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Nonlinear Dimensionality Reduction by Locally Linear Embedding
Science, 2000Many areas of science depend on exploratory data analysis and visualization. The need to analyze large amounts of multivariate data raises the fundamental problem of dimensionality reduction: how to discover compact representations of high-dimensional data.
Roweis, S. T., Lawrence, L. K.
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A Global Geometric Framework for Nonlinear Dimensionality Reduction
Science, 2000Scientists working with large volumes of high-dimensional data, such as global climate patterns, stellar spectra, or human gene distributions, regularly confront the problem of dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. The human brain confronts the same problem in
Tenenbaum, J. B. +2 more
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Nonlinear Dimensionality Reduction Techniques
2022Sylvain Lespinats +2 more
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Data visualization by nonlinear dimensionality reduction
WIREs Data Mining and Knowledge Discovery, 2015In this overview, commonly used dimensionality reduction techniques for data visualization and their properties are reviewed. Thereby, the focus lies on an intuitive understanding of the underlying mathematical principles rather than detailed algorithmic pipelines. Important mathematical properties of the technologies are summarized in the tabular form.
Gisbrecht, Andrej, Hammer, Barbara
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The Physics of Fluids, 2022
Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques for extracting physical information from CFD.
Hunor Csala +2 more
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Computational fluid dynamics (CFD) is known for producing high-dimensional spatiotemporal data. Recent advances in machine learning (ML) have introduced a myriad of techniques for extracting physical information from CFD.
Hunor Csala +2 more
semanticscholar +1 more source
Nonlinear dimensionality reduction for parametric problems: A kernel proper orthogonal decomposition
International Journal for Numerical Methods in Engineering, 2021Reduced‐order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems.
Pedro D'iez +3 more
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C2DNDA: A Deep Framework for Nonlinear Dimensionality Reduction
IEEE transactions on industrial electronics (1982. Print), 2021Dimensionality reduction has attracted much research interest in the past few decades. Existing dimensionality reduction methods like linear discriminant analysis and principal component analysis have achieved promising performance, but the single and ...
Qi Wang, Zequn Qin, F. Nie, Xuelong Li
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Quantum algorithm for the nonlinear dimensionality reduction with arbitrary kernel
Quantum Science and Technology, 2020Dimensionality reduction (DR) techniques play an extremely critical role in the data mining and pattern recognition field. However, most DR approaches involve large-scale matrix computations, which cause too high running complexity to implement in the ...
Yaochong Li +4 more
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Nonlinear barycentric dimensionality reduction
2010 IEEE International Conference on Image Processing, 2010Many high-dimensional datasets can be mapped onto lower-dimensional linear simplexes, parametrized by barycentric coordinates. We present an unsupervised algorithm that is able to find the barycentric coordinates and corresponding vertices of such a high-dimensional dataset, by combining manifold learning with a distance geometry based algorithm for ...
Heylen, Rob, Scheunders, Paul
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Dimensional reduction in nonlinear filtering
Nonlinearity, 2010The theory of nonlinear filtering forms the framework of many data assimilation problems. When the rates of change of different variables differ by orders of magnitude, efficient data assimilation can be accomplished by constructing nonlinear filtering equations for the coarse-grained signal.
J H Park +2 more
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