A Principal Component Estimation Algorithm with Adaptive Learning Rate and Its Convergence Analysis
Source abstract
Abstract
The deterministic discrete-time method is a dominant approach for analyzing neural network algorithms. To address the issue where conventional convergence conditions impose stringent restrictions on the range of learning factors, this paper proposes a principal component estimation algorithm with an adaptive learning factor, which guarantees global convergence. The convergence of the algorithm is analyzed using the deterministic discrete-time method, and conditions ensuring convergence are established. Unlike convergence conditions for other algorithms, the proposed algorithm’s convergence conditions eliminate restrictions on the learning factor, thereby extending its feasible range. Simulation results demonstrate that the proposed algorithm effectively resolves ill-conditioned matrix problems. When compared with existing algorithms, the proposed algorithm exhibits significantly faster convergence speed than several current methods.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Neural Networks and Applications · Machine Learning and ELM · Advanced Adaptive Filtering Techniques
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
The 54th Research Institute of China Electronics Technology Group Corporation, Shijiazhuang 050081, China
College of Weaponry Engineering, Naval University of Engineering, Wuhan 430033, China
Rocket Force University of Engineering, Xi’an 710025, China
Funding
National Natural Science Foundation of China
References (30)
Show source-provided references
1. Du, K.-L., and Swamy, M. (2019). Principal component analysis. Neural Networks and Statistical Learning, Springer.10.1007/978-1-4471-7452-3 ↗
2. Direction-of-arrival estimation for coprime array via virtual array interpolation10.1109/TSP.2018.2872012 ↗
3. Classical vs. neural network-based PCA approaches for lossy image compression: Similarities and differences10.1016/j.asoc.2024.111721 ↗
4. Zhang, Q., Song, C., and Yuan, Y. (2024). Fault diagnosis of vehicle gearboxes based on adaptive wavelet threshold and LT-PCA-NGO-SVM. Appl. Sci., 14.10.3390/app14031212 ↗
5. An improved minor component analysis algorithm based on convergence analysis of 5G multi-dimensional signals10.1109/ACCESS.2019.2927438 ↗
6. Adaptive Learning Algorithm and Its Convergence Analysis with Complex-Valued Error Loss Network10.1016/j.neunet.2025.107677 ↗
7. Cha, G.-W., Choi, S.-H., Hong, W.-H., and Park, C.-W. (2023). Developing a prediction model of demolition-waste generation-rate via principal component analysis. Int. J. Environ. Res. Public Health, 20.10.3390/ijerph20043159 ↗
8. Gao, Y., Dong, H., Xu, Z., Li, H., Li, J., and Yuan, S. (2025). Multiple Minor Components Extraction in Parallel Based on Möller Algorithm. Electronics, 14.10.3390/electronics14204073 ↗
9. Lei, D., Zhang, Y., Lu, Z., Lin, H., Fang, B., and Jiang, Z. (2024). Slope stability prediction using principal component analysis and hybrid machine learning approaches. Appl. Sci., 14.10.3390/app14156526 ↗
10. Liu, Y., and Ruan, X. (2023). Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error. Appl. Sci., 13.10.3390/app13179551 ↗
11. Zhang, F., and Chen, Z. (2024). A Novel Reinforcement Learning-Based Particle Swarm Optimization Algorithm for Better Symmetry between Convergence Speed and Diversity. Symmetry, 16.10.3390/sym16101290 ↗
12. Zhang, Y., Wu, W., He, W., and Zhao, N. (2023). Algorithm design and convergence analysis for coexistence of cognitive radio networks in unlicensed spectrum. Sensors, 23.10.3390/s23249705 ↗
13. Principal component analysis applied to surface electromyography: A comprehensive review10.1109/ACCESS.2016.2593013 ↗
14. Kalla, U.K. (2016, January 25–27). Minor component analysis based anti-hebbian neural network scheme of decoupled voltage and frequency controller (DVFC) for nanohydro system. Proceedings of the 2016 IEEE 7th Power India International Conference (PIICON), Bikaner, India.10.1109/POWERI.2016.8077461 ↗
15. A unified convergence analysis of normalized PAST algorithms for estimating principal and minor components10.1016/j.sigpro.2012.07.020 ↗
16. Generalized minimum noise subspace for array processing10.1109/TSP.2017.2695457 ↗
17. A hebbian/anti-hebbian neural network for linear subspace learning: A derivation from multidimensional scaling of streaming data10.1162/NECO_a_00745 ↗
18. Fast adaptive algorithms for minor component analysis using Householder transformation10.1016/j.dsp.2011.05.001 ↗
19. Adaptive generalized eigen-pairs extraction algorithms and their convergence analysis10.1109/TSP.2016.2537260 ↗
20. Unified and coupled self-stabilizing algorithms for minor and principal eigen-pairs extraction10.1007/s11063-016-9520-3 ↗
21. Adaptive quasi-Newton algorithm for source extraction via CCA approach10.1109/TNNLS.2013.2280285 ↗
22. Kong, X., Hu, C., and Duan, Z. (2017). Principal Component Analysis Networks and Algorithms, Springer.10.1007/978-981-10-2915-8 ↗
23. Adaptive multiple minor directions extraction in parallel using a PCA neural network10.1016/j.tcs.2010.07.021 ↗
24. Necessary and sufficient conditions for convergence of the DDT systems of the normalized PAST algorithms10.1016/j.sigpro.2013.06.017 ↗
25. Convergence analysis of deterministic discrete time system of a unified self-stabilizing algorithm for PCA and MCA10.1016/j.neunet.2012.08.016 ↗
26. Fast subspace tracking and neural network learning by a novel information criterion10.1109/78.700968 ↗
27. Amari. Unified stabilization approach to principal and minor components extraction algorithms10.1016/S0893-6080(01)00116-2 ↗
28. Antoniou, A. (2016). Digital Signal Processing, McGraw-Hill.
29. Stable and orthonormal OJA algorithm with low complexity10.1109/LSP.2011.2108999 ↗
30. A new local polynomial modeling based variable forgetting factor and variable regularized PAST algorithm for subspace tracking10.1109/TAES.2018.2797780 ↗