Lee, J.A., Verleysen, M.: Nonlinear dimensionality reduction of data manifolds with essential loops. Neurocomputing 67 , 29–53 (2005). : 10.1016/j.neucom.2004.11.042John Aldo Lee , Michel Verleysen, Nonlinear dimensionality reduction of data manifolds with essential ...
Nonlinear Dimensionality Reduction by John A. Lee; Michel VerleysenDimensionality reduction is used in almost all areas of science for visualizing, preprocessing, or gaining a better understanding of high dimensional data. Linear methods have been used since the introduction of principal component ...
Verleysen, M., Lee, J.A. (2013). Nonlinear Dimensionality Reduction for Visualization. In: Lee, M., Hirose, A., Hou, ZG., Kil, R.M. (eds) Neural Information Processing. ICONIP 2013. Lecture Notes in Computer Science, vol 8226. Springer, Berlin, Heidelberg. https://doi.org/10.1007...
Dimensionality reduction (DR) is a widely used technique to address the curse of dimensionality when high-dimensional remotely sensed data, such as multi-temporal or hyperspectral imagery, are analyzed. Nonlinear DR algorithms, also referred to as manifold learning algorithms, have been successfully app...
44. Lee J, Verleysen M. Nonlinear Dimensionality Reduction, Information Science and Statistics. Springer: New York, NY, 2007. 45. Sammon JW. A nonlinear mapping for data structure analysis. IEEE Transactions on Computers 1969; 18:401–409. 46. Hérault J, Oliva A, Guérin-Dugué A. Scene...
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Lee, K., Carlberg, K.: Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders. J. Comput. Phys. 404, 108973 (2020) Article MathSciNet Google Scholar Likas, A., Vlassis, N., Verbeek, J.J.: The global k-means clustering algorithm. Pattern Recog...
A novel method for numerical modelling of noncollinear and nonlinear interaction of femtosecond laser pulses is presented. The method relies on a separate treatment of each of the interacting pulses by it’s own rotated unidirectional pulse propagation e
Alternatively, non-linear dimensionality reduction (NLDR) (Lee & Verleysen, 2007) methods are potentially more powerful to model complex high-dimensional data. These methods are well-suited to map the topological structure of the data, especially when the regions of interest cannot be well-separate...
Thus, it suffers from the notorious “dimensionality curse” when data-driven modeling attempts to scale up to high-dimensional material data. Although the innate manifold learning in LCDD allows noise and dimensionality reduction, the proper definition of the metric functions in high-dimensional phase...