{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T12:06:56Z","timestamp":1789819616947,"version":"4.0.1"},"reference-count":39,"publisher":"IOP Publishing","issue":"2","license":[{"start":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T00:00:00Z","timestamp":1614297600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,2,26]],"date-time":"2021-02-26T00:00:00Z","timestamp":1614297600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2021,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remains a highly adaptable method to evolving model architectures and varying amounts of data\u2014in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying M\u00f6bius transformations to augment input images during training. M\u00f6bius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, M\u00f6bius transformations can operate on the sample level and preserve data labels. We show that the inclusion of M\u00f6bius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.<\/jats:p>","DOI":"10.1088\/2632-2153\/abd615","type":"journal-article","created":{"date-parts":[[2020,12,22]],"date-time":"2020-12-22T22:39:19Z","timestamp":1608676759000},"page":"025016","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":16,"title":["Data augmentation with Mobius transformations"],"prefix":"10.1088","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4991-9336","authenticated-orcid":false,"given":"Sharon","family":"Zhou","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiequan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hang","family":"Jiang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Torbj\u00f6rn","family":"Lundh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrew Y","family":"Ng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2021,2,26]]},"reference":[{"key":"mlstabd615bib1","article-title":"The effectiveness of data augmentation in image classification using deep learning","author":"Perez","year":"2017"},{"key":"mlstabd615bib2","article-title":"Improved regularization of convolutional neural networks with cutout","author":"DeVries","year":"2017"},{"key":"mlstabd615bib3","article-title":"Random erasing data augmentation","author":"Zhong","year":"2017"},{"key":"mlstabd615bib4","article-title":"Deep CNN ensemble with data augmentation for object detection","author":"Guo","year":"2015"},{"key":"mlstabd615bib5","first-page":"1451","article-title":"Understanding convolution for semantic segmentation","author":"Wang","year":"2018"},{"key":"mlstabd615bib6","article-title":"Data augmentation instead of explicit regularization","author":"Hern\u00e1ndez-Garc\u00eda","year":"2018"},{"key":"mlstabd615bib7","first-page":"2807","article-title":"DADA: deep adversarial data augmentation for extremely low data regime classification","author":"Zhang","year":"2019"},{"key":"mlstabd615bib8","article-title":"mixup: beyond empirical risk minimization","author":"Zhang","year":"2017"},{"key":"mlstabd615bib9","first-page":"113","article-title":"Autoaugment: learning augmentation strategies from data","author":"Cubuk","year":"2019"},{"key":"mlstabd615bib10","article-title":"Randaugment: practical data augmentation with no separate search","author":"Cubuk","year":"2019"},{"key":"mlstabd615bib11","article-title":"Unsupervised data augmentation","author":"Xie","year":"2019"},{"key":"mlstabd615bib12","article-title":"Mixmatch: a holistic approach to semi-supervised learning","author":"Berthelot","year":"2019"},{"key":"mlstabd615bib13","author":"Thompson","year":"1942"},{"key":"mlstabd615bib14","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1016\/0898-1221(89)90248-4","article-title":"Non-Euclidean geometries and algorithms of living bodies","volume":"17","author":"Petukhov","year":"1989","journal-title":"Comput. Math. Appl."},{"key":"mlstabd615bib15","article-title":"Cross- and triple-ratios of human body parts during development","volume":"294","author":"Lundh","year":"2011","journal-title":"Anatomical Rec."},{"key":"mlstabd615bib16","first-page":"609","article-title":"Extension au cas des trois dimensions de la question du trac\u00e9 g\u00e9ographique","author":"Liouville","year":"1850"},{"key":"mlstabd615bib17","author":"Ahlfors","year":"1989"},{"key":"mlstabd615bib18","author":"Needham","year":"1998"},{"key":"mlstabd615bib19","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1023\/A:1026598000963","article-title":"Single view metrology","volume":"40","author":"Criminisi","year":"2000","journal-title":"Int. J. Comput. Vis."},{"key":"mlstabd615bib20","author":"Lie","year":"1893"},{"key":"mlstabd615bib21","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1080\/10586458.1995.10504331","article-title":"Circle packing: experiments in discrete analytic function theory","volume":"4","author":"Dubejko","year":"1995","journal-title":"Exp. Math."},{"key":"mlstabd615bib22","doi-asserted-by":"publisher","first-page":"7405","DOI":"10.1109\/TGRS.2016.2601622","article-title":"Learning rotation-invariant convolutional neural networks for object detection in VHR optical remote sensing images","volume":"54","author":"Cheng","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"mlstabd615bib23","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1109\/TIP.2018.2867198","article-title":"Learning rotation-invariant and Fisher discriminative convolutional neural networks for object detection","volume":"28","author":"Cheng","year":"2018","journal-title":"IEEE Trans. Image Process."},{"key":"mlstabd615bib24","first-page":"5486","article-title":"Between-class learning for image classification","author":"Tokozume","year":"2018"},{"key":"mlstabd615bib25","article-title":"Data augmentation by pairing samples for images classification","author":"Inoue","year":"2018"},{"key":"mlstabd615bib26","doi-asserted-by":"publisher","first-page":"2917","DOI":"10.1109\/TCSVT.2019.2935128","article-title":"Data augmentation using random image cropping and patching for deep CNNs","volume":"30","author":"Takahashi","year":"2020","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"mlstabd615bib27","first-page":"1262","article-title":"Improved mixed-example data augmentation","author":"Summers","year":"2019"},{"key":"mlstabd615bib28","first-page":"2998","article-title":"Adatransform: adaptive data transformation","author":"Tang","year":"2019"},{"key":"mlstabd615bib29","article-title":"Population based augmentation: efficient learning of augmentation policy schedules","author":"Ho","year":"2019"},{"key":"mlstabd615bib30","article-title":"Fixmatch: simplifying semi-supervised learning with consistency and confidence","author":"Sohn","year":"2020"},{"key":"mlstabd615bib31","first-page":"3236","article-title":"Learning to compose domain-specific transformations for data augmentation","author":"Ratner","year":"2017"},{"key":"mlstabd615bib32","doi-asserted-by":"publisher","first-page":"4698","DOI":"10.1016\/j.cnsns.2011.03.005","article-title":"Complex valued neural network with m\u00f6bius activation function","volume":"16","author":"\u00d6zdemir","year":"2011","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"mlstabd615bib33","article-title":"Deep compositional spatial models","author":"Zammit-Mangion","year":"2019"},{"key":"mlstabd615bib34","first-page":"5345","article-title":"Hyperbolic neural networks","author":"Ganea","year":"2018"},{"key":"mlstabd615bib35","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1109\/TFUZZ.2019.2917124","article-title":"Enabling explainable fusion in deep learning with fuzzy integral neural networks","volume":"28","author":"Islam","year":"2020","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"mlstabd615bib36","first-page":"185","article-title":"The use of Mobius transformations in neural networks and signal processing","volume":"vol 1","author":"Mandic","year":"2000"},{"key":"mlstabd615bib37","first-page":"87.1","article-title":"Learning multiple layers of features from tiny images","author":"Krizhevsky","year":"2009"},{"key":"mlstabd615bib38","article-title":"Tiny imagenet challenge","author":"Wu","year":"2017","journal-title":"Technical Report"},{"key":"mlstabd615bib39","doi-asserted-by":"crossref","DOI":"10.5244\/C.30.87","article-title":"Wide residual networks","author":"Zagoruyko","year":"2016"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T16:11:12Z","timestamp":1642090272000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/abd615"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,26]]},"references-count":39,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,2,26]]},"published-print":{"date-parts":[[2021,6,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/abd615","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,26]]},"assertion":[{"value":"Data augmentation with Mobius transformations","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2021 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2020-09-09","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-12-22","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2021-02-26","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}