Approximation algorithms for 1-Wasserstein distance between persistence diagramsSamantha ChenYusu Wang
We utilize the central limit theorem in Banach space to derive the limit distribution for the Sliced 1-Wasserstein distance. Through viewing the empirical max-Sliced 1-Wasserstein distance as a supremum of an empirical process indexed by some function class, we prove that the function class is P...
This implementation is based on the fact that for given distributions u and v the 1-Wasserstein distance can be written as w 1 ( u , v ) = ∫ − ∞ ∞ | U cdf ( x ) − V cdf ( x ) | d x and the 2-Wasserstein distance as w 2 ( u , v ) 2 = ∫ 0 1 ( U ...
wassersteinWasserstein距离是一种在度量理论中用于比较两个概率分布之间差异的距离度量方法。以下是对Wasserstein距离的详细解释: 一、定义与直观理解 Wasserstein距离,又称为推土机移动距离(Earth Mover’s Distance, EMD),其直观理解可以类比为在地球上移动泥土的过程。假设有两个形状不同的土堆,分...
💡💡💡Wasserstein Distance Loss|亲测在红外弱小目标检测涨点明显,map@0.5 从0.755提升至0.784 1. 红外弱小目标数据集 Single-frame InfraRed Small Target 数据集大小:427张,进行3倍数据增强得到1708张,最终训练集验证集测试集随机分配为8:1:1 ...
(spectral normalization Wasserstein distance transfer network,SNWDTN).该方法首先求出权值矩阵的谱范数,然后利用谱范数再对权值矩阵进行谱归一化处理,以设计出能够满足Lipschitz约束条件的谱归一化层,从而为Wasserstein distance的使用提供更好的约束条件满足.通过公共数据集的实验结果表明,SNWDTN取得了比以往方法更好的...
We compare these matrices using the softassign criterion , which measures the minimum distortion induced by a probabilistic map from the rows of one similarity matrix to the rows of another; this criterion amounts to a regularized version of the Gromov-Wasserstein (GW) distance between metric-...
Wasserstein GAN(Generative Adversarial Networks)是一种生成对抗网络的变体,旨在解决传统GAN中遇到的一些问题。它采用了Wasserstein距离(也称为Earth Mover's Distance)作为训练生成器和判别器之间的损失函数,从而改善了GAN训练中的不稳定性和模式塌陷现象。 WassersteinGAN的核心思想是通过最小化生成样本和真实样本之间的Wa...
In this Note, we show that an optimal coupling for the L 1 -Wasserstein distance, in the case of n space, can be obtained via the resolution of nonlinear equation g(·) = α, where g is a cyclically monotone application. Hence, to get an approximation to the optimal coupling, it ...
On the minimizing movement with the 1-Wasserstein distancedoi:10.1051/COCV/2017055Martial AguehGuillaume CarlierNoureddine IgbidaEDP Sciences