An optimal pairwise merge algorithm improves the quality and consistency of nonnegative matrix factorization.

Area of Science:

• Data Science
• Machine Learning
• Signal Processing

Background:

• Non-negative Matrix Factorization (NMF) is crucial for dimensionality reduction and feature extraction.
• Standard NMF algorithms can converge to suboptimal local minima, affecting solution quality and consistency.

Purpose of the Study:

• To develop an improved NMF method that overcomes limitations of existing algorithms.
• To enhance the consistency and quality of NMF solutions by escaping poor local minima.

Main Methods:

• Performing NMF in an expanded higher-dimensional feature space.
• Iteratively merging components using an efficient, analytically solvable pairwise strategy.
• Reducing occurrences of plateau phenomena near saddle points.

Main Results:

• The proposed method effectively allows optimizers to escape poor local minima.
• Demonstrated greater consistency in NMF solutions through theoretical and experimental validation.
• Achieved computational performance comparable to established methods.

Conclusions:

• The novel NMF approach offers improved performance and solution consistency.
• Recommended as a preferred method for various NMF applications due to its effectiveness.
• Compatible with existing NMF algorithms, enhancing their applicability.