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Efficient hybrid algorithm for nonnegative matrix factorization based on modified nonmonotone linear search
Jing Wu1,2, Wenbo Li1, Lijun Su1
1School of Mathematics, Xi'an University of Technology, Xi'an, China.
Plos One
|July 30, 2026
Summary
This study introduces a modified nonmonotone line search algorithm for nonnegative matrix factorization (NMF). The enhanced hybrid method improves global minimum identification and convergence speed, outperforming existing techniques.
Area of Science:
- Numerical analysis
- Optimization algorithms
- Machine learning
Background:
- Nonnegative matrix factorization (NMF) is crucial for dimensionality reduction and feature extraction.
- Existing NMF algorithms face challenges in convergence speed and identifying global minima.
- Line search methods are essential for optimizing iterative algorithms.
Purpose of the Study:
- To develop a modified nonmonotone line search algorithm for enhanced NMF.
- To improve the global minimum identification and convergence rate of NMF algorithms.
- To propose a hybrid algorithm integrating advanced optimization techniques.
Main Methods:
- A modified nonmonotone line search with a variable parameter was developed.
- A hybrid algorithm combining projected Barzilai-Borwein and block coordinate descent for ANLS subproblems.
- Integration of a larger step size technique to accelerate convergence.
Main Results:
- The modified algorithm enhances global minimum identification and convergence speed.
- The hybrid ANLS approach effectively addresses subproblems.
- Global convergence is established under mild assumptions.
- Numerical experiments show superior efficiency for NMF.
Conclusions:
- The proposed modified nonmonotone line search algorithm offers significant improvements for NMF.
- The hybrid approach demonstrates state-of-the-art performance on synthetic and real datasets.
- This work contributes a more efficient and robust method for nonnegative matrix factorization.
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