Wasserstein distance python. m: The Jan 4, 2023 · PythonOT/POT, This open source Python library provide several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning. wasserstein_distance for 1-dimensional inputs: Sep 21, 2025 · 在数据分析和机器学习领域，我们常常需要衡量两个概率分布之间的差异。Wasserstein距离（也称为推土机距离，Earth Mover's Distance）就是一种强大的工具，用于量化这种差异。与其他距离度量（如KL散度、JS散度）不同，Wasserstein距离具有更好的数学性质和直观的物理意义。本文将聚焦于Wasserstein距离在 Earth mover's distance with Python. Implement them in Python using the NannyML library. scipy use cases 3. wasserstein_distance ¶ scipy. We take the average distance, so we use backend. 25 for the distance. stats Wasserstein_distance This function is fully compatable with back propagation!!! The Wasserstein distance, also called the Earth mover’s distance or the optimal transport distance, is a similarity metric between two probability distributions 1. Definitions 1. This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount of Aug 16, 2021 · Wasserstein Distance Using C# and Python Dr. ot. wasserstein_distance), you use the " Values observed in the (empirical) distributions " as inputs to calculate the Wasserstein Distance W1. The function computes the Bures-Wasserstein distance between μ s = N (m s, Σ s) and μ t = N (m t, Σ t), as discussed in remark 2. Difference between implementations of scipy， POT，and Feb 11, 2020 · This is implemented in the POT: Python Optimal Transport package, for samples (or, generally, discrete measures): use ot. This repository contains a Python implementation of the Wasserstein Distance, Wasserstein Barycenter and Optimal Transport Map of Gaussian Processes. wasserstein_distance), you use the " Values observed in the (empirical) distributions " as inputs to calculate the Wasserstein Distance $W_1$. Source code for persim. The following classes contain the main functionalities of Wasserstein: EMD: Computes the Wasserstein distance between two distributions, including a possible penalty term. Instead, you can use wasserstein_distance_nd available in SciPy 1. Wasserstein-p distance 4. Sometimes the square of this quantity is referred to as the “energy distance” (e. WSDP. wasserstein_distance to get a measure for the difference between two probability distribution. wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None) [source] # Compute the first Wasserstein distance between two 1D distributions. m: The MATLAB code to run SDP on the distance matrix and get results for W-SDP. sliced. 13 and later. Jun 29, 2019 · Wasserstein Distance Calculating the Wasserstein distance is a bit evolved with more parameters. stats import wasserstein_distance and calculate the distance between a vector like [6,1,1,1,1] and any permutation of it where the 6 "moves around", you would get (1) the same Wasserstein Distance, and (2) that would be 0. f. The mode collapse problem is also mitigated when using Wasserstein distance as the objective function. 8. wasserstein_distance for p=1 and no weights, with u_values, v_values the two 1-D distributions, the code comes down to u_ Sliced Wasserstein distance ¶ Sliced Wasserstein Kernels for persistence diagrams were introduced by Carriere et al, 2017 and implemented by Alice Patania. random. Edge lengths are measured in norm p, for \ (1 \leq p \leq \infty\). wasserstein_1d. Why is the Wasserstein distance so far away from zero when samples are drawn from same This open source Python library provides several solvers for optimization problems related to Optimal Transport for signal, image processing and machine learning. gaussian. Both the R and Python are intended solely for the 1D special case. [docs] def sliced_wasserstein_distance( X_s, X_t, a=None, b=None, n_projections=50, p=2, projections=None, seed=None, log=False, ): r""" Computes a Monte-Carlo approximation of the p-Sliced Wasserstein distance . Jul 22, 2024 · INFO This is a pytorch implementation of the Scipy. You may also want to check out all available functions/classes of the module scipy. wasserstein_distance (u_values, v_values, u_weights=None, v_weights=None)# 计算两个离散分布之间的 Wasserstein-1 距离。 Wasserstein 距离，也称为地球移动器距离或最佳运输距离，是两个概率分布之间的相似性度量。在离散情况下，Wasserstein The Wasserstein distance, also called the Earth mover’s distance or the optimal transport distance, is a similarity metric between two probability distributions [1]. wasserstein_distance # scipy. 2017. wasserstein_distance — SciPy v1. wasserstein_distance (). Apr 26, 2025 · scipy. It currently houses implementations of Persistence Images Persistence Landscapes Bottleneck distance Modified Gromov–Hausdorff distance Sliced Wasserstein Kernel Heat Kernel Diagram plotting Sep 10, 2024 · Compare image similarity in Python using Structural Similarity, Pixel Comparisons, Wasserstein Distance (Earth Mover's Distance), and SIFT - measure_img_similarity. It treats frequencies of each bin as a value and then builds the historical distributions from those values and computes the distance. sliced Sliced OT Distances Functions ot. This example is designed to show how to use the Gromov-Wasserstein distance computation in POT. wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None) [source] ¶ Compute the first Wasserstein distance between two 1D distributions. [31] Bonneel, Nicolas, et al. mean () Python Jun 20, 2022 · We ran an experiment to help build an intuition on how popular drift detection methods behave. Note Example added in release: 0. Detailed information about the methods implemented in CAJAL can be found in: Nov 23, 2023 · 本文介绍了Wasserstein距离，又称推土机距离，作为衡量概率分布间差异的一种方法，即使分布没有重叠也能有效评估。相比于KL散度和JS散度，Wasserstein距离具有独特优势。通过一个简单的例子展示了如何将分布P转换为分布Q，并提供了相应的Python代码实现，计算了两个分布之间的Wasserstein距离。 2D Histogram Wasserstein Distance via POT Library. Apr 18, 2023 · I want to use the Wasserstein distance from scipy. So here the Wasserstein distance is obviously 1 because d (i,j)=1 for every i and j. This paper presents an linear programming based implementation of the multi-dimensional Wasserstein distance function in Scipy, a powerful scientific computing package in Python. Learn how to compute the Wasserstein-1 distance between two 1D discrete distributions using SciPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. Wasserstein 距离，也称为 Earth mover’s distance（推土机距离）或最佳传输距离，是两个概率分布之间的相似性度量 [1]。 在离散情况下，Wasserstein 距离可以理解为将一个分布转换为另一个分布的最佳传输方案的成本。 Gromov-Wasserstein example This example is designed to show how to use the Gromov-Wassertsein distance computation in POT. In this post, we take a different approach by approximating the Wasserstein distance with cumulative distribution functions (CDF), providing a more intuitive understanding of the metric. 2. The Wasserstein distance, also called the Earth mover’s distance or the optimal transport distance, is a similarity metric between two probability distributions [1]. . I found May 17, 2019 · scipy. This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount Sliced Wasserstein Distance (SWD) in PyTorch. More than 150 million people use GitHub to discover, fork, and contribute to over 420 million projects. Compute the Wasserstein distance between persistence diagram using Python Optimal Transport backend. kmeansplus. 3. 0. wasserstein_distance, and you may want to look into the definitions from the documentation or code before doing any comparison between the two for the 1D case! Apr 18, 2023 · I found the answer here: Why is the Wasserstein distance between [0, 1] and [1, 0] zero? In short, the Wasserstein distance in scipy is for „1d distributions“; this means that if I have a probability distribution P (A) where a has three states that are observed with probabilities p (a1)=1, p (a2)=p (a3)=0, and another probability distribution P (B), where b has three states that are Dec 7, 2020 · The formula below is a special case of the Wasserstein distance/optimal transport when the source and target distributions, x and y (also called marginal distributions) are 1D, that is, are vectors. What does that tell us ? Apr 29, 2020 · I am trying to understand the implementation that is used in scipy. cn) 页面中 scipy. Jun 18, 2020 · Wasserstein in 1D is a special case of optimal transport. Aug 11, 2021 · We would like to show you a description here but the site won’t allow us. For instance, I would want to convert the first 3 entries for p and q into an array, apply Wasserstein distance and get a value. Bures-Wasserstein This repository presents an efficient PyTorch implementation of the Bures-Wasserstein distance (the Wasserstein distance between multivariate Gaussian distributions) when the square roots of the matrices are known. In this blog, we share the key takeaways and the code to run the tests on your data. 28 of Jul 23, 2025 · Step 2: Define wasserstein loss function To define the wasserstein loss function, we use the following method. A Wasserstein barycenter is a distribution that minimizes its Wasserstein distance with respect to other distributions 16. Its robustness to outliers, ability to capture complex relationships, and applicability to high May 11, 2020 · I want to apply the Wasserstein distance metric on the two distributions of each constituency. EMDFloat32, each of which are instantiations of the C++ template EMD) that can be used to compute EMD distances. readthedocs. scipy 1d Wasserstein distance 2. py: The main Python code to get the results for D-WKM and the distance matrix for W-SDP. 838cfbe Manual (osgeo. In these notes we review some of the basics about this topic. get_projections_sphere(d, n_projections, seed=None, backend=None, type_as=None) [source] Generates n_projections samples from the uniform distribution on the Stiefel manifold of dimension d × 2: V d, 2 = {X ∈ R d × 2, X T X = I 2} Parameters: d (int) – dimension of the space n_projections (int) – number of samples requested seed (int or Wasserstein barycenter In this example, we consider the following Wasserstein barycenter problem η ∗ = min η;;; (1 t) W (μ, η) + t W (η, ν) where m u and n u are reference 1D measures, and t is a parameter ∈ [0, 1]. EMDFloat64 or wasserstein. It could also be seen as an interpolation between Wasserstein and energy distances, more info in this paper. randn(n) b = np. Contribute to antonio-f/Wasserstein_distance development by creating an account on GitHub. ” Journal of Mathematical Imaging and Vision 51. Sinkhorn distance is a regularized version of Wasserstein distance which is used by the package to approximate Wasserstein distance. The problem is handled by a project gradient descent method, where the gradient is computed by pyTorch automatic differentiation. This example illustrates the computation of the sliced Wasserstein Distance as proposed in [31]. Y and Y ′) are independent random variables whose probability distribution is u (resp. Wasserstein Distance as objective function is more stable than using JS divergence. wasserstein_distance 的用法。 用法: scipy. We sample two Gaussian distributions in 2- and 3-dimensional Jul 24, 2023 · In the previous two posts, we’ve discussed the mathematical details of the Wasserstein distance, exploring its formal definition, its computation through linear programming and the Sinkhorn algorithm. I have been using Gudhi, but it appears to be too slow, and I need a faster alternative. stats. Jan 1, 2024 · You cannot compute the Wasserstein distance in multiple dimensions with wasserstein_distance. Jul 23, 2023 · In this post, we take a look at the optimal transport problem, required to calculate the Wasserstein distance, and how to calculate the distance metric in Python. This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount The files in this repository are: Main. Feb 17, 2023 · If you're looking for a metric that can be used to estimate the distance between two sets of data that is not sensitive to the size of each sample or to the scale of the data, you might want to consider the Kolmogorov-Smirnov statistic, which is implemented in scipy here. kmeans_sdp_2. Mar 24, 2020 · I know that the Wasserstein distance can be used to quantify the difference between the two distributions. I don't understand why either (1) and (2) occur, and would love your help understanding. I need a tool to quickly calculate the Wasserstein distance between two two-dimensional point sets. In the discrete case, the Wasserstein distance can be understood as the cost of an optimal The Python Optimal Transport (POT) library takes advantage of Python to make Optimal Transport accessible to the machine learning community. Python/C++ library for computing Wasserstein distances efficiently. wasserstein_distance has experimental support for Python Array API Standard compatible backends in addition to NumPy. The function takes arrays of values and optional weights as inputs and returns the distance as a float. stats , or try the search function . More on the 1D special case can be found in Remark 2. Our goal is to minimize the Wasserstein distance between distribution of generated samples and distribution of real samples. py CAJAL is a Python library for multi-modal cell morphology analyses using Gromov-Wasserstein (GW) distance. Aug 19, 2019 · While the scipy version doesn't accept 2D arrays and it returns an error, the pyemd method returns a value. wasserstein_distance(u_values, v_values, u_weights= None, v_weights= None) 对参数u_values,v_value,u_weights,v_weights解释不清晰。 通过看文章 Wasserstein距离的直观解释_em距离-CSDN博客 对Wasserstein距离的理解和对样例的测试。对搜索 Computes the Entropy-Regularized p-Wasserstein Distance between two d-dimensional point clouds using the Sinkhorn scaling algorithm. As shown in [2], for one-dimensional real-valued variables, the Jan 27, 2022 · Point cloud analysis The Gromov–Wasserstein Distance in Python We will use POT python package for a numerical example of GW distance. More Examples and Tests for other libraries 3. 's so that the distances and amounts to move are multiplied together for corresponding points between and nearest to one another. Learn about key techniques such as the Jensen-Shannon Distance, Hellinger Distance, the Kolmogorov-Smirnov Test, and more. It can be installed using: pip install POT Using the GWdistance we can compute distances with samples that do not belong to the same metric space. We would like to show you a description here but the site won’t allow us. " Advances in Neural Information Processing Systems. m: The MATLAB code for SDP. We first compare 3 solvers to estimate the distance based on Conditional Gradient [24] or Sinkhorn projections [12, 51]. In this notebook, we illustrate the use of Wasserstein distances in pyABC via a simple problem consisting of 100 samples from a 2-dimensional normal distribution. In Dec 7, 2020 · The formula below is a special case of the Wasserstein distance/optimal transport when the source and target distributions, x and y (also called marginal distributions) are 1D, that is, are vectors. Apr 24, 2019 · For anyone interested in timings, computing sliced_wasserstein_distance between two random 300x300 matrices took ~3s on my machine, using 50 projections (the default). Then we compare 2 stochastic solvers to estimate the distance with a lower numerical cost [33]. d. io/en/stable/all. DWKM_utils. bures_wasserstein_distance(ms, mt, Cs, Ct, paired=False, log=False) [source] Return Bures Wasserstein distance between samples. stats import wasserstein_distance def wassersteindist(n): a = np. The q-Wasserstein distance is defined as the minimal value achieved by a perfect matching between the points of the two diagrams (+ all diagonal points), where the value of a matching is defined as the q-th root of the sum of all edge lengths to the power q. 3k362107 asked Aug 19, 2019 at Apr 12, 2021 · if you from scipy. Roland Challenges Need to find transport map, matrix of real numbers, very expensive (NP-hard!) Prev experiment takes half a day to run The following are 21 code examples of scipy. I would do the same for the next 2 rows so that finally my data frame would look something like this: ot. "Learning from uncertain curves: The 2-Wasserstein metric for Gaussian processes. This code will use the GPU if you pass in GPU tensors. Feb 11, 2020 · This is implemented in the POT: Python Optimal Transport package, for samples (or, generally, discrete measures): use ot. If you want to do it for weighted samples (or general discrete distributions with finite support), you can provide the a and b arguments. It is designed to work with numpy arrays efficiently. The EMDYPhi function behaves similarly but implements 2 π periodicity in the second coordinate dimension, and so is suited for using Dec 18, 2023 · 在官方文档 scipy. v). - thaler-lab/Wasserstein 6 days ago · The Wasserstein distance, also known as the Earth mover distance or optimal transport distance, is a widely used measure of simi-larity between probability distributions. from scipy. Diagrams can contain points with infinity coordinates (essential parts). Sep 7, 2023 · In Python (please see scipy. To get started, check out the Python Binder Demo or the C++ Examples. The general idea is to compute an approximation of the Wasserstein distance by computing the distance in 1-dimension repeatedly, and use the results as measure. wasserstein_distance sourcecode analysis 3. Mar 4, 2020 · The Wasserstein distance is the minimum value of this average cost over all possible joinings J. wasserstein """ Implementation of the Wasserstein distance using the Hungarian algorithm Author: Chris Tralie """ import numpy as np from sklearn import metrics from scipy import optimize import warnings __all__ = ["wasserstein"] Jul 7, 2022 · Python package wrapping C++ code for computing Wasserstein distances GitHub is where people build software. If you see from the documentation, it says that it accept only 1D arrays, so I think that the output is wrong. Therefore: What are the " Values observed in the (empirical) distributions " mentioned in Python guidelines as inputs for calculating W1? Regularized Wasserstein Distance Ref: Python Optimal Transport Documentation, “Orthogonal Estimation of Wasserstein Distance”, M. It corresponds to minimizing the following problem by searching a distribution μ such that Sep 18, 2023 · 1. scipy. 本文简要介绍 python 语言中 scipy. wasserstein_distance for p=1 and no weights, with u_values, v_values the two 1-D distributions, the code comes down to u_ Shows the usage of the sliced wasserstein distance to measure the distance between two 2d histograms """ import numpy as np import matplotlib. e, it converges to 0 as the distributions get close to each other and diverges as they get farther away. 31 [15]. Python tools for implementation 2. This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount python machine-learning gaussian stats transfer-learning wasserstein-barycenters wasserstein optimal-transport ot-mapping-estimation domain-adaptation guassian-processes nonparametric-statistics wasserstein-distance Updated on Aug 3, 2020 Python A Wasserstein Distance 题目描述 最近对抗生成网络 (GAN)很火，其中有一种变体WGAN，引入了一种新的距离来提高生成图片的质量。 这个距离就是Wasserstein距离，又名铲土距离。 这个问题可以描述如下: 有两堆泥土，每一堆有n个位置，标号从1~n。 May 27, 2019 · I am trying to validate the earth-mover distance implementation from the python optimal transport library https://pot. Wasserstein distance 1. pyplot as plt from scipy import stats def sliced_wasserstein (X, Y, num_proj): '''Takes: X: 2d (or nd) histogram Y: 2d (or nd) histogram num_proj: Number of random projections to compute the mean over Approximating Wasserstein distances with PyTorch. g. Two equavalent formulas 1. Dec 29, 2018 · wasserstein_distance (histogram1 [0], histogram2 [0]) spits out a number, but it is not the distance between two histograms. Jul 14, 2019 · The Wasserstein Generative Adversarial Network, or Wasserstein GAN, is an extension to the generative adversarial network that both improves the stability when training the model and provides a loss function that correlates with the quality of generated images. In the discrete case, the Wasserstein distance can be understood as the cost of an optimal transport plan to convert one distribution into the other. 1 (2015): 22-45 The Wasserstein distance, also called the Earth mover’s distance or the optimal transport distance, is a similarity metric between two probability distributions [1]. Informally, if the distributions are interpreted as two different ways of piling up earth (dirt) over D, the EMD captures the minimum cost of building the smaller pile using dirt taken from the larger, where cost is defined Jul 5, 2024 · Discover how to tackle univariate drift with our comprehensive guide. WGAN などで使われるWasserstein距離は確率分布の間の距離のひとつです。本稿では、離散型確率分布に対するWasserstein距離の定義と、Pythonによる計算の例を示します。 Wasserstein距離の定義 ふたつのカテゴリカル分布、それぞれ Jul 1, 2020 · Wasserstein distance between two distributions python Asked 5 years, 2 months ago Modified 5 years, 2 months ago Viewed 1k times Sep 27, 2019 · scipy. However, I do not understand how the support matters here. in [2], [4]), but as noted in [1] and [3], only the definition above satisfies the axioms of a distance function (metric). OT barycenters (Wasserstein and GW) for fixed and free support, Fast OT solvers in 1D, on the circle and between Gaussian Mixture Models Aug 19, 2019 · Similarly, it's instructive to see that the result agrees with scipy. It Oct 7, 2020 · what are the shapes of data[0]? it looks like wasserstein_distance_function requires that f1 and f2 contain 20 elements each which it interprets as that as 10 points in 2d - is that right? scipy. It is an important extension to the GAN model and requires a conceptual shift away from a […] In computer science, the earth mover's distance (EMD) [1] is a measure of dissimilarity between two frequency distributions, densities, or measures, over a metric space D. Apr 29, 2020 · I am trying to understand the implementation that is used in scipy. random Jun 29, 2019 · Please note that the implementation of this method is a bit different with scipy. Three intuitive and typical examples 2. Apr 26, 2025 · This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount of distribution weight that must be moved, multiplied by the distance it has to be moved. The projection on the simplex ensures Mar 11, 2025 · Wasserstein distance should, in theory, be zero when we are comparing samples drawn from the same distribution. The main code is written in C++ with a NumPy-based Python wrapper provided via SWIG. Matlab Implementation Masarotto, Valentina, Victor Jan 9, 2024 · The Wasserstein distance, a metric that measures the distance between two probability distributions, is, amongst other things, a two-sample test that I’ve found useful to detect data drift. “Sliced and radon wasserstein barycenters of measures. Based on the papers: Mallasto, Anton, and Aasa Feragen. 6 days ago · The Wasserstein distance, also known as the Earth mover distance or optimal transport distance, is a widely used measure of similarity between probability distributions. Aug 7, 2025 · Differentiable 2-Wasserstein Distance in PyTorch. The algorithm behind both functions rank discrete data according to their c. Mar 4, 2020 · Reference for wasserstein distance function in python Asked 5 years, 8 months ago Modified 2 years, 5 months ago Viewed 8k times Feb 17, 2023 · The wasserstein_distance will be smaller the longer u_values and v_values are. It provides state-of-the-art algorithms to solve the regular OT optimization problems, and related problems such as entropic Wasserstein distance with Sinkhorn algorithm or barycenter computations. My question is when do we consider the distance between these distributions "small" enough? or what does this number mean ? say we obtain 0. GitHub Gist: instantly share code, notes, and snippets. where X and X ′ (resp. Apr 12, 2021 · if you from scipy. py: Provides the functions needed to calculate Bregman Wasserstein barycenter and related algorithms for D-WKM. Contribute to koshian2/swd-pytorch development by creating an account on GitHub. How can I calculate this distance in this case? python scipy statistics distribution earth-movers-distance edited Aug 21, 2019 at 18:56 fuglede 18. 1. This distance is also known as the earth mover’s distance, since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount of The Wasserstein distance | which arises from the idea of optimal transport | is being used more and more in Statistics and Machine Learning. html#module-ot. math:: \mathcal{SWD}_p(\mu, \nu) = \underset{\theta \sim \mathcal{U}(\mathbb{S}^{d-1})}{\mathbb{E}}\left(\mathcal{W}_p^p(\theta_\# \mu, \theta_\# \nu)\right)^{\frac{1}{p}} where Nov 16, 2023 · Wasserstein distance has emerged as a powerful tool for detecting data drift in ML models. May 26, 2024 · I've looked at various different websites that seem to have implementations of Wasserstein distance in the discrete case, however, none of them have the continuous case? What I want to do is someth Sep 17, 2021 · Wasserstein distance is a meaningful metric, i. You can vote up the ones you like or vote down the ones you don't like, and go to the original project or source file by following the links above each example. The following is an efficient implementation of wasserstein loss function where the score is maximum. Contribute to dfdazac/wassdistance development by creating an account on GitHub. James McCaffrey of Microsoft Research shows how to compute the Wasserstein distance and explains why it is often preferable to alternative distance functions, used to measure the distance between two probability distributions in machine learning projects. Python The Python EMD function returns an object (either wasserstein. Persim is a Python package for many tools used in analyzing Persistence Diagrams. dev0+1869. srk 0k abz ih xvwyl xasnc9 sos wkbu 6q h3ku