ADM: adaptive graph diffusion for meta-dimension reduction.

Dimension reduction is essential for analyzing high-dimensional data, with various techniques developed to address diverse data characteristics. However, individual methods often struggle to capture all intricate patterns and complex structures simultaneously. To overcome this limitation, we introduce ADM (Adaptive graph Diffusion for Meta-dimension reduction), a novel meta-dimension reduction method grounded in graph diffusion theory. ADM integrates results from multiple dimension reduction techniques, leveraging their individual strengths while mitigating their specific weaknesses.ADM utilizes dynamic Markov processes to transform Euclidean space results into an information space, revealing intrinsic nonlinear manifold structures that are hard to capture by conventional methods. A critical advancement in ADM is its adaptive diffusion mechanism, which dynamically selects optimal diffusion time scales for each sample, enabling effective representation of multi-scale structures. This approach generates robust, high-quality low-dimensional representations that capture both local and global data structures while reducing noise and technique-specific distortions. We demonstrate ADM's efficacy on simulated and real-world datasets, including various omics data types. Results show that ADM provides clearer separation between biological groups and reveals more meaningful patterns compared to existing methods, advancing the analysis and visualization of complex biological data.