提出PCC方法，显著提升降维后全局结构保留能力。
Preserving clusters and correlations: a dimensionality reduction method for exceptionally high global structure preservation
- 通过保留高维与低维距离间的皮尔逊和斯皮尔曼相关性来优化全局结构
- 在医学影像数据上验证，全局结构保留优于现有方法
- 可与UMAP结合，大幅提升其全局结构保持能力
我们提出一种名为保持聚类与相关性（PCC）的新型降维方法，实现了最先进的全局结构（GS）保留，同时保持了良好的局部结构（LS）保留。该方法优化两个目标：一是通过保留高维与低维距离间的皮尔逊和斯皮尔曼相关性来实现全局结构保留；二是确保高维数据中的聚类在低维空间中仍可分离。实验证明，PCC在全局结构保留方面达到领先水平，且在局部结构保留上表现竞争力。此外，将相关性目标与UMAP结合，可显著提升其全局结构保留能力，同时对局部结构影响极小。我们在多个基准上定量对比了PCC与其他方法，并展示了其在医学影像中的实际应用价值。结果表明，PCC是一种具有优越全局结构保留能力的降维技术。
原文摘要 · Abstract (English)
We present Preserving Clusters and Correlations (PCC), a novel dimensionality reduction (DR) method a novel dimensionality reduction (DR) method that achieves state-of-the-art global structure (GS) preservation while maintaining competitive local structure (LS) preservation. It optimizes two objectives: a GS preservation objective that preserves an approximation of Pearson and Spearman correlations between high- and low-dimensional distances, and an LS preservation objective that ensures clusters in the high-dimensional data are separable in the low-dimensional data. PCC has a state-of-the-art ability to preserve the GS while having competitive LS preservation. In addition, we show the correlation objective can be combined with UMAP to significantly improve its GS preservation with minimal degradation of the LS. We quantitatively benchmark PCC against existing methods and demonstrate its utility in medical imaging, and show PCC is a competitive DR technique that demonstrates superior GS preservation in our benchmarks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。