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Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the dataspace. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and

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rdfs:label	Elastic map (en)
rdfs:comment	Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the dataspace. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and (en)
sameAs	Elastic map
dbp:wikiPageUsesTemplate	dbt:Redirect dbt:Reflist
Subject	Data mining Dimension reduction
thumbnail	wiki-commons:Special:FilePath/Elmap_breastcancer_wiki.png?width=300
foaf:depiction
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Elastic_map?oldid=973199619&ns=0
Wikipage page ID	28476914 (xsd:integer)
page length (characters) of wiki page	12993 (xsd:nonNegativeInteger)
Wikipage revision ID	973199619 (xsd:integer)
Link from a Wikipage to another Wikipage	Machine learning Nonlinear dimensionality reduction Probability density function Support-vector machine Aleksandr Gorban Artificial neural network Backpropagation Self-organizing map Data mining Dimension reduction Geodesic Portfolio (finance) K-means clustering Principal component analysis Spring (device) Trichome Elasticity coefficient Independent component analysis Expectation–maximization algorithm Euclidean space Standard deviation Mechanical equilibrium Classical mechanics Multiphase flow
has abstract	Elastic maps provide a tool for nonlinear dimensionality reduction. By their construction, they are a system of elastic springs embedded in the dataspace. This system approximates a low-dimensional manifold. The elastic coefficients of this system allow the switch from completely unstructured k-means clustering (zero elasticity) to the estimators located closely to linear PCA manifolds (for high bending and low stretching modules). With some intermediate values of the elasticity coefficients, this system effectively approximates non-linear principal manifolds. This approach is based on a mechanical analogy between principal manifolds, that are passing through "the middle" of the data distribution, and elastic membranes and plates. The method was developed by A.N. Gorban, A.Y. Zinovyev and A.A. Pitenko in 1996–1998. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Elastic_map
is Wikipage redirect of	Elastic net
is Link from a Wikipage to another Wikipage of	List of statistics articles Nonlinear dimensionality reduction Aleksandr Gorban Electricity price forecasting Growing self-organizing map Elastic net
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Elastic_map

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