Classical PCA (163 papers)
1. Regular PCA (9 papers)
2. Correlated PCA (9 papers)
2.1 Dynamic PCA (6 papers) [Chemometrics]
2.2 Correlated PCA (3 papers)
3. Adaptive PCA (12 papers)
3.1 Recursive PCA (7 papers) [Chemometrics]
3.2 Moving Window PCA (5 papers) [Chemometrics]
4. Streaming PCA/Subspace Tracking (95 papers) [Slow changes]
4.1 Streaming PCA (21 papers)
4.2 Subspace Tracking / Robust Subpace Tracking (67 papers) [Computer data]
4.3 Incremental PCA (7 papers)
4.4 Incremental SVD (1 paper)
5. Subspace Change-Point Detection (1 paper) [Abrupt changes]
Y. Jiao, Y. Chen, Y. Gu, "Subspace Change-Point Detection: A New Model and Solution", IEEE Journal of Selected Topics in Signal Processing, December 2018.
6. Quantum PCA (3 papers) [Fast algorithm]
S. Lloyd, M. Mohseni, P. Rebentrost, "Quantum principal component analysis", Nature Physics, Volume 10, page 631, July 2014.
A. Daskin, "Obtaining a linear combination of the principal components of a matrix on quantum computers”, Quantum Information Processing, Volume 15, Issue 10, pages 4013-4027, 2016.
I. Tomeo, P. Markopoulos, A. Savakis, “Quantum Annealing for Robust Principal Component Analysis”, Preprint, 2025.
7. PCA in High Dimension (3 papers) [High dimensions]
H. Xu,C. Caramanis, S. Mannor, "Principal component analysis with contaminated data: The high dimensional case", COLT, 2010.
H. Xu,C. Caramanis, S. Mannor, "Outlier-Robust PCA: The High-Dimensional Case", IEEE Transactions on Information Theory, Volume 59, No. 1, pages 546-572, January 2013.
J. Feng, H. Xu, S. Yan, "Robust PCA in high-dimension: A deterministic approach", International Conference on Machine Learning, ICML 2012, 2012.
Fair PCA (12 papers)
Ensemble PCA (2 papers)
B. Gabrys, B. Baruque, E. Corchado, "Outlier resistant PCA ensembles", International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2006, pages 432-440, Bournemouth, UK, October 2006.
O. Dorabiala, A. Aravkin, J. Kutz, "Ensemble Principal Component Analysis", IEEE Access, 2024.
Personalized PCA (2 papers)
N. Shi, R. Kontar, “Personalized PCA: Decoupling Shared and Unique Features”, Journal of Machine Learning Research, 2024.
N. Shi, “Personalized and Distributed Data Analytics in Heterogeneous Environments”, PhD Thesis, University of Michigan, 2025.
Phaseless PCA (4 papers)
Centering PCA (3 papers)
Contrastive PCA (5 papers)
Graph PCA (3 papers)
Classical Robust PCA (203 papers) [Low dimensions]
1. Classical RPCA in Statistics (171 papers) [Basic outliers]
2. Classical RPCA in Neural Networks (20 papers) [Basic outliers]
3. Classical RPCA/RMC in Statistics (2 papers) [Missing data]
4. Classical RPCA with Fuzzy Concepts (7 papers) [Clustering]
5. Classical RPCA with Angle Measurement (3 papers)
Product-PCA (PPCA) (2 papers)
H. Hung, C. Yeh, S. Huang, "On the asymptotic properties of product-PCA under the high-dimensional setting", Preprint, July 2024.
H. Hung, S. Huang, “On the efficiency-loss free ordering-robustness of product-PCA”, Preprint, 2023.
Quaternion RPCA (2 papers)
C. Zou, K. Kou, Y. Hu, Y. Wu, Y. Tang, “Improved quaternion robust principal component analysis for color image recovery”, International Journal of Wavelets, Multiresolution and Information Processing, December 2023.
R. Xu, S. Feng, Y. Wei, H. Yan, “CUR and Generalized CUR Decompositions of Quaternion Matrices and their Applications”, Numerical Functional Analysis and Optimization, February 2024.
Robust PCA via L+S decomposition [Spike outliers] [High dimensions] (555 papers)
Please see DLAM website for the full list of publications [DLAM Website].
Principal Component Pursuit (3 papers) [Element-wise outliers]
RPCA
E. Candes, X. Li, Y. Ma, J. Wright, “Robust Principal Component Analysis”, ACM, Volume 58, No. 3, May 2011.
Stable RPCA
Z. Zhou, X. Li, J. Wright, E. Candes, Y. Ma, "Stable Principal Component Pursuit", ISIT 2010, 2010.
Dynamic RPCA
C. Qiu, N. Vaswani, “Real-time Robust Principal Components Pursuit”, International Conference on Communication Control and Computing, 2010.
Robust Subspace Recovery (3 papers) [Row-wise or column-wise outliers]
H. Xu, C. Caramanis, S. Sanghavi, “Robust PCA via Outlier Pursuit”, International Conference on Neural Information Processing System, NIPS 2010, 2010.
H. Zhang, Z. Lin, C. Zhang, E. Chan, "Exact Recoverability of Robust PCA via Outlier Pursuit with Tight Recovery Bounds", Advancement of Artificial Intelligence, AAI 2015, 2015.
M. Rahmani, G. Atia, "Robust PCA with concurrent column and element-wise outliers", Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017, pages 332-337, 2017.
Robust Matrix Completion (9 papers) [Missing data]
Y. Yang, Y. Feng, J. Suykens, “A Nonconvex Relaxation Approach to Robust Matrix Completion”, Preprint, 2014.
Y. Yang, Y. Feng, J. Suykens, “Correntropy based Matrix Completion”, MDPI Entropy, Volume 20, No. 3, page 171, 2018.
F. Shang, Y. Liu, J. Cheng, H. Cheng, "Recovering low-rank and sparse matrices via robust bilateral factorization", IEEE International Conference on Data Mining, ICDM 2014, 2014.
F. Shang, Y. Liu, H. Tong, J. Cheng, H. Cheng, "Structured Low-Rank Matrix Factorization with Missing and Grossly Corrupted Observations", Preprint, September 2014.
F. Shang, Y. Liu, J. Cheng, H. Cheng, "Robust Principal Component Analysis with Missing Data", ACM International Conference on Information and Knowledge Management, CIKM 2014, 2014.
S. Wang, D. Liu, Z. Zhan, "Nonconvex Relaxation Approaches to Robust Matrix Recovery", International Joint Conference on Artificial Intelligence, 2013.
T. Yokota, A. Cichocki, “A fast automatic low-rank determination algorithm for noisy matrix completion”, Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2015, pages 43-46, Hong Kong, 2015.
Y. Cherapanamjeri, K. Gupta, P. Jain, "Nearly-optimal Robust Matrix Completion", Preprint, December 2016.
M. Ashraphijuo, V. Aggarwal, X. Wang, "On Deterministic Sampling Patterns for Robust Low-Rank Matrix Completion" , IEEE Signal Processing Letters, Volume 25, no. 3, pages 343-347, March 2018.
Adversarial RPCA (1 paper)
D. Pimentel-Alarcon, A. Biswas, C. Sols-Lemus, “Adversarial principal component analysis", IEEE International Symposium on Information Theory, Aachen, Germany, pages 2363-2367, 2017.
Scalable RPCA (4 papers)
PCA
T. Elgamal, M. Yabandeh, A. Aboulnaga, M. Hefeeda, "sPCA: Scalable Principal Component Analysis for Big Data on Distributed Platform", March 2015.
RPCA
S. Hauberg, A. Feragen, M. Black, “Grassmann Averages for Scalable Robust PCA”, RGA 2014, 2014.
S. Hauberg, A. Feragen, R. Enficiaud, M. Black, "Scalable robust principal component analysis using Grassmann averages", IEEETrasanctions on Pattern Analysis and Machine Intelligence, 2015.
R. Chakraborty, S. Hauberg, B. Vemuri, “Intrinsic Grassmann Averages for Online Linear and Robust Subspace Learning”, CVPR 2017, 2017.
Stochastic PCA (7 papers)
R. Arora, A. Cotter, K. Livescu, N. Srebro, "Stochastic optimization for PCA and PLS", Allerton Conference, pages 851-868, 2012.
R. Arora, A. Cotter, N. Srebro, "Stochastic minimization of PCA with capped MSG" , Neural Information Processing Systems, 2013.
J. Goes, T. Zhang, R. Arora, G. Lerman, "Robust stochastic principal component analysis", International Conference on Artificial Intelligence and Statistics, AISTATS 2014, April 2014.
P. Mianjy, R. Arora, “Stochastic PCA with l2 and l1 Regularization”, International Conference on Machine Learning, ICML 2018, pages 3531-3539, 2018.
A. Bhaskara, P. Maheshakya, “On Distributed Averaging for Stochastic k-PCA”, Neural Information Processing Systems, NeurIPS 2019, 2019.
M. Dhanaraj, P. Markopoulos, "Stochastic Principal Component Analysis Via Mean Absolute Projection Maximization", IEEE Global Conference on Signal and Information Processing, GlobalSIP 2019, Ottawa, Canada, pages 1-5, 2019.
M. Dhanaraj, P. Markopoulos, "Robust Stochastic Principal Component Analysis via Barron Loss", Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, USA, pages 1286-1290, 2022.
Heteroscedastic/Heteroskedastic PCA (9 papers)
D. Hong, F. Yang, J. Fessler, L. Balzano, “Optimally weighted PCA for high-dimensional heteroscedastic data", 2018.
D. Hong, L. Balzano, J. Fessler, "Asymptotic performance of PCA for high-dimensional heteroscedastic data", Journal of Multivariate Analysis, Volume 167, pages 435-452, 2018.
D. Hong, L. Balzano, J. Fessler, "Probabilistic PCA for heteroscedastic data", IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, pages 26-30, 2019.
D. Hong, K. Gilman, L. Balzano, J. Fessler, “HePPCAT: Probabilistic PCA for data with heteroscedastic noise",IEEE Transactions on Signal Processing, Volume 69, pages 4819-4834, 2021.
A. Cavazos, J. Fessler, L. Balzano, "ALPCAH: Sample-wise heteroscedastic PCA with tail singular value regularization", International Conference on Sampling Theory and Applications, SampTA 2023, 2023.
K. Gilman, D. Hong, J. Fessler, L. Balzano, “Streaming Probabilistic PCA for Missing Data with Heteroscedastic Noise”, Preprint, 2023.
Y. Yan, Y. Chen, J. Fan,“Inference for heteroskedastic PCA with missing data”, The Annals of Statistics, 2024.
Y. Zhou, Y. Chen, "Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA." Annals of Statistics, Volume 53, No. 1, page 91- 116, February 2025.
J. Cavazos, J. Fessler, L. Balzano,“ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Data”, Preprint, May 2025.
Semi-parametric PCA (1 paper)
F. Han, H. Liu, "Semiparametric principal component analysis", Neural Information in Processing Systems, pages 171-179, NIPS 2012, 2012.
Sparse PCA (21 papers)
Exponential Family PCA (10 papers)
Non-linear PCA (1 paper)
W. Hsieh, “Non-linear principal component analysis of noisy data", Neural Networks, Volume 20, No. 4, pages 434-443, 2007.
Matrix Normal PCA (1 paper)
Probabilistic PCA (10 papers)
Distributed/Decentralized/Federated PCA (44 papers)
Kernel PCA (11 papers)
Elliptical PCA (3 papers)
Spherical PCA (5 papers)
Spherical PCA
N. Locantore, J. Marron, D. Simpson, N. Tripoli, J. Zhang, K. Cohen, "Robust principal component analysis for functional data", Test, pages 1-73, 1999.
J. Fujiki, S. Akaho, "Spherical PCA with Euclideanization", Workshop on Subspace in conjunction with ACCV 2007, 2007.
K. Liu, Q. Li, H. Wang, G. Tang, "Spherical Principal Component Analysis", SIAM International Conference on Data Mining, pages 387-395, 2019.
S. Leyder, J. Raymaekers, "Generalized Spherical Principal Component Analysis", Statistics and Computing, March 2024.
Spherical Kernel PCA
M. Debruyne, M. Hubert, J. Van Horebeek, “Detecting influential observations in kernel PCA”, Computational Statistics and Data Analysis, Volume 54, pages 3007–3019, 2010.
Hyperbolic PCA (1 paper)
P. Tabaghi, M. Khanzadeh, Y. Wang, S. Mirarab, "Principal Component Analysis in Space Forms", Preprint, January 2023.
Local/Global PCA (6 papers)
Local PCA
N. Kambhatla, T. Leen, "Dimension Reduction by Local Principal Component Analysis", Neural Computation, Volume 9, pages 1493–1516, 1997.
N. Migenda, W. Schenck, "Adaptive Dimensionality Reduction for Local Principal Component Analysis", IEEE International Conference on Emerging Technologies and Factory Automation, ETFA 2020, Vienna, Austria, pages 1579-1586, 2020.
Locally Weighted PCA (LWPCA)
M. Charlton, C. Brunsdon, U. Demsar, P. Harris, A. Stewart, “Principal Components Analysis: from Global to Local”, International Conference on Geographic Information Science, 2010.
LGPCA
J. Yu, “Local and global principal component analysis for process monitoring”, Journal of Process Control, Volume 22, Issue 7, pages 1358-1373, 2012.
RWL-AN
R. Zhang, H. Tong, "Robust principal component analysis with adaptive neighbors", Neural Information Processing Systems, NeurIPS 2019, Volume 32, pages 6961-6969, 2019.
Global PCA
H. Qi, T. Wang, J. Birdwell, “Global Principal Component Analysis for Dimensionality Reduction in Distributed Data Mining”, 2004.
Modular PCA (2 papers)
Modular PCA (ModPCA)
R. Gottumukkal, V. Asari, “An improved face recognition technique based on modular PCA approach” Pattern Recognition Letters, pages 429-436, 2004.
Global (GModPCA)
V. Kadappa, A. Negi, “Global Modular Principal Component Analysis”, Signal Processing, Volume 105, pages 381-388, December 2014.
Weighted Principal Component Analysis (WPCA) (4 papers)
Z Fan, E. Liu, B. Xu," Weighted Principal Component Analysis", AICI 2011, pages 569–574, 2011.
D. Hong, J. Fessler, L. Balzano, “Optimally Weighted PCA for High-Dimensional Heteroscedastic Data”, Preprint, November 2018.
D. Hong, J. Fessler, L. Balzano, “Optimally Weighted PCA for High-Dimensional Heteroscedastic Data”, SIAM Journal on Mathematics of Data Science, Volume 5, No. 1, pages 222-250, 2023.
F. Lopez, C. Ordonez, J. Roca, “A Generalized Additive Model (GAM) Approach to Principal Component Analysis of Geographic Data”, Spatial Statistics, Volume 59, March 2024.
Winsorized PCA (1 paper)
S. Han, K. Kim, S. Jung, “Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustness”, Preprint, February 2025.
Dynamic WPCA (2 papers)
S. Wold, "Exponentially weighted moving principal components analysis and projections to latent structures", Chemometrics and Intelligent Laboratory Systems, Volume 23, Issue 1, pages 149-161, 1994.
Y. Tao, H. Shi, B. Song, S. Tan, "A Novel Dynamic Weight Principal Component Analysis Method and Hierarchical Monitoring Strategy for Process Fault Detection and Diagnosis", IEEE Transactions on Industrial Electronics, 2020.
Generalized PCA (2 papers)
R. Vidal, Y. Ma, S. Sastry, "Generalized Principal Component Analysis (GPCA)", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 27, No. 12, pages 1945-1959, December 2005.
Z. Dai, L. Hu, H. Sun, “Robust Generalized PCA for Enhancing Discriminability and Recoverability”, Neural Networks, January 2025.
Non-negative PCA (1 paper)
A. Montanari, E. Richard, “Non-negative principal component analysis: Message passing algorithms and sharp asymptotics,” IEEE Transactions on Information Theory, Volume 62, No. 3, pages 1458-1484, 2016.
Block PCA (2 papers)
J. Mi, Q. Zhu, J. Lu, “Principal component analysis based on block-norm minimization”, Applied Intelligence, pages 1-9, January 2019.
G. Tang, L. Fan, J. Shi, J. Tan, G. Lu, “Avoiding Optimal Mean Robust and Sparse BPCA with L1-norm Maximization”, Journal of Internet Technology, Volume 24, No.4, pages 989-1000, 2023.
2D PCA/ 2D RPCA (19 papers)
D. Hang Z. Zhou, "Two-dimensional PCA: a new approach to appearance-based face representation and recognition,", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 26, No. 1, pages 131-137, 2004.
D. Hang, Z. Zhou, "2D PCA: two-directional two-dimensional PCA for efficient face representation and recognition", Neurocomputing, Volume 69, No. 1, pages 224-234, 2005.
J. Seo, S. Kim, "Recursive On-line 2D2 PCA and Its Application to Long-term Background Subtraction", IEEE Transactions on Multimedia, Volume 16, pages 2333-2344, 2014.
J. Seo, S. Kim, "Dynamic Background Subtraction via Sparse Representation of Dynamic Textures in a Low-dimensional Subspace", Signal, Image and Video Processing, September 2014.
X. Li, Y. Pang, Y. Yuan, "L1-norm-based 2DPCA", IEEE Transactions on Systems, Man, and Cybernetics: Systems, Volume 40, No. 4, pages 1170-1175, 2010.
R. Wang, F. Nie, X. Yang, F. Gao, M. Yao, "Robust 2DPCA with non-greedy l1-norm maximization for image analysis", IEEE Transactions on Cybernetics, Volume 45, No. 5, pages 1108-1112, May 2015.
H. Wang, J. Wang, "2DPCA with L1-norm for simultaneously robust and sparse modelling", Neural Networks, Volume 46, No. 10, pages 190-198, 2013.
J. Wang, "Generalized 2-D principal component analysis by Lp-norm for image analysis", IEEE Transactions on Cybernetics, Volume 46, No. 3, pages 792-802, 2016.
Q. Gao, L. Ma, Y. Liu , X. Gao, F. Nie, "Angle 2DPCA: A New Formulation for 2DPCA", IEEE Transactions on Cybernetics, pages 2168-2267, 2017.
S. Zhou, D. Zhang, “Bilateral Angle 2DPCA for Face Recognition", IEEE Signal Processing Letters, Volume 26, No. 2, pages 317-321, February 2019.
W. Zuo, D. Zhang, K. Wang, “Bidirectional PCA with assembled matrix distance metric for image recognition", IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), Volume 36, No. 4, pages 863-872, Aug. 2006.
Q. Wang, Q. Gao, “Two-dimensional PCA with F-norm minimization", AAAI Conference on Artificial Intelligence, AAAI 2017, pages 2718–2724, 2017.
T. Li, M. Li, Q. Gao, D. Xie, “F-norm distance metric based robust 2DPCA and face recognition", Neural Networks, Volume 94, pages 204–211, 2017.
F. Zhang, J. Yang, J. Qian, Y. Xu, “Nuclear Norm-Based 2-DPCA for Extracting Features from Images", IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 10, pages 2247-2260, 2015.
X. Xiao and Y. Zhou, “Two-Dimensional Quaternion PCA and Sparse PCA", IEEE Transactions on Neural Networks and Learning Systems, Volume 30, No. 7, pages 2028-2042, July 2019.
Q. Gao, S. Xu, F. Chen, C. Ding, X. Gao, Y. Li, “R1-2-DPCA and Face Recognition", IEEE Transactions on Cybernetics, Volume 49, No. 4, pages 1212-1223, April 2019.
G. Zhou, G. Xu, J. Hao, S. Chen, J. Xu, X. Zheng, “Generalized Centered 2-D Principal Component Analysis,” IEEE Transactions on Cybernetics, Volume 51, No. 3, pages 1666-1677, March 2021.
M. Luo, F. Nie, X. Chang, Y. Yang, A. Hauptmann, Q. Zheng, “Avoiding optimal mean robust PCA/2DPCA with non-greedy L1-norm maximization”, International Joint Conference on Artificial Intelligence, 2016.
M. Luo, F. Nie, X. Chang, Y. Yang, A. Hauptmann, Q. Zheng, “Avoiding Optimal Mean l2,1-Norm Maximization-based Robust PCA for Reconstruction”, Neural Computation, Volume 29, Issue 4, April 2017.
M. Wang, X. Jiang, J. Gao, T. Wang, C. Hu, F. Liu, “Minimum Unbiased Risk Estimate based 2DPCA for Color Image Denoising”, Neurocomputing, Volume 440, pages 127-144, 2021.
R-3MPCA (1 paper)
M. Wang, J. Gao, X. Jiang, C. Hu, Q. Feng, T. Wang, “Rescaled Three-Mode Principal Component Analysis: An Approach to Subspace Recovery”, Neural Networks, June 2025.
Randomized PCA (2 papers)
M. Wojnowicz, D. Zhang, G. Chisholm, X. Zhao, M. Wolff “Projecting “better than randomly": How to reduce the dimensionality of very large datasets in a way that outperforms random projections”, Preprint, January 2019.
N. Halko, P. Martinsson, Y. Shkolnisky, M. Tygert, “An algorithm for the principal component analysis of large data sets”, SIAM Journal on Scientific computing, Volume 33, No. 5, pages 2580-2594, 2011.
Uncertainty-Aware PCA (1 paper)
J. Gortler, T. Spinner, D. Streeb, D. Weiskopf, O. Deussen “Uncertainty-Aware Principal Component Analysis”, Preprint, May 2019.
Unlabeled PCA (1 paper)
Y. Yao, L. Peng, M. Tsakiris, “Unlabeled Principal Component Analysis and Matrix Completion”, Journal of Machine Learning Research, Volume 25, 2024.
Personalized PCA (2 papers)
N. Shi, R. Kontar, "Personalized PCA: Decoupling shared and unique features", Journal of Machine Learning Research, Volume 25, No. 4, pages 1-82, February 2024.
N. Shi, R. Kontar, S. Fattahi. Heterogeneous matrix factorization: When features differ by datasets", Preprint, March 2024.
Quaternion PCA (1 paper)
X. Xiao, Y. Zhou, "Two-Dimensional Quaternion PCA and Sparse PCA”, IEEE Transactions on Neural Networks and Learning Systems, Volume 30, No. 7, pages 2028-2042, July 2019.