Diffusion Maps for dimensionality reduction and visualization of meteorological data
Entity
UAM. Departamento de Ingeniería InformáticaPublisher
Elsevier Inc.Date
2015-09-02Citation
10.1016/j.neucom.2014.08.090
Neurocomputing 163 (2015): 25-37
ISSN
0925-2312 (print); 1872-8286 (online)DOI
10.1016/j.neucom.2014.08.090Funded by
The authors acknowledge partial support from Spain's grant TIN2010-21575-C02-01 and the UAM{ADIC Chair for Machine Learning. The first author is also supported by an FPI{UAM grant and kindly thanks the Applied Mathematics Department of Yale University for receiving her during her visits.Project
Gobierno de España. TIN2010-21575-C02-01Editor's Version
http://dx.doi.org/10.1016/j.neucom.2014.08.090Subjects
Natural Clustering; Compressed Data; Diffusion Maps; Nyström formula; Laplacian Pyramids; InformáticaNote
This is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Neurocomputing, VOL 163, (2015) DOI 10.1016/j.neucom.2014.08.090Rights
© 2015 Elsevier B.V. All rights reserved
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
The growing interest in big data problems implies the need for unsupervised methods for data visualization and dimensionality reduction. Diffusion Maps (DM) is a recent technique that can capture the lower dimensional geometric structure underlying the sample patterns in a way which can be made to be independent of the sampling distribution. Moreover, DM allows us to define an embedding whose Euclidean metric relates to the sample's intrinsic one which, in turn, enables a principled application of k-means clustering. In this work we give a self-contained review of DM and discuss two methods to compute the DM embedding coordinates to new out-of-sample data. Then, we will apply them on two meteorological data problems that involve time and spatial compression of numerical weather forecasts and show how DM is capable to, first, greatly reduce the initial dimension while still capturing relevant information in the original data and, also, how the sample-derived DM embedding coordinates can be extended to new patterns.
Files in this item
Google Scholar:Fernández Pascual, Ángela
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González, Ana M
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Díaz García, Julia
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Dorronsoro Ibero, José Ramón
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