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.

翻译：在分类任务中，有意义地利用数据中包含的信息至关重要。尽管许多相关工作致力于构建复杂的算法基础设施来以黑箱方式处理输入，但如何在将数据输入算法之前利用数据的不同方面却鲜为人知。本文聚焦于后者，提出了一种受物理学启发的动态系统，该系统将最优传输原理适配到有效利用图像颜色分布中。我们的动态系统调控了在基于图像构建的网络上传输的不可混色流。它并不汇聚颜色，而是将其视为不同商品，这些商品在网络边缘上共享容量进行交互。由此产生的最优流随后可输入标准分类器，用于区分不同类别的图像。我们展示了在颜色信息重要的数据集的图像分类任务中，我们的方法如何能够超越竞争方法。