The study of high dimensional data sets often rely on their low dimensional projections that preserve the local geometry of the original space. While numerous methods have been developed to summarize this space as variations of tree-like structures, they are usually non-parametric and "static" in nature. As data may come from systems that are dynamical such as a differentiating cell, a static, non-parametric characterization of the space may not be the most appropriate. Here, we developed a framework, the principal flow, that is capable of characterizing the space in a dynamical manner. The principal flow, defined using neural ODEs, directs motion of a particle through the space, where the trajectory of the particle resembles the principal curve of the dataset. We illustrate that our framework can be used to characterize shapes of various complexities, and is flexible to incorporate summaries of relaxation dynamics.

研究高维数据集通常依赖于保留原始空间的局部几何的低维投影。本研究中，我们开发了一个能够动态地表征空间的框架，即主导流动。主导流动利用神经ODEs定义，通过将粒子的轨迹指导沿空间移动，使其轨迹类似于数据集的主曲线。我们证明了我们的框架可以用于表征各种复杂的形状，并能灵活地整合松弛动力学的摘要。

利用神经ODE构建可解释的主曲线