DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction

2025/08/19 by Noël Kury, Dmitry Kobak, Kury, Noël +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Image Processing and 3D Reconstruction #Machine Learning (cs.LG)

paper · pdf · doi:10.48550/arxiv.2508.13747

openalex publication_date 2025/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., t-SNE, UMAP) or global (e.g., MDS, PCA) structure of the data, but none of the established methods can represent both aspects well. In this paper, we present DREAMS (Dimensionality Reduction Enhanced Across Multiple Scales), a method that combines the local structure preservation of t-SNE with the global structure preservation of PCA via a simple regularization term. Our approach generates a spectrum of embeddings between the locally well-structured t-SNE embedding and the globally well-structured PCA embedding, efficiently balancing both local and global structure preservation. We benchmark DREAMS across eleven real-world datasets, showcasing qualitatively and quantitatively its superior ability to preserve structure across multiple scales compared to previous approaches.

Citations

• EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
• Cluster and then Embed: A Modular Approach for Visualization
• UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction
• Low-dimensional embeddings of high-dimensional data
• StarMAP: Global Neighbor Embedding for Faithful Data Visualization
• Balancing between the Local and Global Structures (LGS) in Graph Embedding
• Geometric Autoencoders -- What You See is What You Decode
• SQuadMDS: a lean Stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP
• TriMap: Large-scale Dimensionality Reduction Using Triplets
• From Principal Subspaces to Principal Components with Linear Autoencoders
• UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction
• Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms
• Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
• Generalized Procrustes Analysis
• Multidimensional Scaling by Optimizing Goodness of Fit to a Nonmetric Hypothesis
• Gradient-based learning applied to document recognition
• Analysis of a complex of statistical variables into principal components.

Cited by

• Cluster and then Embed: A Modular Approach for Visualization

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