{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T16:37:24Z","timestamp":1770827844370,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,3,11]],"date-time":"2020-03-11T00:00:00Z","timestamp":1583884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010193","name":"Korea Electric Power Corporation","doi-asserted-by":"publisher","award":["R18XA05"],"award-info":[{"award-number":["R18XA05"]}],"id":[{"id":"10.13039\/501100010193","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2019R1A2C1002706"],"award-info":[{"award-number":["2019R1A2C1002706"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>We introduce a distance metric between two distributions and propose a Generative Adversarial Network (GAN) model: the Simplified Fr\u00e9chet distance (SFD) and the Simplified Fr\u00e9chet GAN (SFGAN). Although the data generated through GANs are similar to real data, GAN often undergoes unstable training due to its adversarial structure. A possible solution to this problem is considering Fr\u00e9chet distance (FD). However, FD is unfeasible to realize due to its covariance term. SFD overcomes the complexity so that it enables us to realize in networks. The structure of SFGAN is based on the Boundary Equilibrium GAN (BEGAN) while using SFD in loss functions. Experiments are conducted with several datasets, including CelebA and CIFAR-10. The losses and generated samples of SFGAN and BEGAN are compared with several distance metrics. The evidence of mode collapse and\/or mode drop does not occur until 3000k steps for SFGAN, while it occurs between 457k and 968k steps for BEGAN. Experimental results show that SFD makes GANs more stable than other distance metrics used in GANs, and SFD compensates for the weakness of models based on BEGAN-based network structure. Based on the experimental results, we can conclude that SFD is more suitable for GAN than other metrics.<\/jats:p>","DOI":"10.3390\/s20061548","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T04:13:57Z","timestamp":1583986437000},"page":"1548","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Simplified Fr\u00e9chet Distance for Generative Adversarial Nets"],"prefix":"10.3390","volume":"20","author":[{"given":"Chung-Il","family":"Kim","sequence":"first","affiliation":[{"name":"School of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8081-0489","authenticated-orcid":false,"given":"Meejoung","family":"Kim","sequence":"additional","affiliation":[{"name":"Research Institute for Information and Communication Technology, Korea University, Seoul 02841, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seungwon","family":"Jung","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0418-4092","authenticated-orcid":false,"given":"Eenjun","family":"Hwang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea University, Seoul 02841, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Borji, A. 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