Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps
A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a low-dimensional representation that captures the intrinsic topological structure of the input data and then to analyze this...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.45.6320 2023-05-15T18:32:40+02:00 Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps J. Bruske G. Sommer The Pennsylvania State University CiteSeerX Archives 1997 application/postscript http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.6320 en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.6320 Metadata may be used without restrictions as long as the oai identifier remains attached to it. ftp://ftp.informatik.uni-kiel.de/pub/kiel/publications/CognitiveSystems/Ps_Z/1997_tr03.ps.Z text 1997 ftciteseerx 2016-01-08T05:48:28Z A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a low-dimensional representation that captures the intrinsic topological structure of the input data and then to analyze this representation, i.e. estimate the intrinsic dimensionality. More specifically, the representation we extract is an optimally topology preserving feature map (OTPM) which is an undirected parametrized graph with a pointer in the input space associated with each node. Estimation of the intrinsic dimensionality is based on local PCA of the pointers of the nodes in the OTPM and their direct neighbors. The method has a number of important advantages compared with previous approaches: First, it can be shown to have only linear time complexity w.r.t. the dimensionality of the input space, in contrast to conventional PCA based approaches which have cubic complexity and hence become computational imp. Text The Pointers Unknown |
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A new method for analyzing the intrinsic dimensionality (ID) of low dimensional manifolds in high dimensional feature spaces is presented. The basic idea is to first extract a low-dimensional representation that captures the intrinsic topological structure of the input data and then to analyze this representation, i.e. estimate the intrinsic dimensionality. More specifically, the representation we extract is an optimally topology preserving feature map (OTPM) which is an undirected parametrized graph with a pointer in the input space associated with each node. Estimation of the intrinsic dimensionality is based on local PCA of the pointers of the nodes in the OTPM and their direct neighbors. The method has a number of important advantages compared with previous approaches: First, it can be shown to have only linear time complexity w.r.t. the dimensionality of the input space, in contrast to conventional PCA based approaches which have cubic complexity and hence become computational imp. |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
J. Bruske G. Sommer |
spellingShingle |
J. Bruske G. Sommer Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
author_facet |
J. Bruske G. Sommer |
author_sort |
J. Bruske |
title |
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
title_short |
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
title_full |
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
title_fullStr |
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
title_full_unstemmed |
Intrinsic Dimensionality Estimation with Optimally Topology Preserving Maps |
title_sort |
intrinsic dimensionality estimation with optimally topology preserving maps |
publishDate |
1997 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.6320 |
genre |
The Pointers |
genre_facet |
The Pointers |
op_source |
ftp://ftp.informatik.uni-kiel.de/pub/kiel/publications/CognitiveSystems/Ps_Z/1997_tr03.ps.Z |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.6320 |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766216868328112128 |