Knowledge and Data Engineering, 2023.
F. Nie, S. Wang, Z. Wang, R. Wang, X. Li, "Discrete Robust Principal Component Analysis via Binary Weights Self-Learning”, IEEE Transactions on Neural Networks and Learning Systems, Volume 34, No. 11, pages 9064-9077, 2023.
Y. Gao, X. Wang, J. Xie, J. Pan, P Yan, F. Nie, "Robust Principal Component Analysis Based on Fuzzy Local Information Reservation", IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024.
RSL
F. De La Torre, M. Black, “Robust Principal Component Analysis for Computer Vision”, International Conference on Computer Vision, ICCV 2001, Vancouver, Canada, July 2001.
F. De La Torre, M. Black, “A framework for robust subspace learning”, International Journal on Computer Vision, pages 117-142, 2003.
A. Rekavandi, A. Seghouane, "Robust Principal Component Analysis using Alpha Divergence”, IEEE International Conference on Image Processing, ICIP 2020, pages 1-6, Abu Dhabi, United Arab Emirates, 2020.
A. Rekavandi, A. Seghouane, R. Evans, "Learning Robust and Sparse Principal Components with the α-Divergence", IEEE Transactions on Image Processing, 2024.
Regression-type Optimization Problem (9 papers)
1. Least Trimmed Squares (LTS) (6 papers)
L. Liu, L. Hawkins, D. Ghosh, S. Young, "Robust singular value decomposition analysis of microarray data, National Academy of Sciences of the USA, Volume 100, pages 167-172, 2003.
M. Wolbers, “Linear unmixing of multivariate observations”, PhD thesis, 2002.
R. Maronna, “ Principal components and orthogonal regression based on robust scales”, Technometrics, 2005.
S. Engelen, M. Hubert, K. Vanden Branden, "A comparison of three procedures for robust PCA in high dimensions", Austrian Journal of Statistics, Volume 34, pages 117-126, 2005.
C. Croux, L. Garcia-Escudero, A. Gordaliza, C. Ruwet, R. Martin, "Robust principal component analysis based on trimming around affine subspaces", Statistica Sinica, Volume 27, No. 3, pages 1437–1459, 2017.
A. Gonzalez-Cebrian, A. Folch-Fortuny, F. Arteaga, “RadarTSR: A new algorithm for cellwise and rowwise outlier detection and missing data imputation”, Chemometrics and Intelligent Laboratory Systems, Volume 247, April 2024.
2. Least Absolute Deviation (LAD) (3 papers)
LAD (1 paper)
D. Hawkins, L. Liu, S. Young, "Robust singular value decomposition", National Institute of Statistical Sciences Technical Report 122, 2001.
Weighted LAD (2 papers)
C. Croux, P. Filzmoser, G. Pison, P. Rousseeuw, "Fitting multiplicative models by robust alternating regressions", Statistics and Computing, Volume 13, pages 23-36, 2003.
K. Jung, "Robust Singular Value Decomposition based on Weighted Least Absolute Deviation Regression", Communications of the Korean Statistical Society, Volume 17, No. 6, pages 803-810, 2010.
lp- Norm Minimization - l1p- Norm Minimization (42 papers) [Outliers][High dimension]
1. l1-Norm Minimization (24 papers)
G. Lerman, T. Zhang, "lp-Recovery of the most significant subspace among multiple subspaces with outliers”, Constructive Approximation, Volume 40, No. 3, pages 329–385, 2014.
S. Kundu, P. Markopoulos, D. Pados, "Fast computation of the l1-principal component of real-valued data", ICASSP 2014, pages 8028–8032, 2014.
P. Markopoulos, G. Karystinos, D. Pados, "Optimal algorithms for l1-subspace signal processing", IEEE Transactions on Signal Processing, Volume. 62, No. 19, pages 5046–5058, 2014.
N. Tsagkarakis, P. Markopoulos, D. Pados, "Direction finding by complex l1-principal-component analysis" IEEE International Workshop on Signal Processing Advances in Wireless Communications, SPAW 2015, pages 475-479, 2015.
P. Markopoulos, S Kundu, S. Chamadia, D. Pados, "Efficient l1-norm principal-component analysis via bit flipping", Preprint, 2016.
S. Chamadia, D. Pados, "Outlier processing via l1- principal subspaces", Florida Artificial. Intelligence. Research Society, FLAIRS 2017, Florida, May 2017.
P. Markopoulos, D. Pados, G. Karystinos, M. Langberg, "l1-norm principal-component analysis in l2-norm-reduced-rank data subspaces", SPIE Defense and Commercial Sensing, DCS 2017, 2017.
N. Tsagkarakis, P. Markopoulos, D. Pados, "l1-norm principal-component analysis of complex data", IEEE Transactions on Signal Processing, March 2018.
D. Chachlakis, P. Markopoulos, "Reduced-rank filtering with complex l1-norm principal-component analysis", IEEE Transactions on Signal Processing, 2018.
M. Dhanaraj, P. Markopoulos, "Novel algorithm for incremental l1-norm principal-component analysis", European Signal Processing Conference, EUSIPCO 2018, Rome, Italy, September 2018.
M. Dhanaraj, “Incremental and Adaptive l1-Norm Principal Component Analysis: Novel Algorithms and Applications, PhD Thesis, Rochester Institute of Technology, 2018.
P. Markopoulos, S. Kundu, S. Chamadia, N. Tsagkarakis, D. Pados, "Outlier-resistant data processing with l1-norm principal component analysis", Chapter in Advances in Principal Component Analysis: Research and Development, Springer, pages 121-135, 2018.
P. Markopoulos, M. Dhanaraj, A. Savakis, "Adaptive L1-norm Principal-Component Analysis with Online Outlier Rejection", IEEE Journal of Selected Topics in Signal Processing, December 2018.
M. Dhanaraj, P. Markopoulos ,“Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization”, IEEE Global Conference on Signal and Information Processing, GlobalSIP 2019, pages 1-5, Ottawa, Canada, 2019.
Y. Liu, D. Pados, "Conformity Evaluation of Data Samples by L1-Norm Principal Component Analysis", SPIE, April 2018.
H. Kamrani, A. Asli, P. Markopoulos, M. Langberg, D. Pados, G. Karystinos, "Reduced-rank L1-norm principal-component analysis with performance guarantees", IEEE Transactions on Signal Processing, Volume 69, pages 240-255, 2020.
S. Colonnese, G. Scarano, M. Marra, P. Markopoulos, D. Pados, “Joint analysis and segmentation of time-varying data with outliers”, Digital Signal Processing, Volume 145 , February 2024.
Y. Liu, Z. Bellay, P. Bradsky, G. Chandler, B. Craig, "Edge-to-fog computing for color-assisted moving object detection", SPIE Big Data: Learning, Analytics, and Applications, May 2019.
F. Nie, H. Huang, C. Ding, D. Luo, H. Wang, “Robust principal component analysis with non-greedy l1-norm maximization", IJCAI 2011, pages 1433-1438, 2011.
J. Brooks, J. Dula, E. Boone, "A pure l1-norm principal component analysis", Computational Statistics and Data Analysis, Volume 61 pages 83-98, 2013.
J. Brooks, J. Dula, "Estimating L1-Norm Best-Fit Lines for Data", Optimization Online, August 2019.
J. Brooks, X. Ling, "L1-norm Regularized L1-norm Best-fit line problem", Graduate Research Posters, 2020.
P. Wang, H. Liu, A. So, “Linear Convergence of a Proximal Alternating Minimization Method with Extrapolation for l1-Norm Principal Component Analysis”, SIAM Journal on Optimization, Volume 33, Issue 2, 2023.
I. Tomeo, P. Markopoulos, A. Savakis, "L1-PCA with quantum annealing", SPIE Big Data VI: Learning, Analytics, and Applications, 2024.
R1-norm [Rotationally invariant] (3 papers)
D. Ding, D. Zhou, X. He, H. Zha, “R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization”, ACM, pages 281-288, 2006.
X. Li, P. Li, H. Zhang, K. Zhu, R. Zhang, "Pivotal-Aware Principal Component Analysis”, IEEE Transactions on Neural Networks and Learning Systems, 2023.
T. Jana, N. Raghav, A. Majumdar, M. Sahidullah, "Exact Rotation Invariant Robust PCA", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2025, Hyderabad, India, 2025.
l1-norm [Rotationally invariant] (2 papers)
N. Kwak, "Principal component analysis based on l1-norm maximization", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 30, No. 9, pages 1672–1680, 2008.
T. Zheng, P. Wang, A. So , "A Linearly Convergent Algorithm for Rotationally Invariant l1-Norm Principal Component Analysis", Preprint, October 2022.
Half-Quadratic PCA (HQ-PCA) [Rotationally invariant] (2 papers)
R. He, B. Hu, W. Zheng, X. Kong, “Robust Principal Component Analysis based on Maximum Correntropy Criterion", IEEE Transactions on Image Processing, pages 1485-1494, 2011.
J. Chereau, B. Scalzo, D. Mandic, "Robust PCA Through Maximum Correntropy Power Iterations", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2021, Toronto, Canada, pages 4985-4989, 2021.
2. lp-Norm Minimization (2 papers)
N. Kwak, "Principal component analysis by lp-norm maximization"; IEEE Transactions on Cybernetics, Volume 44, No. 5, pages 594-609, 2014.
Z. Liang, S. Xia, Y. Zhou, L. Zhang, Y. Li, "Feature extraction based on lp-norm generalized principal component analysis", Pattern Recognition Letters, Volume 34, No.9, pages 1037-1045, 2013.
3. l21-Norm Minimization (3 papers)
F. Nie, J. Yuan, H. Huang, "Optimal Mean Robust Principal Component Analysis", International Conference on Machine Learning, ICML 2014, 2014.
X. Shi, F. Nie, Z. Lai, Z. Guo, "Robust Principal Component Analysis via Optimal Mean by Joint l21 and Schatten p-Norms Minimization", Neurocomputing, Volume 283, pages 205-213, 2018.
S. Yi, F. Nie, Y. Liang, W. Liu, Z. He, Q. Liao, "Fast Extended Inductive Robust Principal Component Analysis with Optimal Mean", IEEE Transactions on Knowledge and Data Engineering, Volume 34, No. 10, pages 4812-4825, October 2022.
4. l2p-Norm Minimization (6 papers)
P. Bi, X. Du, "Arbitrary Triangle Structure Adaptive Mean PCA and Image Recognition", IEEE Transactions on Circuits and Systems for Video Technology, 2023.
Y. Gao, J. Xie, Z. Zheng, C. Cao, J. Wang, "Normalized l2,p-Norm Robust PCA with Optimal Mean", IEEE Chinese Control and Decision Conference, CCDC 2022, Hefei, China, pages 4343-4349, 2022.
K. Liu, Y. Cao, “Robust Principal Component Analysis: A Construction Error Minimization Perspective”, Preprint, 2021.
F. Nie, D. Wu, R. Wang, X. Li, "Truncated Robust Principal Component Analysis with A General Optimization Framework", IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020.
R. Zhang, H. Tong, "Robust Principal Component Analysis with Adaptive Neighbors", NeuIPS 2019, 2019.
Z. Dai, L. Hu, H. Sun, "Robust generalized PCA for enhancing discriminability and recoverability", Neural Networks, October 2024.
Maximum Entropy (2 papers)
MaxEnt-PCA
R. He, B. Hu, X. Yuan, W. Zheng, "Principal component analysis based on non-parametric maximum entropy", Neurocomputing, Volume 73, pages 1840-1852, 2010
MaxCorrEnt-PCA
R. He, B. Hu, W. Zheng, X. Kong, "Robust principal component analysis based on maximum correntropy criterion", IEEE Transactions on Image Processing, Volume 20, No. 6, pages 1485-1494, 2011.
Generalized Mean (2 papers) [Arithmetic][Geometric][Harmonic]
J. Oh, N. Kwak, "Generalized Mean for Robust Principal Component Analysis", Pattern Recognition, Volume 54, pages 116-127, 2016.
J. Oh, N. Kwak, “Robust PCAs and PCA using Generalized Mean”, Chapter in Advances in Principal Component Analysis, pages 71-98, 2018.
Moment PCA (1 paper)
Z. Lou, Y. Wang, S. Lu, P. Sun,“Process monitoring using a novel robust PCA scheme”, Industrial and Engineering Chemistry, Volume 60, No. 11, pages 4397-4404, 2021.
Median of Means (1 paper)
D. Paul, S. Chakraborty, S. Das, "Robust Principal Component Analysis: A Median of Means Approach", IEEE Transactions on Neural Networks and Learning Systems, 2023.
Self-paced PCA (1 paper)
Z. Kang, H. Liu, J. Li, X. Zhu, “Self-paced principal component analysis”, Pattern Recognition, Volume 142, October 2023.
Flagged PCA (1 paper)
N. Mankovich, G. Camps-Valls, T. Birdal, “Fun with Flags: Robust Principal Directions via Flag Manifolds”, Preprint, January 2024.
How many components k need to be selected? (3 papers)
Predicted Residual Error Sum of Squares (PRESS) (3 papers)
PRESS
I. Jollife, "Principal Component Analysis", New York: Springer-Verlag, 2002.
R-PRESS
M. Hubert, S. Engelen, “Fast cross-validation for high-breakdown resampling algorithms for PCA, 2004.
S. Engelen, M. Hubert, “Fast cross-validation for robust PCA”, Computational Statistics, Physica-Verlag, pages 989-996, 2004.