影响因子：

1.5

DOI码：

10.1016/j.cagd.2018.10.005

所属单位：

ELSEVIER

发表刊物：

COMPUTER AIDED GEOMETRIC DESIGN

刊物所在地：

RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS

关键字：

Optimal Mass Transportation;Monge-Ampere;GAN;Wasserstein distance

摘要：

In this work, we give a geometric interpretation to the Generative Adversarial Networks (GANs). The geometric view is based on the intrinsic relation between Optimal Mass Transportation (OMT) theory and convex geometry, and leads to a variational approach to solve the Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. By using the optimal transportation view of GAN model, we show that the discriminator computes the Wasserstein distance via the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a close-form formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms the traditional Wasserstein GAN for approximating probability measures with multiple clusters in low dimensional space. (C) 2018 Elsevier B.V. All rights reserved.

合写作者：

Cui Li,Yau Shing-Tung,Gu Xianfeng

第一作者：

Lei Na

论文类型：

文章

通讯作者：

Su Kehua

文献类型：

J

卷号：

68

页面范围：

1-21

ISSN号：

0167-8396

是否译文：

否

发表时间：

2019-01-01

收录刊物：

SCI、EI