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Nonlinear dimensionality reduction by curvature minimization
2016 23rd International Conference on Pattern Recognition (ICPR), 2016In this paper, we introduce a nonlinear dimensionality reduction (NLDR) technique that can construct a low-dimensional embedding efficiently and accurately with low embedding distortions. The key idea is to divide NLDR into nonlinearity reduction and linear dimensionality reduction, which simplifies the overall NLDR process.
Yusuke Yoshiyasu, Eiichi Yoshida
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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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Linear versus Nonlinear Dimensionality Reduction of High-Dimensional Dynamical Systems
SIAM Journal on Scientific Computing, 2004The author uses combinations of the K-L decomposition and neural networks to obtain the intrinsic or true dimension of two PDEs, namely, the 1-d K-S equation and the 2-d N-S equations. For the 1-d K-S equation, he investigates one particular dynamical behavior which, in phase space, is represented by a heteroclinic connection.
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Supervised Nonlinear Dimensionality Reduction for Visualization and Classification
IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics), 2005When performing visualization and classification, people often confront the problem of dimensionality reduction. Isomap is one of the most promising nonlinear dimensionality reduction techniques. However, when Isomap is applied to real-world data, it shows some limitations, such as being sensitive to noise. In this paper, an improved version of Isomap,
Xin, Geng, De-Chuan, Zhan, Zhi-Hua, Zhou
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Dimensional Reduction of Nonlinear Delay Systems
2002Time delays usually give rise to great difficulty in the dynamic analysis of controlled mechanical systems. The difficulty increases so dramatically with an increase of system dimensions that the analytical results for the dynamics of delay systems of high dimensions are considerably few.
Haiyan Hu, Zaihua Wang
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Some aspects of nonlinear dimensionality reduction
Computational StatisticszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liwen Wang +3 more
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Nonlinear Representation and Dimensionality Reduction
2023Hye Sun Yun +3 more
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