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Impact Factor:1.5

DOI number:10.1016/j.cagd.2018.10.005

Affiliation of Author(s):ELSEVIER

Journal:COMPUTER AIDED GEOMETRIC DESIGN

Place of Publication:RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS

Key Words:Optimal Mass Transportation;Monge-Ampere;GAN;Wasserstein distance

Abstract: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.

Co-author:Cui Li,Yau Shing-Tung,Gu Xianfeng

First Author:Lei Na

Indexed by:Article

Correspondence Author:Su Kehua

Document Type:J

Volume:68

Page Number:1-21

ISSN No.:0167-8396

Translation or Not:no

Date of Publication:2019-01-01

Included Journals:SCI、EI