Model Selection for Non-Negative Tensor Factorization with Minimum Description Length.

Area of Science:

• Multi-way data analysis
• Machine learning
• Statistical modeling

Background:

• Non-negative Tensor Factorization (NTF) is crucial for multi-way data analysis.
• Determining the non-negative rank in NTF is challenging, often relying on expert opinion or trial-and-error.
• Existing rank selection methods lack robustness and accuracy.

Purpose of the Study:

• To propose a novel, principled rank selection criterion for NTF.
• To enhance the accuracy of factor matrix estimation and missing data imputation in NTF.
• To facilitate knowledge discovery from high-order non-negative data.

Main Methods:

• Developed a Minimum Description Length (MDL) based rank selection criterion for NTF.
• Applied the MDL principle to tensor slices to address data-tensor/factor-matrix size imbalance.
• Utilized Normalized Maximum Likelihood (NML) for histogram densities within the MDL framework.

Main Results:

• The proposed MDL-based method significantly outperforms existing criteria in estimating true ranks.
• The new criterion demonstrates superior accuracy in completing missing values within tensors.
• Empirical validation on synthetic and real-world data confirms the method's effectiveness.

Conclusions:

• The novel MDL-based rank selection criterion offers a robust and accurate approach for NTF.
• This method provides a data-driven solution for a critical parameter in NTF.
• The improved rank selection facilitates more reliable knowledge discovery from complex datasets.