Optimization and expansion of non-negative matrix factorization.

Area of Science:

• Bioinformatics
• Signal Processing
• Artificial Intelligence

Background:

• Non-negative Matrix Factorization (NMF) is a widely used technique across AI, signal processing, and bioinformatics.
• Existing NMF algorithms struggle with large matrices, slow convergence, and missing data.
• Most NMF research focuses on blind decomposition, neglecting prior knowledge and robust hyperparameter selection.

Purpose of the Study:

• To develop a faster NMF algorithm with improved convergence rates.
• To leverage NMF's natural handling of missing values for rank determination.
• To incorporate prior knowledge into NMF for more meaningful decompositions and explore novel applications.

Main Methods:

• Sequential coordinate-wise descent for enhanced convergence.
• Utilizing NMF's inherent missing value handling for rank hyperparameter determination.
• Employing masking techniques to inject prior knowledge and desired properties.

Main Results:

• The proposed NMF implementation demonstrates faster convergence compared to existing methods.
• NMF effectively handles missing values, enabling a novel rank determination strategy.
• New applications of NMF are showcased, including tumor content deconvolution with results comparable to ISOpure.
• Missing value imputation shows superior accuracy and computational efficiency over conventional methods.

Conclusions:

• The novel NMF approach offers significant improvements in speed and accuracy.
• The proposed rank tuning method based on missing value imputation is theoretically sound.
• The R package NNLM, containing these algorithms, is freely available.