We propose a novel strategy for incorporating hierarchical supervised label information into nonlinear dimensionality reduction techniques. Specifically, we extend t-SNE, UMAP, and PHATE to include known or predicted class labels and demonstrate the efficacy of our approach on multiple single-cell RNA sequencing datasets. Our approach, "Haisu," is applicable across domains and methods of nonlinear dimensionality reduction. In general, the mathematical effect of Haisu can be summarized as a variable perturbation of the high dimensional space in which the original data is observed. We thereby preserve the core characteristics of the visualization method and only change the manifold to respect known or assumed class labels when provided. Our strategy is designed to aid in the discovery and understanding of underlying patterns in a dataset that is heavily influenced by parent-child relationships. We show that using our approach can also help in semi-supervised settings where labels are known for only some datapoints (for instance when only a fraction of the cells is labeled). In summary, Haisu extends existing popular visualization methods to enable a user to incorporate known, relevant relationships via a user-defined hierarchical distancing factor.

中文翻译：

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Haisu：分层监督的非线性降维

我们提出了一种将分层监督标签信息纳入非线性降维技术的新策略。具体来说，我们将t-SNE，UMAP和PHATE扩展为包括已知或预测的类别标签，并证明我们的方法在多个单细胞RNA测序数据集上的功效。我们的方法“ Haisu”适用于非线性降维的各个领域和方法。通常，Haisu的数学效应可以概括为对高维空间的可变扰动，在其中可以观察到原始数据。因此，我们保留了可视化方法的核心特征，仅在提供时更改歧管以尊重已知或假定的类别标签。我们的策略旨在帮助发现和理解受父子关系严重影响的数据集中的基础模式。我们表明，使用我们的方法还可以在仅针对某些数据点才知道标签的半监督设置中提供帮助（例如，仅对一部分单元格进行标记时）。总而言之，Haisu扩展了现有的流行可视化方法，以使用户能够通过用户定义的分层距离因子并入已知的相关关系。