{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T03:17:11Z","timestamp":1777778231855,"version":"3.51.4"},"reference-count":57,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T00:00:00Z","timestamp":1589760000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100002322","name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100002322","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2017\/25835-9"],"award-info":[{"award-number":["2017\/25835-9"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Information Visualization"],"published-print":{"date-parts":[[2020,7]]},"abstract":"<jats:p>Dimensionality reduction methods, also known as projections, are often used to explore multidimensional data in machine learning, data science, and information visualization. However, several such methods, such as the well-known t-distributed stochastic neighbor embedding and its variants, are computationally expensive for large datasets, suffer from stability problems, and cannot directly handle out-of-sample data. We propose a learning approach to construct any such projections. We train a deep neural network based on sample set drawn from a given data universe, and their corresponding two-dimensional projections, compute with any user-chosen technique. Next, we use the network to infer projections of any dataset from the same universe. Our approach generates projections with similar characteristics as the learned ones, is computationally two to four orders of magnitude faster than existing projection methods, has no complex-to-set user parameters, handles out-of-sample data in a stable manner, and can be used to learn any projection technique. We demonstrate our proposal on several real-world high-dimensional datasets from machine learning.<\/jats:p>","DOI":"10.1177\/1473871620909485","type":"journal-article","created":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T07:31:04Z","timestamp":1589787064000},"page":"247-269","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":49,"title":["Deep learning multidimensional projections"],"prefix":"10.1177","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1922-4309","authenticated-orcid":false,"given":"Mateus","family":"Espadoto","sequence":"first","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nina Sumiko Tomita","family":"Hirata","sequence":"additional","affiliation":[{"name":"Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandru C","family":"Telea","sequence":"additional","affiliation":[{"name":"University of Groningen, Groningen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,5,18]]},"reference":[{"issue":"3","key":"bibr1-1473871620909485","first-page":"495","volume":"19","author":"Kehrer J","year":"2013","journal-title":"IEEE TVCG"},{"issue":"3","key":"bibr2-1473871620909485","first-page":"1249","volume":"23","author":"Liu S","year":"2015","journal-title":"IEEE TVCG"},{"issue":"8","key":"bibr3-1473871620909485","first-page":"2650","volume":"25","author":"Nonato L","year":"2019","journal-title":"IEEE TVCG"},{"key":"bibr4-1473871620909485","volume-title":"Dimensionality reduction: a comparative review","author":"van der Maaten L","year":"2009"},{"key":"bibr5-1473871620909485","volume":"14032877","author":"Sorzano C","year":"2014","journal-title":"arXiv preprint arXiv"},{"key":"bibr6-1473871620909485","first-page":"2579","volume":"9","author":"van der Maaten L","year":"2008","journal-title":"JMLR"},{"key":"bibr7-1473871620909485","doi-asserted-by":"crossref","unstructured":"Wattenberg M. 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