DREAMS同时保留数据的局部与全局结构，实现更全面的降维可视化。
DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction
- 通过正则化融合t-SNE的局部保真与PCA的全局保真
- 在11个真实数据集上均优于传统方法
- 适合需要兼顾局部细节与整体分布的研究场景
降维技术广泛用于高维数据的二维可视化。现有方法通常只能较好地保持局部结构（如t-SNE、UMAP）或全局结构（如MDS、PCA），但无法同时兼顾两者。本文提出DREAMS（Dimensionality Reduction Enhanced Across Multiple Scales），通过简单正则化项，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。该方法生成从t-SNE到PCA的连续嵌入谱，高效平衡局部与全局结构的保真度。我们在11个真实世界数据集上进行了基准测试，定性与定量结果均表明，DREAMS在多尺度结构保持方面显著优于以往方法。
原文摘要 · Abstract (English)
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.
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