Fast and Tuning-free Nonlinear Data Embedding and Integration based on DCOL

The rapid progress of single-cell technology has facilitated faster and more cost-effective acquisition of diverse omics data, enabling biologists to unravel the intricacies of cell populations, disease states, and developmental lineages. Additionally, the advent of multimodal single-cell omics technologies has opened up new avenues for studying interactions within biological systems. However, the high-dimensional, noisy, and sparse nature of single-cell omics data poses significant analytical challenges. Therefore, dimension reduction (DR) techniques play a vital role in analyzing such data. While many DR methods have been developed, each has its limitations. For instance, linear methods like PCA struggle to capture the highly diverse and complex associations between cell types and states effectively. In response, nonlinear techniques have been introduced; however, they may face scalability issues in high-dimensional settings, be restricted to single omics data, or primarily focus on visualization rather than producing informative embeddings for downstream tasks. Here, we formally introduce DCOL (Dissimilarity based on Conditional Ordered List) correlation, a functional dependency measure for quantifying nonlinear relationships between variables. Based on this measure, we propose DCOL-PCA and DCOL-CCA, for dimension reduction and integration of single- and multi-omics data. In simulation studies, our methods outperformed eight other DR methods and four joint dimension reduction (jDR) methods, showcasing stable performance across various settings. It proved highly effective in extracting essential factors even in the most challenging scenarios. We also validated these methods on real datasets, with our method demonstrating its ability to detect intricate signals within and between omics data and generate lower-dimensional embeddings that preserve the essential information and latent structures in the data.