K-Nearest-Neighbors Induced Topological PCA for scRNA Sequence Data Analysis

• URL: http://arxiv.org/abs/2310.14521v1
• Date: Mon, 23 Oct 2023 03:07:50 GMT
• Title: K-Nearest-Neighbors Induced Topological PCA for scRNA Sequence Data Analysis
• Authors: Sean Cottrell, Yuta Hozumi, Guo-Wei Wei
• Abstract summary: We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L$_2,1$ norm regularization. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse scRNA-seq datasets.
• Score: 0.3683202928838613
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis. Traditional PCA, a main workhorse in dimensionality reduction, lacks the ability to capture geometrical structure information embedded in the data, and previous graph Laplacian regularizations are limited by the analysis of only a single scale. We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L$_{2,1}$ norm regularization to address multiscale and multiclass heterogeneity issues in data. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. Rather than inducing filtration via the varying of a distance threshold, we introduced kNN-tPCA, where filtrations are achieved by varying the number of neighbors in a kNN network at each step, and find that this framework has significant implications for hyper-parameter tuning. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse benchmark scRNA-seq datasets, and showcase that our methods outperform other unsupervised PCA enhancements from the literature, as well as popular Uniform Manifold Approximation (UMAP), t-Distributed Stochastic Neighbor Embedding (tSNE), and Projection Non-Negative Matrix Factorization (NMF) by significant margins.

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