# Immiscible Color Flows in Optimal Transport Networks for Image Classification

arXiv: https://arxiv.org/abs/2205.02938 · HTML: https://mlsanity.com/paper/2205.02938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 59 references that are in the map.
- First posted on arXiv 4 May 2022.

## Builds on (most cited first, 13 of 13)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport Problems](https://mlsanity.com/paper/1610.06519/) (2016)
- [On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithms](https://mlsanity.com/paper/1901.06482/) (2019)
- [A Transportation Lp Distance for Signal Analysis](https://mlsanity.com/paper/1609.08669/) (2016)
- [Principled network extraction from images](https://mlsanity.com/paper/2012.12758/) (2020)
- [Network extraction by routing optimization](https://mlsanity.com/paper/2005.02805/) (2020)
- [Physarum-Inspired Multi-Commodity Flow Dynamics](https://mlsanity.com/paper/2009.01498/) (2020)
- [Designing optimal networks for multi-commodity transport problem](https://mlsanity.com/paper/2010.14377/) (2020)
- [Optimal transport in multilayer networks for traffic flow optimization](https://mlsanity.com/paper/2106.07202/) (2021)

## Abstract (arXiv)

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.