DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction

2025-08-19

AI Summary

Existing dimensionality reduction methods typically emphasize either local structure (e.g., t-SNE, UMAP) or global structure (e.g., PCA, MDS), failing to simultaneously preserve multi-scale data characteristics. To address this, we propose DREAMS—a novel unified framework that jointly preserves local and global fidelity. DREAMS introduces a tunable regularization term to co-optimize t-SNE’s local similarity preservation and PCA’s global covariance constraints; it further incorporates a cross-scale loss function and symmetric adjacency matrix modeling to enable continuous embedding spectra spanning local to global scales. Notably, DREAMS is the first method to explicitly support balanced multi-scale structure preservation within a single, cohesive framework. Extensive experiments across seven real-world datasets—including single-cell transcriptomics and population genetics data—demonstrate that DREAMS consistently outperforms state-of-the-art methods both qualitatively (in visual interpretability) and quantitatively (on metrics such as Trustworthiness and Continuity).

Technology Category

• Machine Learning: Dimensionality Reduction/Feature Selection
• Computer Vision: Multi-modal Vision
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 seven real-world datasets, including five from single-cell transcriptomics and one from population genetics, showcasing qualitatively and quantitatively its superior ability to preserve structure across multiple scales compared to previous approaches.

Problem

• Balancing local and global structure preservation in dimensionality reduction
• Combining t-SNE's local preservation with PCA's global structure
• Generating embeddings that maintain both local and global data relationships

Innovation

• Combines local and global structure preservation
• Uses regularization term to balance embeddings
• Generates spectrum between t-SNE and PCA