[759] - Principal manifold learning by sparse grids

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Citation
Feuersänger, C., Griebel, M., 2009. Principal manifold learning by sparse grids. Computing, 85, 267 - 299. DOI: 10.1007/s00607-009-0045-8.
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Identification
Title(s):Main Title: Principal manifold learning by sparse grids
Description(s):Abstract: In this paper, we deal with the construction of lower-dimensional manifolds from high-dimensional data which is an important task in data mining, machine learning and statistics. Here, we consider principal manifolds as the minimum of a regularized, non-linear empirical quantization error functional. For the discretization we use a sparse grid method in latent parameter space. This approach avoids, to some extent, the curse of dimension of conventional grids like in the GTM approach. The arising non-linear problem is solved by a descent method which resembles the expectation maximization algorithm.We present our sparse grid principal manifold approach, discuss its properties and report on the results of numerical experiments for one-, two and three-dimensional model problems.
Identifier(s):DOI: 10.1007/s00607-009-0045-8
Responsible Party
Creator(s):Author: Christian Feuersänger
Author: Michael Griebel
Publisher:Springer
Topic
TR32 Topic:Other
Subject(s):CRC/TR32 Keywords: Sparse Grids, Regularized Principal Manifolds, High-Dimensional Data
File Details
File Name:2009_Feuersaenger_Computing.pdf
Data Type:Text
Size(s):33 Pages
File Size:5822 kB (5.686 MB)
Date(s):Date Accepted: 2009-04-28
Issued: 2009-07-28
Mime Type:application/pdf
Data Format:PDF
Language:English
Status:Completed
Constraints
Download Permission:OnlyTR32
General Access and Use Conditions:For internal use only
Access Limitations:For internal use only
Licence:TR32DB Data policy agreement
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Measurement Region:None
Measurement Location:--None--
Specific Informations - Publication
Status:Published
Review:PeerReview
Year:2009
Type:Article
Article Type:Journal
Source:Computing
Volume:85
Number Of Pages:33
Page Range:267 - 299
Metadata Details
Metadata Creator:Harrie-Jan Hendricks-Franssen
Metadata Created:2013-12-03
Metadata Last Updated:2013-12-03
Subproject:D5
Funding Phase:1
Metadata Language:English
Metadata Version:V40
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