An Adaptive Multi-Scale Manifold Embedding Preprocessing Framework for High-Dimensional Data Visualization

To improve the robustness of neighborhood construction and the separation of intra-cluster and inter-cluster structures in high-dimensional visualization, this paper proposes Adaptive Multi-Scale Manifold Embedding (AMSME), an ordinal distance based preprocessing framework for existing manifold embedding algorithms. The framework introduces ordinal distance to replace traditional Euclidean distances. Under an idealized high-dimensional Gaussian setting, our analysis shows that ordinal distance can improve the stability of neighborhood ordering between homogeneous and heterogeneous samples, thereby mitigating the adverse effects of distance concentration. Building upon this, we design an adaptive neighborhood adjustment strategy to construct similarity graphs that simultaneously optimize intra-cluster compactness and inter-cluster separability. The core mechanism of AMSME lies in transforming these similarity graphs into structure-enhanced distance matrices, which serve as optimized inputs for three manifold embedding algorithms-t-SNE, UMAP, and PaCMAP-thereby enhancing visualization and downstream analysis performance. Experimental results on multiple real-world datasets demonstrate that AMSME improves inter-cluster separation while better preserving intra-cluster topological structures. Furthermore, in a case study on mouse lumbar dorsal root ganglion (DRG) single-cell RNA sequencing (scRNA-seq) data, AMSME suggests candidate neuronal subtypes, and marker gene analysis provides preliminary evidence for their transcriptional differences.