Nonlinear Dimensionality Reduction

By John Aldo Lee, Michel Verleysen. 2007

409 citations recorded by the source corpus.

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Citations in the corpus

A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines (2018, background): “The latter ones are usually known as manifold learning [34] algorithms, and fall in the scope of nonlinear dimensionality reduction techniques [35].”
Learning algebraic varieties from samples (2018, unknown): “For instance, the textbook by Lee and Verleysen [38] employs the “Swiss roll” and the “open box” for its running examples (cf. [38, §1.5]).”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “Over the past few decades, a variety of NonLinear DRTs (NLDRTs) have been developed to work with applications having complex non-linear structures [20,181,182] .”
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition (2014, methodology): “a basis for FD, but in many circumstances this cannot be done without prior knowledge of M. As a result, there are likely benets to combining EDMD with manifold learning techniques (see, e.g., Refs. [46,47,54,55]). These methods can numerically approximate M, which could allow a more eective choice ”
Kernel Principal Component Analysis for the Classification of Hyperspectral Remote Sensing Data over Urban Areas (2009, background): “To better understand the link and the difference between PCA and KPCA, one must note that the eigenvectors of Σ x can be obtained from those of XX T , where X = [x 1 , x 2 , . . . , x ] T [36].”