PLPCA: Persistent Laplacian-Enhanced PCA for Microarray Data Analysis.

Area of Science:

• Bioinformatics
• Computational Biology
• Machine Learning

Background:

• Principal Component Analysis (PCA) is a standard for gene expression data dimensionality reduction.
• Existing PCA methods struggle with interpretability, class ambiguity, and capturing complex data structures.
• Current regularized PCA approaches face challenges in multiscale analysis and higher-order interactions.

Purpose of the Study:

• To introduce Persistent Laplacian-enhanced Principal Component Analysis (PLPCA) for improved gene expression data analysis.
• To overcome the limitations of traditional and existing regularized PCA methods.
• To enhance the identification of disease-causing genes through advanced dimensionality reduction.

Main Methods:

• Developed PLPCA by integrating persistent spectral graph theory and persistent Laplacians with PCA.
• Utilized persistent Laplacians for multiscale analysis via filtration.
• Incorporated higher-order simplicial complexes to capture higher-order data interactions.

Main Results:

• PLPCA demonstrated superior performance on ten benchmark microarray datasets.
• Achieved up to a 12% improvement over state-of-the-art PCA models.
• Showcased enhanced classification accuracy across five evaluation metrics.

Conclusions:

• PLPCA offers a significant advancement in gene expression data analysis and dimensionality reduction.
• The method effectively addresses multiscale and higher-order interaction challenges.
• PLPCA provides improved interpretability and classification performance compared to existing techniques.