Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

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...

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Autores principales:	Le Li, Benjamin Guedj
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/16617bdbcbda4d09a3e9fb9cc38aeb99
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id	oai:doaj.org-article:16617bdbcbda4d09a3e9fb9cc38aeb99
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spelling	oai:doaj.org-article:16617bdbcbda4d09a3e9fb9cc38aeb992021-11-25T17:30:42ZSequential Learning of Principal Curves: Summarizing Data Streams on the Fly10.3390/e231115341099-4300https://doaj.org/article/16617bdbcbda4d09a3e9fb9cc38aeb992021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1534https://doaj.org/toc/1099-4300When 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.Le LiBenjamin GuedjMDPI AGarticlesequential learningprincipal curvesdata streamsregret boundsgreedy algorithmsleeping expertsScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1534, p 1534 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	sequential learning principal curves data streams regret bounds greedy algorithm sleeping experts Science Q Astrophysics QB460-466 Physics QC1-999 Le Li Benjamin Guedj Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
description	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.
format	article
author	Le Li Benjamin Guedj
author_facet	Le Li Benjamin Guedj
author_sort	Le Li
title	Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
title_short	Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
title_full	Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
title_fullStr	Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
title_full_unstemmed	Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
title_sort	sequential learning of principal curves: summarizing data streams on the fly
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/16617bdbcbda4d09a3e9fb9cc38aeb99
work_keys_str_mv	AT leli sequentiallearningofprincipalcurvessummarizingdatastreamsonthefly AT benjaminguedj sequentiallearningofprincipalcurvessummarizingdatastreamsonthefly
_version_	1718412270301609984

Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly

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