Developments and Applications of Nonlinear Principal Component Analysis â€“ a Review *Principal Manifolds for Data Visualization and Dimension Reduction* In Principal Manifolds for Data Visualization and Dimension Reduction, Vol. 58 (2008), pp. 1-43, doi:10.1007/978-3-540-73750-6_1 by Uwe Kruger, Junping Zhang, Lei Xie edited by Alexander N. Gorban, BalÃ¡zs KÃ©gl, Donald C. Wunsch, Andrei Y. Zinovyev

@incollection{kruger-et-al-2008, abstract = {Although linear principal component analysis ({PCA}) originates from the work of Sylvester [67] and Pearson [51], the development of nonlinear counterparts has only received attention from the 1980s. Work on nonlinear {PCA}, or {NLPCA}, can be divided into the utilization of autoassociative neural networks, principal curves and manifolds, kernel approaches or the combination of these approaches. This article reviews existing algorithmic work, shows how a given data set can be examined to determine whether a conceptually more demanding {NLPCA} model is required and lists developments of {NLPCA} algorithms. Finally, the paper outlines problem areas and challenges that require future work to mature the {NLPCA} research field.}, author = {Kruger, Uwe and Zhang, Junping and Xie, Lei}, booktitle = {Principal Manifolds for Data Visualization and Dimension Reduction}, citeulike-article-id = {1647435}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-540-73750-6\_1}, citeulike-linkout-1 = {http://link.springer.com/chapter/10.1007/978-3-540-73750-6\_1}, doi = {10.1007/978-3-540-73750-6\_1}, editor = {Gorban, Alexander N. and K\'{e}gl, Bal\'{a}zs and Wunsch, Donald C. and Zinovyev, Andrei Y.}, journal = {Principal Manifolds for Data Visualization and Dimension Reduction}, keywords = {dimensionality-reduction, learning, pca, unsupervised-learning}, pages = {1--43}, posted-at = {2015-03-17 14:23:09}, priority = {2}, publisher = {Springer Berlin Heidelberg}, series = {Lecture Notes in Computational Science and Enginee}, title = {Developments and Applications of Nonlinear Principal Component Analysis – a Review}, url = {http://dx.doi.org/10.1007/978-3-540-73750-6\_1}, volume = {58}, year = {2008} }

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