Enhanced High-Dimensional Data Visualization through Adaptive Multi-Scale Manifold Embedding
This addresses the problem of visualizing complex high-dimensional data for researchers in fields like bioinformatics, though it appears incremental as it builds on existing manifold embedding techniques.
The paper tackles the challenge of visualizing high-dimensional data by proposing an Adaptive Multi-Scale Manifold Embedding (AMSME) algorithm, which uses ordinal distance and adaptive neighborhood adjustment to improve intra-cluster structure preservation and inter-cluster separation, achieving significant improvements on real-world datasets and discovering novel neuronal subtypes in a mouse scRNA-seq dataset.
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.