Enhanced High-Dimensional Data Visualization through Adaptive Multi-Scale Manifold Embedding

• URL: http://arxiv.org/abs/2503.13954v2
• Date: Wed, 19 Mar 2025 05:21:06 GMT
• Title: Enhanced High-Dimensional Data Visualization through Adaptive Multi-Scale Manifold Embedding
• Authors: Tianhao Ni, Bingjie Li, Zhigang Yao,
• Abstract summary: We propose an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm.<n>By introducing ordinal distance, we demonstrate that ordinal distance overcomes the constraints of the curse of dimensionality in high-dimensional spaces.<n> Experimental results demonstrate that AMSME significantly preserves intra-cluster topological structures and improves inter-cluster separation on real-world datasets.
• Score: 0.7705234721762716
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: To address the dual challenges of the curse of dimensionality and the difficulty in separating intra-cluster and inter-cluster structures in high-dimensional manifold embedding, we proposes an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm. By introducing ordinal distance to replace traditional Euclidean distances, we theoretically demonstrate that ordinal distance overcomes the constraints of the curse of dimensionality in high-dimensional spaces, effectively distinguishing heterogeneous samples. We design an adaptive neighborhood adjustment method to construct similarity graphs that simultaneously balance intra-cluster compactness and inter-cluster separability. Furthermore, we develop a two-stage embedding framework: the first stage achieves preliminary cluster separation while preserving connectivity between structurally similar clusters via the similarity graph, and the second stage enhances inter-cluster separation through a label-driven distance reweighting. Experimental results demonstrate that AMSME significantly preserves intra-cluster topological structures and improves inter-cluster separation on real-world datasets. Additionally, leveraging its multi-resolution analysis capability, AMSME discovers novel neuronal subtypes in the mouse lumbar dorsal root ganglion scRNA-seq dataset, with marker gene analysis revealing their distinct biological roles.

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