Constructing interpretable principal curve using Neural ODEs
This work addresses the need for dynamic, interpretable low-dimensional projections in fields like biology, where data from systems such as differentiating cells require more than static, non-parametric methods, though it is incremental as it builds on existing principal curve and neural ODE concepts.
The authors tackled the problem of summarizing high-dimensional data from dynamical systems by developing a framework called principal flow, which uses neural ODEs to create interpretable principal curves that characterize data shapes and incorporate relaxation dynamics.
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.