# optimal transport

Published articles for optimal transport.

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## Earthmover Distance

DevFeed: [Earthmover Distance](<https://devfeed.tech/articles/earthmover-distance-40419.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2018/03/05/earthmover-distance/>)

Published: 2018-03-05T08:00:15Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Code](<https://devfeed.tech/topics/code.md>), [Python](<https://devfeed.tech/topics/python.md>), [Library](<https://devfeed.tech/topics/library.md>)

Tags: [code](<https://devfeed.tech/tags/code.md>), [earthmover-distance](<https://devfeed.tech/tags/earthmover-distance.md>), [gerrymandering](<https://devfeed.tech/tags/gerrymandering.md>), [library](<https://devfeed.tech/tags/library.md>), [linear-programming](<https://devfeed.tech/tags/linear-programming.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [optimal-transport](<https://devfeed.tech/tags/optimal-transport.md>), [optimization](<https://devfeed.tech/tags/optimization.md>), [probability-theory](<https://devfeed.tech/tags/probability-theory.md>), [python](<https://devfeed.tech/tags/python.md>), [wasserstein-metric](<https://devfeed.tech/tags/wasserstein-metric.md>)

### AI overview

This tutorial explains how to measure distance between point sets with uncertain locations by treating each sample set as a discrete probability distribution. It formulates Earthmover distance as a linear program that minimizes the cost of moving probability mass between points.

### Source excerpt

Problem: Compute distance between points with uncertain locations (given by samples, or differing observations, or clusters). For example, if I have the following three "points" in the plane, as indicated by their colors, which is closer, blue to green, or blue to red? It's not obvious, and there are multiple factors at work: the red points have fewer samples, but we can be more certain about the position; the blue points are less certain, but the closest non-blue point to a blue point is green; and the green points are equally plausibly "close to red" and "close to blue.