Random Projection Methods Outperform Principal Component Analysis for Dimensionality Reduction in Single Cell RNA-Seq

Principal component analysis (PCA) is one of the most frequently used dimensionality reduction methods for high-dimensional datasets, especially single-cell RNA sequencing (scRNA-seq). Despite its popularity, PCA faces challenges, particularly related to its performance degrading as the dataset size increases. Additionally, PCA is sensitive to outliers and assumes linearity. Random projection (RP) methods have emerged as a promising alternative to address several of PCA's limitations. In this study, we conduct a systematic and comprehensive evaluation of PCA and RP methods, including singular value decomposition (SVD) and randomized SVD approaches, against multiple RP methods including sparse random projection, Gaussian random projection, and we introduce a Matching Sparsity Random Projection algorithm that adaptively calibrates projection matrix density according to input data sparsity patterns, emphasizing both computational scalability and effectiveness in downstream analytical tasks. We evaluated these methods on multiple publicly available scRNA-seq datasets that include both labeled and unlabeled scenarios. Clustering performance is assessed using Hierarchical Clustering and Spherical K-Means algorithms, with labeled datasets evaluated through Hungarian algorithm accuracy and Mutual Information metrics. For unlabeled datasets, we used the Dunn Index and Gap Statistic to quantify cluster separation quality. Across both dataset types, the Within-Cluster Sum of Squares metric is used to assess variability. Moreover, locality preservation is examined, with RP methods, including our adaptive sparsity approach, outperforming PCA in several of the evaluated metrics. Our experimental results show that RP methods not only deliver substantial computational speed improvements over PCA but also rival, and in some cases, exceed PCA in preserving data variability and clustering quality. Through this comprehensive methodological comparison, our work provides critical guidance for selecting appropriate dimensionality reduction strategies that effectively balance computational demands, scalability requirements, and analytical quality in downstream analyses.