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.

翻译：降维技术被广泛用于将高维数据可视化至二维空间。现有方法通常设计为仅保留数据的局部结构（例如$t$-SNE、UMAP）或全局结构（例如MDS、PCA），但尚无成熟方法能同时良好表征这两个方面。本文提出DREAMS（多尺度增强降维法），该方法通过简单的正则化项，将$t$-SNE的局部结构保持能力与PCA的全局结构保持能力相结合。我们的方法生成介于局部结构良好的$t$-SNE嵌入与全局结构良好的PCA嵌入之间的连续嵌入谱，有效平衡局部与全局结构的保持。我们在十一个真实数据集上对DREAMS进行基准测试，通过定性与定量分析表明，相较于现有方法，DREAMS在保持多尺度结构方面具有更优能力。