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

2025-03-18

AI Summary

To address the dual challenges of severe curse of dimensionality and poor intra-cluster structural fidelity and inter-cluster separability in high-dimensional manifold embedding, this paper proposes Adaptive Multi-Scale Manifold Embedding (AMSME). AMSME innovatively replaces Euclidean distance with ordinal distance to construct an adaptive similarity graph; designs a label-driven two-stage graph embedding framework that jointly optimizes topological preservation and inter-class separation; and incorporates distance reweighting and multi-resolution manifold analysis. Evaluated on multiple real-world datasets, AMSME significantly improves intra-cluster structural consistency and inter-cluster discriminability. Furthermore, it successfully identifies novel neuronal subtypes in mouse dorsal root ganglia—characterized by distinct marker gene expression profiles and biological functions—demonstrating strong biological interpretability and practical utility.

Technology Category

• Machine Learning: Learning with Manifolds
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Overcomes curse of dimensionality in high-dimensional data visualization.
• Improves intra-cluster compactness and inter-cluster separability in manifold embedding.
• Discovers novel neuronal subtypes in scRNA-seq datasets.

Innovation

• Adaptive Multi-Scale Manifold Embedding algorithm
• Ordinal distance replaces Euclidean distance
• Two-stage embedding framework enhances separation