Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the manifold learning interpretations from many prior works are inaccurate and that the misuse stems from a lack of data-independent notions of embedding maps, which project high-dimensional data into a lower-dimensional space. Leveraging the leave-one-out principle, we introduce LOO-map, a framework that extends embedding maps beyond discrete points to the entire input space. We identify two forms of map discontinuity that distort visualizations: one exaggerates cluster separation and the other creates spurious local structures. As a remedy, we develop two types of point-wise diagnostic scores to detect unreliable embedding points and improve hyperparameter selection, which are validated on datasets from computer vision and single-cell omics.

翻译：高维数据可视化对于理解生物医学数据和深度学习模型至关重要。邻域嵌入方法（如t-SNE和UMAP）被广泛使用，但可能引入误导性的视觉伪影。我们发现许多先前研究中的流形学习解释并不准确，这种误用源于缺乏独立于数据的嵌入映射概念——这些映射将高维数据投影到低维空间。基于留一法原理，我们提出了LOO-map框架，将嵌入映射从离散点扩展到整个输入空间。我们识别出两种导致可视化失真的映射不连续性形式：一种会夸大聚类分离度，另一种则会产生虚假的局部结构。作为解决方案，我们开发了两种点级诊断评分来检测不可靠的嵌入点并改进超参数选择，这些方法在计算机视觉和单细胞组学数据集上得到了验证。