Rank Selection in Nonnegative Matrix Factorization using Minimum Description Length.

Area of Science:

• Machine Learning
• Data Science
• Computational Statistics

Background:

• Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique.
• NMF factorizes data into basis and coefficient matrices, promoting sparse, parts-based representations.
• Extracting interpretable, real parts enhances data analysis over holistic features.

Purpose of the Study:

• To propose a novel mechanism for selecting the optimal subspace size in NMF.
• To improve the interpretability and accuracy of NMF feature extraction.
• To provide a robust method for determining the number of features in NMF.

Main Methods:

• Utilized a minimum description length (MDL) technique for subspace size selection.
• Applied NMF to factorize nonnegative data matrices.
• Validated the method on both synthetic and real-world datasets.

Main Results:

• The proposed MDL technique provides plausible subspace size estimates for real data.
• The method accurately predicts the known subspace size for synthetic data.
• Demonstrated effective noise minimization while extracting key features.

Conclusions:

• The minimum description length technique offers an effective approach for NMF subspace size selection.
• This method enhances the interpretability and reliability of NMF applications.
• An implementation in Matlab is provided for practical use.