Rank selection for non-negative matrix factorization.

Area of Science:

• Computational biology
• Data science
• Bioinformatics

Background:

• Non-Negative Matrix Factorization (NMF) is a key dimension reduction technique.
• NMF extracts features interpreted as data sub-structures, with rank controlling model complexity.
• Accurate rank selection is crucial but challenging due to NMF computation errors.

Purpose of the Study:

• To develop a novel, accurate, and efficient rank selection method for NMF.
• To address the difficulties in NMF rank selection caused by optimization errors.
• To improve the interpretability of extracted features and subcommunities.

Main Methods:

• Developed a new rank selection method based on hypothesis testing.
• Utilized a deconvolved bootstrap distribution for accurate significance level assessment.
• Compared the proposed method against bootstrap without deconvolution and cross-validation.

Main Results:

• The proposed method accurately estimates true NMF ranks, especially for hard-to-distinguish features.
• Demonstrated superior accuracy and computational efficiency compared to existing methods.
• Successfully applied to real microbiome data (OTU and functional metagenomic data).

Conclusions:

• The novel rank selection method provides accurate and efficient NMF rank determination.
• The method enhances the extraction of interpretable subcommunities from complex biological data.
• This approach offers a robust solution for NMF applications in various scientific fields.