A statistical framework for non-negative matrix factorization based on generalized dual divergence.

Area of Science:

• Machine Learning
• Statistical Modeling
• Data Analysis

Background:

• Non-negative matrix factorization (NMF) is a widely used dimensionality reduction technique.
• Existing NMF methods often rely on specific noise assumptions or divergences.
• There is a need for more flexible and generalized NMF frameworks.

Purpose of the Study:

• To propose a novel statistical framework for NMF based on generalized dual Kullback-Leibler divergence.
• To develop a family of algorithms within this framework, including those with sparsity constraints.
• To provide a generalized and adaptable NMF approach for diverse applications.

Main Methods:

• Development of a statistical framework utilizing generalized dual Kullback-Leibler divergence.
• Algorithm design incorporating sparsity constraints.
• Convergence proofs using the Expectation-Maximization algorithm.
• Introduction of a goodness-of-fit measure for NMF.

Main Results:

• A generalized NMF framework accommodating exponential family models and various noise structures.
• Convergence of developed algorithms proven via Expectation-Maximization.
• Demonstrated utility in unsupervised and semi-supervised learning through cancer genomics application.
• Performance validated on both simulated and real-world data.

Conclusions:

• The proposed framework offers a valuable alternative to existing NMF methods.
• The framework is adaptable to deep learning paradigms, including reinforcement learning and neural networks.
• This generalized approach enhances NMF's applicability in complex data analysis, such as genomics.