DEEP NEURAL NETWORK-BASED APPROACH FOR COMPUTING SINGULAR VALUES OF MATRICES

Authors

  • Diyari A. Hassan Faculty of Engineering & Computer Science, Qaiwan International University Sulaymaniyah, Kurdistan Region-Iraq

DOI:

https://doi.org/10.25271/sjuoz.2025.13.1.1345

Keywords:

Singular Value Decomposition, Matrix Factorization, Convolutional Neural Networks, Computational Compelxity

Abstract

Matrix factorization techniques, such as Singular Value Decomposition (SVD), Eigenvalue Decomposition (EVD), and QR decomposition, have long been pivotal in computational mathematics, particularly for applications in signal processing, machine learning, and data analysis. With the growing size and complexity of data, traditional methods of matrix factorization face challenges in efficiency and scalability. This paper investigates the implementation of Convolutional Neural Networks (CNNs) for computing the singular values of both real and complex matrices. By leveraging the hierarchical feature extraction capabilities of CNNs, this approach aims to enhance the accuracy, efficiency, and scalability of SVD calculations. The proposed CNN-based SVD method is evaluated against the conventional SVD algorithm, demonstrating superior performance in terms of computational time and accuracy.

References

Albawi, S., Bayat, O., Al-Azawi, S., & Ucan, O. N. (2018). Social touch gesture recognition using convolutional neural network. Computational Intelligence and Neuroscience,2018(1),6973103.DOI:https://doi.org/10.1155/2018/6973103

Anwar, S. M., Majid, M., Qayyum, A., Awais, M., Alnowami, M., & Khan, M. K. (2018). Medical image analysis using convolutional neural networks: a review. Journal of medicalsystems,42,1-13.DOI: https://doi.org/10.1007/s10916-018-1088-1

Finol, D., Lu, Y., Mahadevan, V., & Srivastava, A. (2019). Deep convolutional neural networks for eigenvalue problems in mechanics. International Journal for Numerical Methods in Engineering, 118(5), 258-275. DOI: https://doi.org/10.1002/nme.6012

Golub, G. H., & Van Loan, C. F. (2013). Matrix computations. JHUpress.DOI: https://doi.org/10.1137/1.9781421407944

Han, J., Lu, J., & Zhou, M. (2020). Solving high-dimensional eigenvalue problems using deep neural networks: A diffusion Monte Carlo like approach. Journal of ComputationalPhysics,423,109792.DOI: https://doi.org/10.1016/j.jcp.2020.109792

Hang, T., Yang, G., Yu, B., Liang, X., & Tang, Y. (2013). Neural network based algorithm for generalized eigenvalue problem. In 2013 International Conference on Information Science and Cloud Computing Companion (pp.446-451).IEEE.DOI: https://doi.org/10.1109/ISCC-C.2013.93

Hogben, L. (Ed.). (2006). Handbook of linear algebra. CRC press. DOI: https://doi.org/10.1201/9781420010572

Hassan, M. M., & Taher, S. A. (2022). Analysis and classification ofautismdata using machine learning algorithms. Science Journal of University of Zakho, 10(4),206-212.DOI: https://doi.org/10.25271/sjuoz.2022.10.4.1036

Hsia, S. C., Wang, S. H., & Chang, C. Y. (2021). Convolution neural network with low operation FLOPS and high accuracy for image recognition. Journal of Real-Time Image Processing, 18(4), 1309-1319 DOI: https://doi.org/10.1007/s11554-021-01140-9

Hsu, C. H., & Kremer, U. (2003). The design, implementation, and evaluation of a compiler algorithm for CPU energy reduction. In Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation(pp.38-48).DOI: https://doi.org/10.1145/781131.781137

Hu, Z. (2022). Estimation and application of matrix eigenvalues based on deep neural network. Journal of Intelligent Systems,31(1),1246-1261.DOI: https://doi.org/10.1515/jisys-2022-0126

LeCun, Y. (1998). The MNIST database of handwritten digits. http://yann. lecun. com/exdb/mnist/.

Li, Z., Liu, F., Yang, W., Peng, S., & Zhou, J. (2021). A survey of convolutional neural networks: analysis, applications, and prospects. IEEE transactions on neural networks and learning systems, 33(12), 6999-7019. DOI: 10.1109/TNNLS.2021.3084827

Mala, Y. H., & Mohammad, M. A. (2022). Brain Waves Signal Modeling for Object Classification Using Random Forest Method. Science Journal of University of Zakho, 10(1), 16-23. DOI:https://doi.org/10.25271/sjuoz.2022.10.1.876

Nguyen, D. M., Tsiligianni, E., & Deligiannis, N. (2018). Matrix factorization via deep learning. arXiv preprint arXiv:1812.01478.DOI:https://doi.org/10.48550/arXiv.1812.01478

Rawat, W., & Wang, Z. (2017). Deep convolutional neural networks for image classification: A comprehensive review. Neural computation, 29(9), 2352-2449. DOI: 10.1162/neco_a_00990

Strang, G. (2022). Introduction to linear algebra. Wellesley-Cambridge Press. DOI: 10.4236/jamp.2020.87104

Wu, C. H., & Tsai, P. Y. (2019). An SVD processor based on Golub–Reinsch algorithm for MIMO precoding with adjustable precision. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(7), 2572-2583. DOI: 10.1109/TCSI.2019.2899211

Yi, Z., Fu, Y., & Tang, H. J. (2004). Neural networks based approach for computing eigenvectors and eigenvalues of symmetric matrix. Computers & Mathematics with Applications,47(8-9),1155-1164.DOI:https://doi.org/10.1016/S0898-1221(04)90110-1

Zhang, X. D. (2017). Matrix analysis and applications. CambridgeUniversityPress.DOI:https://doi.org/10.1017/9781108277587

Zou, X., Tang, Y., Bu, S., Luo, Z., & Zhong, S. (2013). Neural-network-based approach for extracting eigenvectors and eigenvalues of real normal matrices and some extension to real matrices. Journal of Applied Mathematics, 2013. DOI:https://doi.org/10.1155/2013/597628

Downloads

Published

2025-01-05

How to Cite

Hassan, D. A. (2025). DEEP NEURAL NETWORK-BASED APPROACH FOR COMPUTING SINGULAR VALUES OF MATRICES. Science Journal of University of Zakho, 13(1), 1–6. https://doi.org/10.25271/sjuoz.2025.13.1.1345

Issue

Section

Science Journal of University of Zakho