Hessian regularization based symmetric nonnegative matrix factorization for clustering gene expression and microbiome...

Area of Science:

• Machine Learning
• Bioinformatics
• Data Mining

Background:

• Nonnegative matrix factorization (NMF) and Symmetric NMF (SNMF) are effective clustering methods.
• Laplacian regularization enhances NMF/SNMF but has limitations in extrapolating to new data.
• Existing methods struggle with generalizing to unseen data points.

Purpose of the Study:

• To propose a novel variant of SNMF called Hessian regularization based symmetric nonnegative matrix factorization (HSNMF).
• To address the weak extrapolating ability of Laplacian regularization in NMF and SNMF.
• To enhance the performance of clustering algorithms, particularly for biological data.

Main Methods:

• Developed HSNMF by incorporating Hessian regularization into the SNMF framework.
• Compared HSNMF against traditional NMF, SNMF, and Laplacian regularization-based methods.
• Validated the proposed method on diverse datasets, including text, gene expression, and Human Microbiome Project (HMP) data.

Main Results:

• HSNMF demonstrated superior performance across various datasets compared to existing methods.
• The proposed Hessian regularization exhibited better data fitting and extrapolation capabilities than Laplacian regularization.
• HSNMF showed significant potential for application in biological data clustering tasks.

Conclusions:

• HSNMF offers an improved approach to clustering by enhancing extrapolation abilities.
• The method shows promise for analyzing complex biological datasets like gene expression and microbiome data.
• HSNMF represents a valuable advancement in nonnegative matrix factorization techniques for clustering.