Historical Subspace Tracking (33 papers)
These subspace tracking methods are based on constrained and unconstrained least-squares optimization problems, aimed at online estimation of the principal eigenvectors. The problem with these solutions is that least-squares optimization is sensitive to the presence of outliers.
1. Oja's method [Algebraic Algorithm]
Oja
E. Oja, "Simplified neuron model as a principal component analyzer", Journal of mathematical biology, Volume 15, No. 3, pages 267-273, 1982.
Orthogonal Oja (OOja)
K. Abed-Meraim, S. Attallah, A. Chkeif, Y. Hua, “Orthogonal Oja algorithm", IEEE Signal Processing Letters, Volume 7, no. 5, pages 116-119, 2000.
Fast Orthogonal Oja (FOOja)
S. Bartelmaos, K. Abed-Meraim, "Principal and Minor Subspace Tracking: Algorithms and Stability Analysis", IEEE International Conference on Acoustics Speech and Signal Processing, 2006.
Normalized orthogonal Oja (NOOja)
L. Sun, G. Bi, L. Zhang, "Orthonormal Subspace Tracking Algorithm for Space–Time Multiuser Detection in Multipath CDMA Channels", IEEE Transactions on Vehicular Technology, Volume 56, No. 6, pages 3838-3845, November 2007.
Power-Oja (P-Oja)
S. Wu, H. Wai, A. Scaglione, N. Jacklin, “The Power-Oja method for decentralized subspace estimation/tracking”, IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2017, pages 3524-3528, 2017.
2. Krasulina' method [Algebraic Algorithm]
T. Krasulina, "The method of stochastic approximation for the determination of the least eigenvalue of a symmetrical matrix", USSR Computational Mathematics and Mathematical Physics, Volume 9, no. 6, pages 189-195, 1969.
3. Power' method [Algebraic Algorithm]
Y. Hua, Y. Xiang, T. Chen, K. Abed-Meraim, Y. Miao, "A new look at the power method for fast subspace tracking", Digital Signal Processing, Volume 9, No. 4, pages 297-314, 1999.
M. Hardt, E. Price, "The noisy power method: A meta algorithm with applications", Advances in Neural Information Processing Systems, pages 2861-2869, 2014.
T. Rabbani, A. Jain, A. Rajkumar, F. Huang, “Practical and Fast Momentum-Based Power Methods”, Mathematical and Scientific Machine Learning Conference, Volume 145, pages 721-756, 2021.
Z. Xu, P. Li, “Faster Noisy Power Method”, International Conference on Algorithmic Learning Theory, ALT 2022, Volume 167, pages 1138-1164, 2022.
4. Full rank updates
S. Smith, "Subspace tracking with full rank updates", Signals, Systems and Computers, 1997.
5. Least Mean Square Error Reconstruction (LMSER)
L. Xu, “Least mean square error reconstruction principle for self-organizing neural nets", Neural Networks, Volume 6, pages 627–648, 1993.
6. Projection Approximation Subspace Tracking (PAST)
PAST [Geometric Algorithm]
B. Yang, “Projection approximation subspace tracking", IEEE Transactions on Signal Processing, Volume 43, pages 95–107, January 1995.
PAST-d
H. Zhu, W. Shi, P. Cai, "A novel algorithm of subspace tracking based on the PAST method", IEEE International Conference on Electronics, Communications and Control, ICECC 2011, 2011.
Orthogonal PAST (OPAST)
K. Abed-Meraim, A. Chkeif, Y. Hua, “Fast orthonormal PAST algorithm,” IEEE Signal Processing Letters, Volume 7, No. 3, pages 60–62, 2000.
NewOPAST
H. Zhang, G. Ren, H. Zhang, J. Zhang, "An improved OPAST algorithm for spatio-temporal multiuser detection technique based on subspace tracking", IEEE International Conference onCommunications System, ICCS 2004, pages 401-404, 2001.
Variable Regularized PAST (VR-PAST)
S. Chan, H. Tan, J. Lin, B. Liao, "A New Local Polynomial Modeling Based Variable Forgetting Factor and Variable Regularized PAST Algorithm for Subspace Tracking", IEEE Transactions on Aerospace and Electronic Systems, Volume 54, No. 3, pages 1530-1544, June 2018.
EIV-PAST
S. Chan, H. Tan and J. Lin, "A New Variable Forgetting Factor and Variable Regularized Square Root Extended Instrumental Variable PAST Algorithm With Applications", IEEE Transactions on Aerospace and Electronic Systems, Volume 56, No. 3, pages 1886-1902, June 2020.
PAST-MD
W. Zhao, S. Chan, J. Lin, "Efficient Hardware Realization of a New Variable Regularized PAST Algorithm With Multiple Deflation", IEEE Access, Volume 9, pages 240-255, 2021.
7. APST
M. Vila, C. Lopez, J. Riba, "Affine Projection Subspace Tracking", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2021, pages 3705-3709, 2021.
NIC
Y. Miao, Y. Hua, "Fast Subspace Tracking and Neural Network Learning by a Novel Information Criterion", IEEE Transactions on Signal Processing, Volume 46, No.7, pages 1967-1978, July 1998.
D. Feng, W. Zheng, "On convergence of fast subspace tracking based on novel information criterion", IEEE International Conference on Neural Networks and Signal Processing, pages 261-264, 2003.
FAPI
R. Badeau, B. David, G. Richard, “Fast approximated power iteration subspace tracking,” IEEE Transactions on Signal Processing, pages 2931-2941, 2005.
MFAPI
Q. Wu, J. Zheng, Z. Dong, E. Panayirci, Z. Wu, R. Qingnuobu, "An Improved Adaptive Subspace Tracking Algorithm Based on Approximated Power Iteration", IEEE Access, Volume 6, pages 136-145, 2018.
DPM/FDPM
X. Doukopoulos, G. Moustakides, "The Fast Data Projection Method for Stable Subspace Tracking", European Signal Processing Conference, 2005.
X. Doukopoulos, G. Moustakides, “Fast and stable subspace tracking", IEEE Transactions on Signal Processing, Volume 56, No. 4, pages 1452-1465, 2008.
R. Wang, M. Yao, D. Zhang, H. Zou, "A Novel Orthonormalization Matrix Based Fast and Stable DPM Algorithm for Principal and Minor Subspace Tracking", IEEE Transactions on Signal Processing, pages 466-472, January 2012.
YAST
R. Badeau, G. Richard, B. David, “Fast and stable YAST algorithm for principal and minor subspace tracking", IEEE Transactions on Signal Processing, pages 3437-3446, 2008.
M. Lari, M. Karimi, "Stability and convergence analysis of the YAST subspace tracking algorithm", IEEE International Symposium on Telecommunications, pages 679-684, 2010.
obYAST
F. Yger, M. Berar, G. Gasso, A. Rakotomamonjy, "Oblique principal subspace tracking on manifold", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2012, pages 2429-2432, 2012.
GYAST
M. Arjomandi-Lari , M. Karimi , "Generalized YAST algorithm for signal subspace tracking", Signal Processing, Volume 117, pages 82-95, 2015.
LORAF/Fast LORAF/LORAF2
P. Strobach, "Low-rank adaptive filters", IEEE Transactions on Signal Processing, Volume 44, No 12, 1996.
OPIT
T. Le, K. Abed-Meraim, N. Trung, A. Hafiane, "OPIT: A Simple but Effective Method for Sparse Subspace Tracking in High-Dimension and Low-Sample-Size Context", IEEE Transactions on Signal Processing, Volume 72, pages 521-534, 2024.
Modern Subspace Tracking (18 papers)
These subspace tracking methods enable subspace tracking in the presence of partly observed data.
1. GROUSE [Geometric Algorithm]
L. Balzano, R. Nowak, B. Recht, “Online identification and tracking of subspaces from highly incomplete information", Allerton Conference on Communication, Control and Computing, 2010.
L. Balzano, S. Wright, “On GROUSE and Incremental SVD", IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing CAMSAP 2013, pages 1–4, 2013.
L. Balzano, S. Wright, “Local Convergence of an Algorithm for Subspace Identification from Partial Data", 2013.
P. Xiao, L. Balzano, “Online Sparse and Orthogonal Subspace Estimation from Partial Information", Allerton Conference on Communication, Control, and Computing, Allerton 2016, 284–291, 2016.
D. Zhang, L. Balzano, “Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation", International Conference on Artificial Intelligence and Statistics, 1460–1468, 2016.
G. Ongie, D. Hong, D. Zhang, L. Balzano, “Online Estimation of Coherent Subspaces with Adaptive Sampling", IEEE Workshop on Statistical Signal Processing, 2017.
G. Ongie, D. Hong, L. Balzano, D. Zhang, “Enhanced Online Subspace Estimation via Adaptive Sensing", Asilomar Confernce on Signals, Systems, and Computers, 2018.
R. Kennedy, R. Taylor, L. Balzano, “Online Completion of Ill-Conditioned Low-Rank Matrices", IEEE Global Conference on Signal and Information Processing, GlobalSIP 2014, 507–511, 2014.
L. Balzano, Y. Chi, Y. Luz, "Streaming PCA and Subspace Tracking: The Missing Data Case", Proceedings of IEEE, July 2018.
L Balzano, “On the equivalence of Oja's algorithm and GROUSE”, International Conference on Artificial Intelligence and Statistics, AISTATS 2022, Valencia, Spain, March 2022.
A. Falcon, B. Ancelin, J. Romberg, “Subspace Tracking with Dynamical Models on the Grassmannian”, Preprint, February 2024.
A. Falcon, B. Ancelin, J. Romberg,,"Subspace Tracking with Dynamical Models on the Grassmannian", IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2024, pages 1-5, 2024.
2. GREAT [Geometric Algorithm]
A. Sasfi, A. Padoan, I. Markovsky, F. Dorfler, "Subspace Tracking For Online System Identification", Preprint, 2024.
3. PETRELS [Geometric Algorithm]
PETRELS
Y. Chi, Y. Eldar, R. Calderbank, "PETRELS: Subspace Estimation and Tracking from Partial Observations", International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2012, 2012.
Y. Chi, R. Calderbank, Y. Eldar, “PETRELS: Parallel subspace estimation and tracking by recursive least squares from partial observations", IEEE Transactions on Signal Processing, Volume 61, No. 23, pages 5947–5959, 2013.
PETRELS with Detect-Skip-CFAR/SW-PETRELS
N. Linh-Trung, V. Nguyen, M. Thameri, T. Minh-Chinh, K. Abed-Meraim, "Low-complexity adaptive algorithms for robust subspace tracking", IEEE Journal of Selected Topics in Signal Processing, Volume 12, No. 6, pages 1197-1212, 2018.
PETRELS-ADMM
L. Trung-Thanh, V. Nguyen, N. Linh-Trung, K. Abed-Meraim, "Robust Subspace Tracking with Missing Data and Outliers via ADMM", European Signal Processing Conference, EUSIPCO 2019, 2019.
L. Thanh, N. Dung, N. Linhtrung, K. Abed Meraim, "Robust Subspace Tracking with Missing Data and Outliers: Novel Algorithm with Convergence Guarantee", IEEE Transactions on Signal Processing, 2021.
4. ST Miss/Robust ST Miss/Fed ST Miss (6 papers)
P. Narayanamurthy, V. Daneshpajooh, N. Vaswani, "Subspace Tracking from Missing and Outlier Corrupted Data", Preprint, October 2018.
P. Narayanamurthy, V. Daneshpajooh, N. Vaswani, "Provable Subspace Tracking with Missing Entries", IEEE International Symposium on Information Theory, ISIT 2019, pages 1867-1871, July 2019.
P. Narayanamurthy, N. Vaswani, A. Ramamoorth, "Federated Over-the-Air Subspace Learning from Incomplete Data", Preprint, February 2021.
P. Narayanamurthy, N. Vaswani, A. Ramamoorthy, "Federated Over-Air Robust Subspace Tracking from Missing Data", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2022, Volume 5598-5602, 2022.
P. Narayanamurthy, N. Vaswani, A. Ramamoorthy, "Federated Over-Air Subspace Tracking from Incomplete and Corrupted Data", IEEE Transactions on Signal Processing, 2022.