id
	16374
Url
	https://chloe.cnr.it/s/BiDiAr/item/16374
Resource template
	Academic Article
Resource class
	bibo:AcademicArticle
Title
	A Global Geometric Framework for Nonlinear Dimensionality Reduction
Creator
	Tenenbaum, Joshua B.
	Silva, Vin de
	Langford, John C.
Date
	2000
Language
	eng
Abstract
	Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in everyday perception, extracting from its high-dimensional sensory inputs—30,000 auditory nerve fibers or 106 optic nerve fibers—a manageably small number of perceptually relevant features. Here we describe an approach to solving dimensionality reduction problems that uses easily measured local metric information to learn the underlying global geometry of a data set. Unlike classical techniques such as principal component analysis (PCA) and multidimensional scaling (MDS), our approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In contrast to previous algorithms for nonlinear dimensionality reduction, ours efficiently computes a globally optimal solution, and, for an important class of data manifolds, is guaranteed to converge asymptotically to the true structure.
Is Part Of
	Science
Doi
	https://www.science.org/doi/10.1126/science.290.5500.2319
Issue
	5500
Pages
	2319-2323
Volume
	290
Homepage
	https://www.zotero.org/groups/5293298/bidiar/items/MPT46K46item-list

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