2000 NonlinearDimensionalityReductio

• (Roweis & Saul, 2000) ⇒ Sam T. Roweis, and Lawrence K. Saul. (2000). “Nonlinear Dimensionality Reduction by Locally Linear Embedding.” In: Science Journal, 290(5500). doi:10.1126/science.290.5500.2323

Subject Headings: Locally-Linear Embedding Algorithm

Cited By

• http://scholar.google.com/scholar?q=%22Nonlinear+dimensionality+reduction+by+locally+linear+embedding%22+2000

Quotes

Abstract

Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data. Here, we introduce locally linear embedding (LLE), an unsupervised learning algorithm that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. Unlike clustering methods for local dimensionality reduction, LLE maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. By exploiting the local symmetries of linear reconstructions, LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text.

References

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2000 NonlinearDimensionalityReductio	Lawrence K. Saul Sam T. Roweis			Nonlinear Dimensionality Reduction by Locally Linear Embedding				10.1126/science.290.5500.2323		2000