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Fast nonlinear dimension reduction
IEEE International Conference on Neural Networks, 2002A new algorithm for nonlinear dimension reduction is presented. The algorithm builds a piecewise linear model of the data. It provides compression that is superior to the globally linear model produced by principal component analysis. On several examples the piecewise linear model also provides compression that is superior to the global nonlinear model
Nandakishore Kambhatla, Todd K. Leen
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PLS and dimension reduction for classification
Computational Statistics, 2007Different techniques of dimension reduction in classification problems are compared. The main attention is paid to the partial least squares (PLS) and its modification, oriented PLS (OPLS). These techniques are compared to the principal components analysis (PCA) used as pre-processing before linear discriminant analysis (LDA). A ridge-like technique is
Yushu Liu, William S. Rayens
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Groupwise Bayesian dimension reduction
2017 International Joint Conference on Neural Networks (IJCNN), 2017Nearly all existing estimations of the central subspace in regression take the frequentist approach. However, when the predictors fall naturally into a number of groups, these frequentist methods treat all predictors indiscriminately and can result in loss of the group-specific relation between the response and the predictors.
Bo Zhang +3 more
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Reduction of Dimension and Turnpike Theory
IFAC Proceedings Volumes, 1986Abstract We give here the description of asymptotical properties of solutions to a class of scale-invariant dynamic optimization models arising in mathematical economics. These results are based on the geometric theory of Hamiltonian differential equations possessing the group of symmetries.
A.D. Tsvirkun, S.Yu. Yakovenko
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COLLABORATIVE OPTIMIZATION WITH DIMENSION REDUCTION
International Journal of Modeling, Simulation, and Scientific Computing, 2010Collaborative optimization (CO) method is widely used in solving multidisciplinary design optimization (MDO) problems, yet its computation requirement has been an obstacle to the applications, leading to doubts about CO's convergence property. The feasible domain of CO problem is first examined and it is proven that feasible domain remains the same ...
Zhenxiao Gao, Tianyuan Xiao, Wenhui Fan
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Sufficient Dimension Reduction and Kernel Dimension Reduction
2023Benyamin Ghojogh +3 more
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Dimension Reduction in Continuum Mechanics
2002This lecture is devoted to some progress of recent ideas in Γ-convergence with varying domains for dimensional reduction problems. More precisely, we consider, as a sequence of functionals, the stored energy of a thin isotropic linear elastic body possibly damaged at meso-scale, whose cross section or whose thickness is very small.
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A Brief Survey of Dimension Reduction
2018Dimension reduction problem is a big concern which can reduce the scale of a database and keep the main features of these data simultaneously. This paper aims at reviewing and comparing different dimension reduction algorithms. Mainly, the performances of four basic algorithms (PCA, LDA, LLE and LE), their improved methods and deep learning methods are
Li Song +4 more
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