DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction

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.