Thresholding Approach for Low-Rank Correlation Matrix Based on MM Algorithm.

Area of Science:

• Statistics
• Bioinformatics
• Data Science

Background:

• Low-rank approximation of correlation matrices can lead to misinterpretations when estimated values deviate significantly from zero.
• Existing methods may produce inaccurate results, hindering the reliable interpretation of complex data structures.

Purpose of the Study:

• To develop a novel approach for estimating sparse low-rank correlation matrices.
• To enhance the interpretability of correlation matrix features using visualization tools.
• To overcome limitations of existing methods that lead to misinterpretations.

Main Methods:

• Proposed a novel method for estimating sparse low-rank correlation matrices using threshold values.
• Introduced a new cross-validation function to tune threshold values.
• Utilized the MM algorithm for matrix estimation and grid search for threshold selection.

Main Results:

• The proposed method demonstrated superior performance in terms of false positive rate (FPR), interpretability, and average relative error compared to the tandem approach.
• In microarray gene expression analysis, the proposed method achieved significantly lower FPRs (0.128-0.197) than the tandem approach (0.285).

Conclusions:

• A novel approach for estimating sparse low-rank correlation matrices was successfully developed.
• The proposed method enhances interpretability through heatmap visualization, effectively preventing misinterpretations.
• The method's superiority was validated through numerical simulations and real-world data applications.