Vol. 5 No. 1 (2025): Issue 5
Articles

Nonnegative Matrix Factorization with Fast Bayesian Inference

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  • Lucas Pereira,
  • Mariana Santos,
  • Rafael Oliveira
Lucas Pereira
Department of Computational Mathematics, Universidade Federal do Espírito Santo, Serra, 29175-000, Brazil
Mariana Santos
Institute of Advanced Computing, Universidade Federal de Alagoas, Arapiraca, 57309-005, Brazil
Rafael Oliveira
Center for Applied Mathematics and Computational Modeling, Universidade Federal de Sergipe, Itabaiana, 49500-000, Brazil

Published 2025-01-21

Keywords

  • Nonnegative Matrix Factorization,
  • Bayesian Inference,
  • Computational Efficiency,
  • Latent Feature Extraction,
  • Data Analysis

How to Cite

Pereira, L., Santos, M., & Oliveira, R. (2025). Nonnegative Matrix Factorization with Fast Bayesian Inference. Journal of Computational Biology and Medicine, 5(1). Retrieved from https://journal.mri-pub.com/index.php/JCBM/article/view/68

Abstract

Nonnegative Matrix Factorization (NMF) has been widely employed in various fields for its ability to extract meaningful latent features from high-dimensional data. However, the existing NMF algorithms often suffer from computational inefficiency, limiting their applicability to large-scale datasets. In light of this, this paper addresses the pressing need for a faster and more efficient Bayesian inference method for NMF. Despite the significant research efforts dedicated to improving NMF algorithms, challenges remain in achieving both speed and accuracy. To fill this gap, we propose a novel approach that combines the benefits of nonnegative constraints and Bayesian inference, leading to a Fast Bayesian Inference method for NMF. Our method not only accelerates the computation process but also enhances the interpretability of the extracted features. Through comprehensive experiments on diverse datasets, we demonstrate the superior performance of our proposed method in terms of both speed and accuracy, highlighting its potential for widespread applications in data analysis and pattern recognition.

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References

  1. D. Cai et al., "Graph Regularized Nonnegative Matrix Factorization for Data Representation," IEEE Trans. Pattern Anal. Mach. Intell., vol. 33, pp. 1548-1560, 2011.
  2. K. Berahmand et al., "Graph Regularized Nonnegative Matrix Factorization for Community Detection in Attributed Networks," IEEE Trans. Network Sci. Eng., vol. 10, pp. 372-385, 2023.
  3. Z. Liu et al., "A High-Order Proximity-Incorporated Nonnegative Matrix Factorization-Based Community Detector," IEEE Trans. Emerging Topics Comput. Intell., vol. 7, pp. 700-714, 2023.
  4. X. Li et al., "A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization," IEEE Trans. Knowl. Data Eng., vol. 35, pp. 2206-2219, 2023.
  5. C.-J. Lin, "Projected Gradient Methods for Nonnegative Matrix Factorization," Neural Comp., vol. 19, pp. 2756-2779, 2007.
  6. W. Wang et al., "Heart-lung sound separation by nonnegative matrix factorization and deep learning," Biomed. Signal Process. Control., vol. 79, p. 104180, 2023.
  7. A. Hajiveiseh et al., "Deep asymmetric nonnegative matrix factorization for graph clustering," Pattern Recognit., vol. 148, p. 110179, 2023.
  8. E. Nasiri et al., "Robust graph regularization nonnegative matrix factorization for link prediction in attributed networks," Multimedia Tools Appl., vol. 82, pp. 3745-3768, 2022.
  9. C. He et al., "A Survey of Community Detection in Complex Networks Using Nonnegative Matrix Factorization," IEEE Trans. Comput. Social Syst., vol. 9, pp. 440-457, 2022.
  10. S. Zhou et al., "Fast Bayesian Inference of Reparameterized Gamma Process With Random Effects," in IEEE Transactions on Reliability, vol. 73, 2024.
  11. Z. C. Quiroz et al., "Fast Bayesian inference of block Nearest Neighbor Gaussian models for large data," in Statistics and Computing, vol. 33, 2023.
  12. M. Adachi et al., "Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination," in Neural Information Processing Systems, 2022.
  13. H. Yan and D. Shao, ‘Enhancing Transformer Training Efficiency with Dynamic Dropout’, Nov. 05, 2024, arXiv: arXiv:2411.03236. doi: 10.48550/arXiv.2411.03236.
  14. A. Gu et al., "GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling," in Astrophysical Journal, vol. 935, 2022.
  15. M. Teimouri, "Fast Bayesian Inference for Birnbaum-Saunders Distribution," in Computational Statistics, vol. 38, 2022.
  16. O. Gressani and P. Lambert, "Laplace approximations for fast Bayesian inference in generalized additive models based on P-splines," in Computational Statistics & Data Analysis, vol. 154, 2021.
  17. C. C. Monnahan and K. Kristensen, "No-U-turn sampling for fast Bayesian inference in ADMB and TMB: Introducing the adnuts and tmbstan R packages," in PLoS ONE, vol. 13, 2018.
  18. H. Kim, "Fast Bayesian Inference for Gaussian Cox Processes via Path Integral Formulation," in Neural Information Processing Systems, 2021.
  19. A. Diana et al., "Fast Bayesian inference for large occupancy datasets," in Biometrics, vol. 79, 2021.