Nonparametric Tikhonov Regularized NMF and Its Application in Cancer Clustering

Area of Science:

• Computational Biology
• Data Science
• Machine Learning

Background:

• Tikhonov regularized nonnegative matrix factorization (TNMF) is widely used in data analysis but often relies on fixed regularization parameters.
• Learning regularization parameters directly from data is a significant challenge in TNMF algorithm development.
• The quality of Tikhonov regularized solutions is sensitive to the choice of regularization parameters.

Purpose of the Study:

• To develop methods for automatically learning regularization parameters in TNMF directly from datasets.
• To propose a convergent additive update algorithm for TNMF.

Main Methods:

• The L-curve approach is utilized to derive two novel formulas for automatic regularization parameter selection.
• A convergent algorithm for TNMF is developed based on additive update rules.

Main Results:

• The proposed formulas enable data-driven learning of regularization parameters for TNMF.
• The developed algorithm demonstrates effectiveness in practical applications.
• The study successfully applies the enhanced TNMF to cancer clustering tasks.

Conclusions:

• Automatic learning of regularization parameters significantly improves TNMF performance.
• The proposed L-curve based method offers a robust approach for parameter selection in TNMF.
• The developed TNMF algorithm and parameter learning strategy are effective for complex data analysis, including cancer clustering.