# Show Reference: "Learning Nonlinear Principal Manifolds by Self-Organising Maps"

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.

}
}