K-Nearest-Neighbors Induced Topological PCA for Single Cell RNA-Sequence Data Analysis.

Area of Science:

• Computational Biology
• Genomics
• Data Science

Background:

• Single-cell RNA sequencing (scRNA-seq) reveals cellular heterogeneity but faces analysis challenges due to data sparsity and high dimensionality.
• Traditional dimensionality reduction methods like PCA may not capture complex geometrical structures or multiscale information inherent in scRNA-seq data.

Approach:

• Propose topological Principal Components Analysis (tPCA) combining persistent Laplacian (PL) and L2,1 norm regularization to address multiscale and multiclass heterogeneity.
• Introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique (kNN-PL) to enhance the robustness of PL and address limitations of traditional persistent homology.
• Develop kNN-tPCA, where filtration is achieved by varying kNN neighbors, offering implications for hyper-parameter tuning.

Key Points:

• tPCA and kNN-tPCA methods were validated on 11 diverse scRNA-seq datasets.
• Both methods demonstrate superior performance compared to unsupervised PCA enhancements, UMAP, tSNE, and NMF.
• tPCA showed significant improvements in classification (F1 metric) and kNN-tPCA in clustering (ARI metric).

Conclusions:

• The proposed tPCA and kNN-tPCA methods offer effective solutions for dimensionality reduction and feature selection in scRNA-seq data analysis.
• These topological approaches successfully capture multiscale and multiclass heterogeneity, outperforming existing state-of-the-art methods.
• The kNN-tPCA framework provides a novel approach to hyper-parameter tuning in topological data analysis.