{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T12:36:48Z","timestamp":1776083808557,"version":"3.50.1"},"reference-count":0,"publisher":"MIT Press - Journals","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>UMAP is a nonparametric graph-based dimensionality reduction algorithm using applied Riemannian geometry and algebraic topology to find low-dimensional embeddings of structured data. The UMAP algorithm consists of two steps: (1) computing a graphical representation of a data set (fuzzy simplicial complex) and (2) through stochastic gradient descent, optimizing a low-dimensional embedding of the graph. Here, we extend the second step of UMAP to a parametric optimization over neural network weights, learning a parametric relationship between data and embedding. We first demonstrate that parametric UMAP performs comparably to its nonparametric counterpart while conferring the benefit of a learned parametric mapping (e.g., fast online embeddings for new data). We then explore UMAP as a regularization, constraining the latent distribution of autoencoders, parametrically varying global structure preservation, and improving classifier accuracy for semisupervised learning by capturing structure in unlabeled data.<\/jats:p>","DOI":"10.1162\/neco_a_01434","type":"journal-article","created":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T22:39:41Z","timestamp":1630622381000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":134,"title":["Parametric UMAP Embeddings for Representation and Semisupervised Learning"],"prefix":"10.1162","author":[{"given":"Tim","family":"Sainburg","sequence":"first","affiliation":[{"name":"University of California San Diego, La Jolla, CA 92093, U.S.A. timsainb@gmail.com"}]},{"given":"Leland","family":"McInnes","sequence":"additional","affiliation":[{"name":"Tutte Institute for Mathematics and Computing, Ottawa, Ontario Canada leland.mcinnes@gmail.com"}]},{"given":"Timothy Q.","family":"Gentner","sequence":"additional","affiliation":[{"name":"University of California San Diego, La Jolla, CA 92093, U.S.A. tgentner@ucsd.edu"}]}],"member":"281","published-online":{"date-parts":[[2021,8,30]]},"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/direct.mit.edu\/neco\/article-pdf\/doi\/10.1162\/neco_a_01434\/1959528\/neco_a_01434.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/direct.mit.edu\/neco\/article-pdf\/doi\/10.1162\/neco_a_01434\/1959528\/neco_a_01434.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,9,2]],"date-time":"2021-09-02T22:39:42Z","timestamp":1630622382000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/doi\/10.1162\/neco_a_01434\/107068\/Parametric-UMAP-Embeddings-for-Representation-and"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,30]]},"references-count":0,"URL":"https:\/\/doi.org\/10.1162\/neco_a_01434","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,30]]}}}