ADM: Adaptive Graph Diffusion for Meta-Dimension Reduction

Abstract

Dimension reduction is ubiquitous in high dimensional data analysis. Divergent data characteristics have driven the development of various techniques in this field. Although individual techniques can capture specific aspects of data, they often struggle to grasp all the intricate and complex patterns and structures. To address this limitation, we introduce ADM (Adaptive graph Diffusion for Metadimension reduction), a novel meta-dimension reduction method grounded in graph diffusion theory. ADM integrates results from diverse dimension reduction techniques to leverage the unique strength of each individual technique. By employing dynamic Markov processes, ADM simulates information propagation for each dimension reduction result, thereby transforming traditional spatial measurements into dynamic diffusion distances. Importantly, ADM incorporates an adaptive mechanism to tailor the time scale of information diffusion according to sample-specific attributes. This improvement facilitates a more thorough exploration of the datasets overall structure and allows the heterogeneity among samples.