Nonlinear dimensionality reduction based visualization of single-cell RNA sequencing data

Single-cell multi-omics technology has catalyzed a transformative shift in contemporary cell biology, illuminating the nuanced relationship between genotype and phenotype. This paradigm shift hinges on the understanding that while genomic structures remain uniform across cells within an organism, the expression patterns dictate physiological traits. Leveraging high throughput sequencing, single-cell RNA sequencing (scRNA-seq) has emerged as a powerful tool, enabling comprehensive transcriptomic analysis at unprecedented resolution. This paper navigates through a landscape of dimensionality reduction techniques essential for distilling meaningful insights from the scRNA-seq datasets. Notably, while foundational, Principal Component Analysis may fall short of capturing the intricacies of diverse cell types. In response, nonlinear techniques have garnered traction, offering a more nuanced portrayal of cellular relationships. Among these, Pairwise Controlled Manifold Approximation Projection (PaCMAP) stands out for its capacity to preserve local and global structures. We present an augmented iteration, Compactness Preservation Pairwise Controlled Manifold Approximation Projection (CP-PaCMAP), a novel advancement for scRNA-seq data visualization. Employing benchmark datasets from critical human organs, we demonstrate the superior efficacy of CP-PaCMAP in preserving compactness, offering a pivotal breakthrough for enhanced classification and clustering in scRNA-seq analysis. A comprehensive suite of metrics, including Trustworthiness, Continuity, Mathew Correlation Coefficient, and Mantel test, collectively validate the fidelity and utility of proposed and existing techniques. These metrics provide a multi-dimensional evaluation, elucidating the performance of CP-PaCMAP compared to other dimensionality reduction techniques.