{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T09:17:11Z","timestamp":1771492631280,"version":"3.50.1"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T00:00:00Z","timestamp":1637193600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>When confronted with massive data streams, summarizing data with dimension reduction methods such as PCA raises theoretical and algorithmic pitfalls. A principal curve acts as a nonlinear generalization of PCA, and the present paper proposes a novel algorithm to automatically and sequentially learn principal curves from data streams. We show that our procedure is supported by regret bounds with optimal sublinear remainder terms. A greedy local search implementation (called slpc, for sequential learning principal curves) that incorporates both sleeping experts and multi-armed bandit ingredients is presented, along with its regret computation and performance on synthetic and real-life data.<\/jats:p>","DOI":"10.3390\/e23111534","type":"journal-article","created":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T02:43:09Z","timestamp":1637289789000},"page":"1534","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9191-9367","authenticated-orcid":false,"given":"Le","family":"Li","sequence":"first","affiliation":[{"name":"Department of Statistics, Central China Normal University, Wuhan 430079, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1237-7430","authenticated-orcid":false,"given":"Benjamin","family":"Guedj","sequence":"additional","affiliation":[{"name":"Inria, Lille-Nord Europe Research Centre and Inria London, France and Centre for Artificial Intelligence, Department of Computer Science, University College London, London WC1V 6LJ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/14786440109462720","article-title":"On lines and planes of closest fit to systems of point in space","volume":"2","author":"Pearson","year":"1901","journal-title":"Philos. 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