Nonlinear embedding and integration of omics data: a fast and tuning-free approach.

The rapid progress of single-cell technology has facilitated cost-effective acquisition of diverse omics data, allowing biologists to unravel the complexities of cell populations, disease states, and more. Additionally, single-cell multi-omics technologies have opened new avenues for studying biological interactions. However, the high dimensionality and sparsity of omics data present significant analytical challenges. Dimension reduction (DR) techniques are hence essential for analyzing such complex data, yet many existing methods have inherent limitations. Linear methods like principal component analysis (PCA) struggle to capture intricate associations within data. In response, nonlinear techniques have emerged, but they may face scalability issues, be restricted to single-omics data, or prioritize visualization over generating informative embeddings. Here, we introduce dissimilarity based on conditional ordered list (DCOL) correlation, a novel measure for quantifying nonlinear relationships between variables. Based on this measure, we propose DCOL-PCA and DCOL-Canonical Correlation Analysis for dimension reduction and integration of single- and multi-omics data. In simulations, our methods outperformed nine DR methods and four joint dimension reduction methods, demonstrating stable performance across various settings. 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.