About: Nonlinear dimensionality reduction

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Nonlinear dimensionality reduction, also known as manifold learning, refers to 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. 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.

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rdf:type	Thing
rdfs:label	تقليل الأبعاد غير الخطية (ar) Nonlinear dimensionality reduction (en) 非线性降维 (zh)
rdfs:comment	Nonlinear dimensionality reduction, also known as manifold learning, refers to 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. 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. (en) 高维数据，意味着数据需要多于两个或三个维度来表示，一般很难被解释。一种简化的方法是假设数据嵌在高维空间的一个非线性流形上。如果这个流形维数足够低，那么数据可以在低维空间中被可视化。 (zh) قد يكون من الصعب تفسير البيانات متعددة الأبعاد، وهي البيانات التي تتطلب أكثر من بعدين أو ثلاثة أبعاد لتمثيلها. تتمثل إحدى طرق تمثيلها في افتراض أن البيانات ذات الأهمية تكمن في مساحة أقل بُعدًا. إذا كانت البيانات ذات الأهمية منخفضة بشكل كافٍ، فيمكن تصور البيانات في الفضاء ذي الأبعاد المنخفضة. (ar)
rdfs:seeAlso	Manifold regularization
foaf:depiction
dcterms:subject	Dimension reduction
Wikipage page ID	309261 (xsd:integer)
Wikipage revision ID	1124009505 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Elastic map Neural network Bergman kernel Degree matrix Invariant manifold Coulomb's law Radial basis function network Eigendecomposition of a matrix Gaussian process Geodesic Concentration of measure Local tangent space alignment Singular value decomposition Feature learning Hamming space Kernel principal component analysis T-distributed stochastic neighbor embedding Swiss roll Backpropagation Torus Trevor Hastie Whitney embedding theorem Fourier series Diffusion Diffusion map Dimensionality reduction Floyd–Warshall algorithm Global cascades model Graduated optimization Isomap Principal component analysis Restricted Boltzmann machine Riemannian manifold Riemannian metric Dynamical systems Charles-Augustin de Coulomb K-nearest neighbor algorithm Laplace operator Latent variable model Diffeomorphic Distance matrix Autoencoder Dimension reduction Manifold Sparse matrix Sphere Growing self-organizing map Maximum Variance Unfolding Klein bottle Orthogonal projection Random walk Multidimensional scaling Self-organizing map Maximum variance unfolding Locally connected Locally linear embeddings Euclidean distance Multidimensional Scaling Manifold alignment Manifold hypothesis Sammon mapping Stress majorization Markov Chain Spectral submanifold Takens's theorem Sammon's mapping Sammon's projection Similarity matrix Discriminant analysis Generative topographic mapping Geodesic distance Latent manifold dbr:Density_networks dbr:Curvilinear_component_analysis dbr:Gaussian_process_latent_variable_model dbr:Hessian_LLE dbr:Locally-linear_Embedding dbr:NeuroScale

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