Learning Nonlinear Principal Manifolds by Self-Organising Maps *Principal Manifolds for Data Visualization and Dimension Reduction* In Principal Manifolds for Data Visualization and Dimension Reduction (2007), pp. 68-95, doi:10.1007/978-3-540-73750-6_3 by Hujun Yin

@inbook{yin-2007, abstract = {This chapter provides an overview on the self-organised map ({SOM}) in the context of manifold mapping. It first reviews the background of the {SOM} and issues on its cost function and topology measures. Then its variant, the visualisation induced {SOM} ({ViSOM}) proposed for preserving local metric on the map, is introduced and reviewed for data visualisation. The relationships among the {SOM}, {ViSOM}, multidimensional scaling, and principal curves are analysed and discussed. Both the {SOM} and {ViSOM} produce a scaling and dimension-reduction mapping or manifold of the input space. The {SOM} is shown to be a qualitative scaling method, while the {ViSOM} is a metric scaling and approximates a discrete principal curve/surface. Examples and applications of extracting data manifolds using {SOM}-based techniques are presented.}, author = {Yin, Hujun}, booktitle = {Principal Manifolds for Data Visualization and Dimension Reduction}, chapter = {3}, doi = {10.1007/978-3-540-73750-6\_3}, journal = {Principal Manifolds for Data Visualization and Dimension Reduction}, keywords = {ann, learning, manifolds, pca, som, unsupervised-learning}, pages = {68--95}, posted-at = {2013-01-11 10:43:38}, priority = {2}, publisher = {Springer}, title = {Learning Nonlinear Principal Manifolds by {Self-Organising} Maps}, url = {http://dx.doi.org/10.1007/978-3-540-73750-6\_3}, year = {2007}, editor = {Gorban, Alexander N. and Kégl, Balázs and Wunsch, Donald C. and Zinovyev, Andrei Y. } }

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