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Statements

Subject Item
dbr:Elastic_map
rdfs:label
Elastic map
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
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n7:Elmap_breastcancer_wiki.png?width=300
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n7:Elmap_breastcancer_wiki.png n7:SlideQualityLife.png
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dbr:Portfolio_(finance) dbr:Mechanics dbr:Nonlinear_dimensionality_reduction dbr:Independent_component_analysis dbr:Self-organizing_map dbr:Artificial_neural_network dbr:Principal_component_analysis n9:SlideQualityLife.png dbr:Aleksandr_Gorban dbr:Trichome dbr:K-means_clustering dbr:Support-vector_machine dbr:Euclidean_space dbr:Geodesic dbc:Data_mining dbr:Expectation–maximization_algorithm dbr:Multiphase_flow dbr:Mechanical_equilibrium dbr:Probability_density_function n9:Elmap_breastcancer_wiki.png dbr:Spring_(device) dbr:Standard_deviation dbr:Machine_learning dbr:Elasticity_coefficient dbr:Backpropagation dbc:Dimension_reduction
dbo: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.
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