Immiscible Color Flows in Optimal Transport Networks for Image Classification

In classification tasks, it is crucial to meaningfully exploit the information contained in data. While much of the work in addressing these tasks is devoted to building complex algorithmic infrastructures to process inputs in a black-box fashion, less is known about how to exploit the various facets of the data, before inputting this into an algorithm. Here, we focus on this latter perspective, by proposing a physics-inspired dynamical system that adapts Optimal Transport principles to effectively leverage color distributions of images. Our dynamics regulates immiscible fluxes of colors traveling on a network built from images. Instead of aggregating colors together, it treats them as different commodities that interact with a shared capacity on edges. The resulting optimal flows can then be fed into standard classifiers to distinguish images in different classes. We show how our method can outperform competing approaches on image classification tasks in datasets where color information matters.