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• Nonlinear_dimensionality_reduction abstract "High-dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lie on an embedded non-linear manifold within the higher-dimensional space. If the manifold is of low enough dimension, the data can be visualised in the low-dimensional space.Below is a summary of some of the important algorithms from the history of manifold learning and nonlinear dimensionality reduction (NLDR). Many of these non-linear dimensionality reduction methods are related to the linear methods listed below. Non-linear methods can be broadly classified into two groups: those that provide a mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa), and those that just give a visualisation. In the context of machine learning, mapping methods may be viewed as a preliminary feature extraction step, after which pattern recognition algorithms are applied. Typically those that just give a visualisation are based on proximity data – that is, distance measurements.".
• Nonlinear_dimensionality_reduction thumbnail Lle_hlle_swissroll.png?width=300.
• Nonlinear_dimensionality_reduction wikiPageExternalLink isomap.stanford.edu.
• Nonlinear_dimensionality_reduction wikiPageExternalLink edrt.
• Nonlinear_dimensionality_reduction wikiPageExternalLink DD-HDS-homepage.html.
• Nonlinear_dimensionality_reduction wikiPageExternalLink RankVisu-homepage.html.
• Nonlinear_dimensionality_reduction wikiPageExternalLink diffusion_maps.pdf.
• Nonlinear_dimensionality_reduction wikiPageExternalLink waffles.sourceforge.net.
• Nonlinear_dimensionality_reduction wikiPageExternalLink www.VisuMap.com.
• Nonlinear_dimensionality_reduction wikiPageExternalLink lle.
• Nonlinear_dimensionality_reduction wikiPageExternalLink gplvm.
• Nonlinear_dimensionality_reduction wikiPageExternalLink thesis.htm.
• Nonlinear_dimensionality_reduction wikiPageExternalLink GTM.
• Nonlinear_dimensionality_reduction wikiPageExternalLink www.nlpca.org.
• Nonlinear_dimensionality_reduction wikiPageExternalLink RpmOverview.
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• Nonlinear_dimensionality_reduction wikiPageWikiLink Artificial_neural_network.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Autoencoder.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Backpropagation.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Category:Dimension.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Category:Dimension_reduction.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Category:Multivariate_statistics.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Charles-Augustin_de_Coulomb.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Concentration_of_measure.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Coulombs_law.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Curse_of_dimensionality.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Curvilinear_component_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Degree_matrix.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Density_networks.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Diffusion_map.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Dimension.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Dimensionality_reduction.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Discriminant_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Distance.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Distance_(graph_theory).
• Nonlinear_dimensionality_reduction wikiPageWikiLink Distance_matrix.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Dynamic_time_warping.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Dynamical_system.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Dynamical_systems.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Eigendecomposition_of_a_matrix.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Elastic_map.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Euclidean_distance.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Expectation-maximization_algorithm.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Expectation–maximization_algorithm.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Factor_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Feature_extraction.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Feature_learning.
• Nonlinear_dimensionality_reduction wikiPageWikiLink File:Letters_pca.png.
• Nonlinear_dimensionality_reduction wikiPageWikiLink File:Nldr.jpg.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Floyd–Warshall_algorithm.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Fourier_series.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Gaussian_process.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Gaussian_process_latent_variable_model.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Generative_topographic_map.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Generative_topographic_mapping.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Geodesic.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Geodesic_distance.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Graduated_optimization.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Growing_self-organizing_map.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Hamming_space.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Hessian_LLE.
• Nonlinear_dimensionality_reduction wikiPageWikiLink High-dimensional.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Independent_component_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Isomap.
• Nonlinear_dimensionality_reduction wikiPageWikiLink K-nearest_neighbor_algorithm.
• Nonlinear_dimensionality_reduction wikiPageWikiLink K-nearest_neighbors_algorithm.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Karhunen–Loève_transform.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Kernel_method.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Kernel_principal_component_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Kernel_trick.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Klein_bottle.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Laplace–Beltrami_operator.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Latent_variable_model.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Linear_discriminant_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Local_tangent_space_alignment.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Locally-Linear_Embedding.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Locally_linear_embeddings.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Machine_learning.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Manifold.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Manifold_alignment.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Manifold_learning.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Markov_Chain.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Markov_chain.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Maximum_Variance_Unfolding.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Maximum_variance_unfolding.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Multidimensional_Scaling.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Multidimensional_scaling.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Multilinear_subspace_learning.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Neural_network.
• Nonlinear_dimensionality_reduction wikiPageWikiLink NeuroScale.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Nonlinear_dimensionality_reduction.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Ohio_State_University.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Pairwise_distance_methods.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Pattern_recognition.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Principal_component_analysis.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Principal_curve.
• Nonlinear_dimensionality_reduction wikiPageWikiLink Projective_space.

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