Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization.

Area of Science:

• Computational Biology
• Data Science
• Machine Learning

Background:

• Non-negative Matrix Factorization (NMF) is a matrix decomposition technique used for dimensionality reduction.
• Determining the optimal number of components (k) in NMF is a critical challenge.
• NMF decomposes a data matrix X into W and H matrices, where all values are non-negative.

Purpose of the Study:

• To assess methods for estimating the number of components (k) in NMF using synthetic data.
• To examine the impact of data normalization on the accuracy of k estimation in empirical datasets.
• To provide guidance on selecting k for NMF applications.

Main Methods:

• Evaluation of various k estimation methods on synthetic datasets with known component structures.
• Analysis of the effect of different normalization techniques on k estimation accuracy using real-world data.
• Comparison of methods including PCA-based approaches and Brunet's Cophenetic Correlation Coefficient.

Main Results:

• In synthetic data with orthogonal components, PCA-based methods and Brunet's CCC showed high accuracy for estimating k.
• Normalization exhibited an unpredictable effect on k estimation accuracy in empirical data.
• Different k estimation methods yielded highly variable results across various normalization strategies.

Conclusions:

• It is recommended to avoid normalization when estimating k in NMF.
• For orthogonal components, Velicer's MAP or Minka's Laplace-PCA methods may be optimal.
• When component orthogonality is unknown, no single method for estimating k is consistently preferable.