On multidimensional scaling and the embedding of self-organising maps

@article{citeulike:2537891, abstract = {The self-organising map (SOM) and its variant, visualisation induced SOM (ViSOM), have been known to yield similar results to multidimensional scaling (MDS). However, the exact connection has not been established. In this paper, a review on the SOM and its cost function and topological measures is provided first. We then examine the exact scaling effect of the SOM and ViSOM from their objective functions. The SOM is shown to produce a qualitative, nonmetric scaling, while the local distance-preserving ViSOM produces a quantitative or metric scaling. Their relationship with the principal manifold is also discussed. The SOM-based methods not only produce topological or metric scaling but also provide a principal manifold. Furthermore a growing ViSOM is proposed to aid the adaptive embedding of highly nonlinear manifolds. Examples and comparisons with other embedding methods such as Isomap and local linear embedding are also presented.}, author = {Yin, Hujun }, booktitle = {Advances in Neural Networks Research: IJCNN '07, 2007 International Joint Conference on Neural Networks IJCNN '07}, citeulike-article-id = {2537891}, doi = {10.1016/j.neunet.2007.12.027}, journal = {Neural Networks}, keywords = {machine-learning}, month = {}, number = {2-3}, pages = {160--169}, posted-at = {2008-03-15 21:47:41}, priority = {2}, title = {On multidimensional scaling and the embedding of self-organising maps}, url = {http://dx.doi.org/10.1016/j.neunet.2007.12.027}, volume = {21}, year = {2008} }

TY - JOUR ID - citeulike:2537891 L3 - citeulike-article-id:2537891 TI - On multidimensional scaling and the embedding of self-organising maps T2 - Advances in Neural Networks Research: IJCNN '07, 2007 International Joint Conference on Neural Networks IJCNN '07 JF - Neural Networks VL - 21 IS - 2-3 SP - 160 EP - 169 N2 - The self-organising map (SOM) and its variant, visualisation induced SOM (ViSOM), have been known to yield similar results to multidimensional scaling (MDS). However, the exact connection has not been established. In this paper, a review on the SOM and its cost function and topological measures is provided first. We then examine the exact scaling effect of the SOM and ViSOM from their objective functions. The SOM is shown to produce a qualitative, nonmetric scaling, while the local distance-preserving ViSOM produces a quantitative or metric scaling. Their relationship with the principal manifold is also discussed. The SOM-based methods not only produce topological or metric scaling but also provide a principal manifold. Furthermore a growing ViSOM is proposed to aid the adaptive embedding of highly nonlinear manifolds. Examples and comparisons with other embedding methods such as Isomap and local linear embedding are also presented. KW - machine-learning AU - Yin, Hujun PY - 2008/0// UR - http://dx.doi.org/10.1016/j.neunet.2007.12.027 ER -