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Nonlinear dimensionality reduction information


Top-left: a 3D dataset of 1000 points in a spiraling band (a.k.a. the Swiss roll) with a rectangular hole in the middle. Top-right: the original 2D manifold used to generate the 3D dataset. Bottom left and right: 2D recoveries of the manifold respectively using the LLE and Hessian LLE algorithms as implemented by the Modular Data Processing toolkit.

Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping (either from the high-dimensional space to the low-dimensional embedding or vice versa) itself.[1][2] The techniques described below can be understood as generalizations of linear decomposition methods used for dimensionality reduction, such as singular value decomposition and principal component analysis.

  1. ^ Lawrence, Neil D (2012). "A unifying probabilistic perspective for spectral dimensionality reduction: insights and new models". Journal of Machine Learning Research. 13 (May): 1609–38. arXiv:1010.4830. Bibcode:2010arXiv1010.4830L.
  2. ^ Lee, John A.; Verleysen, Michel (2007). Nonlinear Dimensionality Reduction. Springer. ISBN 978-0-387-39350-6.

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Nonlinear dimensionality reduction

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Nonlinear dimensionality reduction, also known as manifold learning, is any of various related techniques that aim to project high-dimensional data onto...

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Dimensionality reduction

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Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the...

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Isomap

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Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing...

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Model order reduction

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vascular walls. Dimension reduction Metamodeling Principal component analysis Singular value decomposition Nonlinear dimensionality reduction System identification...

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Diffusion map

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linear dimensionality reduction methods such as principal component analysis (PCA), diffusion maps are part of the family of nonlinear dimensionality reduction...

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Spectral submanifold

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be extended to a nonlinear system, and therefore motivates the use of SSMs in nonlinear dimensionality reduction. Consider a nonlinear ordinary differential...

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Machine learning

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ISBN 978-3-642-27644-6. Roweis, Sam T.; Saul, Lawrence K. (22 Dec 2000). "Nonlinear Dimensionality Reduction by Locally Linear Embedding". Science. 290 (5500): 2323–2326...

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Manifold hypothesis

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high-dimensional data sets by considering a few common features. The manifold hypothesis is related to the effectiveness of nonlinear dimensionality reduction...

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Latent space

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Clustering algorithm Intrinsic dimension Latent semantic analysis Manifold hypothesis Nonlinear dimensionality reduction Self-organizing map Liu, Yang;...

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Principal component analysis

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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data...

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Isometry

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Aarhus University. p. 125. Roweis, S.T.; Saul, L.K. (2000). "Nonlinear dimensionality reduction by locally linear embedding". Science. 290 (5500): 2323–2326...

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LTSA

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LTSA may refer to: Local tangent space alignment, a nonlinear dimensionality reduction method Land Title and Survey Authority in British Columbia, Canada...

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Word embedding

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1145/1031171.1031284. Roweis, Sam T.; Saul, Lawrence K. (2000). "Nonlinear Dimensionality Reduction by Locally Linear Embedding". Science. 290 (5500): 2323–6...

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Outline of machine learning

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Neuroph Niki.ai Noisy channel model Noisy text analytics Nonlinear dimensionality reduction Novelty detection Nuisance variable One-class classification...

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Spectral clustering

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(eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is...

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Exploratory data analysis

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plots Dimensionality reduction: Multidimensional scaling Principal component analysis (PCA) Multilinear PCA Nonlinear dimensionality reduction (NLDR)...

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Kernel principal component analysis

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Cluster analysis Nonlinear dimensionality reduction Spectral clustering Schölkopf, Bernhard; Smola, Alex; Müller, Klaus-Robert (1998). "Nonlinear Component Analysis...

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Autoencoder

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(December 2014). "Anomaly Detection Using Autoencoders with Nonlinear Dimensionality Reduction". Proceedings of the MLSDA 2014 2nd Workshop on Machine Learning...

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Feature learning

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Retrieved 2013-07-14. Roweis, Sam T; Saul, Lawrence K (2000). "Nonlinear Dimensionality Reduction by Locally Linear Embedding". Science. New Series. 290 (5500):...

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Multifactor dimensionality reduction

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Multifactor dimensionality reduction (MDR) is a statistical approach, also used in machine learning automatic approaches, for detecting and characterizing...

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Linear model

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"linear model" is not usually applied. One example of this is nonlinear dimensionality reduction. General linear model Generalized linear model Linear predictor...

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Thin plate spline

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the method of elastic maps, is used for data mining and nonlinear dimensionality reduction. In simple words, "the first term is defined as the error...

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List of statistics articles

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parameter Nonlinear autoregressive exogenous model Nonlinear dimensionality reduction Non-linear iterative partial least squares Nonlinear regression...

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Outline of statistics

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analysis Cluster analysis Multiple correspondence analysis Nonlinear dimensionality reduction Robust statistics Heteroskedasticity-consistent standard errors...

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Semidefinite embedding

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uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. It is motivated by the observation...

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Generative topographic map

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Neural Network Connectionism Data mining Machine learning Nonlinear dimensionality reduction Neural network software Pattern recognition Bishop, Svensen...

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Whitney embedding theorem

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immersion theorem Nash embedding theorem Takens's theorem Nonlinear dimensionality reduction Universal space See section 2 of Skopenkov (2008) Whitney...

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