K-nearest-neighbors induced topological PCA for single cell RNA-sequence data analysis.

Area of Science:

• Computational Biology
• Bioinformatics
• Data Science

Background:

• Single-cell RNA sequencing (scRNA-seq) data analysis faces challenges due to sparsity and high dimensionality.
• Traditional dimensionality reduction techniques like PCA may not capture complex geometrical structures or multiscale heterogeneity inherent in scRNA-seq data.
• Existing graph Laplacian regularization methods are often limited to single-scale analysis.

Purpose of the Study:

• To develop novel dimensionality reduction and feature selection methods for scRNA-seq data.
• To address multiscale and multiclass heterogeneity issues in scRNA-seq datasets.
• To improve the robustness and performance of topological data analysis in scRNA-seq data interpretation.

Main Methods:

• Proposed topological Principal Components Analysis (tPCA) integrating persistent Laplacian (PL) with L2,1 norm regularization.
• Introduced k-Nearest-Neighbor (kNN) persistent Laplacian (kNN-PL) to enhance the robustness of the PL method.
• Developed kNN-tPCA by varying kNN neighbors for filtration, offering improved hyper-parameter tuning.

Main Results:

• Validated tPCA and kNN-tPCA on 11 diverse scRNA-seq datasets.
• Demonstrated superior performance of tPCA and kNN-tPCA over unsupervised PCA enhancements, UMAP, tSNE, and NMF.
• Achieved significant improvements in classification (F1 metric) and clustering (ARI metric) compared to existing methods.

Conclusions:

• tPCA and kNN-tPCA are effective methods for dimensionality reduction and feature selection in scRNA-seq data analysis.
• These topological approaches successfully capture multiscale heterogeneity, outperforming traditional and other advanced methods.
• The proposed kNN-tPCA framework provides a robust and adaptable solution for analyzing complex single-cell data.