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Everything about Nonlinear dimensionality reduction
Projection of data onto lower-dimensional manifolds
Nonlinear dimensionality reduction (NLDR), also known as manifold learning, is any of various related techniques that aim to project high-dimensional data, potentially existing across non-linear manifolds which cannot be adequately captured by linear decomposition methods, onto lower-dimensional latent manifolds, with the goal of either visualizing the data in the low-dimensional space, or learning the mapping 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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Nonlinear dimensionality reductionA 5-minute orientation
- Skim a recent paper: Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modelingInfluential work since 2022
- Pick up a classic book: Advances in Computational IntelligenceThe most-reprinted book on the subject
- Read the landmark paper: Nonlinear Dimensionality Reduction by Locally Linear EmbeddingCited 11,883 times
- Go sideways: IsomapA closely related topic
- Go sideways: Dimensionality reductionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Nonlinear Dimensionality Reduction by Locally Linear Embedding
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Supervised Nonlinear Dimensionality Reduction for Visualization and Classification
Parametric nonlinear dimensionality reduction using kernel t-SNE
Incremental nonlinear dimensionality reduction by manifold learning
Nonlinear Dimensionality Reduction with Local Spline Embedding
Nonlinear dimensionality reduction of data manifolds with essential loops
Data visualization by nonlinear dimensionality reduction
🆕 Influential since 2022
Comparing different nonlinear dimensionality reduction techniques for data-driven unsteady fluid flow modeling
Linear and nonlinear dimensionality reduction from fluid mechanics to machine learning
Dimensionality Reduction via Multiple Neighborhood-Aware Nonlinear Collaborative Analysis for Hyperspectral Image Classification
A Nonlinear Dimensionality Reduction Search Improved Differential Evolution for large-scale optimization
Classifying FRB spectrograms using nonlinear dimensionality reduction techniques
📚 Books worth reading
Advances in Computational IntelligenceIgnacio Rojas · 2013- 📕Study of one- and two-dimensional filtering and deconvolution algorithms for a streaming array computerGeorge E. Ioup · 1985
- 📕Structural Aspects of Quantum Field Theory and Noncommutative GeometryGerhard Grensing · 2013
Nonlinear dimensionality reductionMichel Verleysen, John A. Lee · 2007- 📕Nonlinear Dimensionality Reduction TechniquesSylvain Lespinats, Benoit Colange · 2021
- 📕A non-linear dimensionality reduction method for improving nearest neighbour classificationRenqiang Min · 2005
2-D page map analysisEmilio Marengo, Elisa Robotti · 2016
PrecalculusMcGraw-Hill-Glencoe Staff, McGraw-Hill Education Staff · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Isomap Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing…
- Dimensionality reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the…
- Diffusion map Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a…
- Manifold alignment Manifold alignment is a class of machine learning algorithms that produce projections between sets of data, given that the original data sets lie on a…
- Semidefinite embedding Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to…
- Kernel method In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These…
- T-distributed stochastic neighbor embedding t-distributed stochastic neighbor embedding (t-SNE) is a statistical method for visualizing high-dimensional data by giving each datapoint a location in…
- Shogun (toolbox) Free and open-source software portal Shogun is a free, open-source machine learning software library written in C++. It offers numerous algorithms and…