DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction

Noël Kury, Dmitry Kobak, Sebastian Damrich

Authors that are also TMLR Expert Reviewers: ~Dmitry_Kobak2

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.

Certifications: Expert Certification

Submission Length: Regular submission (no more than 12 pages of main content)

Code: https://github.com/berenslab/dreams-experiments/tree/tmlr

Assigned Action Editor: ~Arto_Klami1

Submission Number: 5677