SOMM – Self-Organized Manifold Mapping
The Self Organizing Map (SOM)  proposed by Kohonen has proved to be remarkable in terms of its range of applications. It can be used for high dimensional space visualization, pattern recognition, input space dimensionality reduction and for generating prototyping to extrapolate information. Basically, tasks conducted by the SOM method are closely related with input space mapping in order to preserve topological and metric relationship between samples. These maps are meant to create a low dimensional output representation of high dimensional input space. Although maps higher than two dimensions can be created by SOM, it is common to work with the limit of one or two dimensions. This work presents a methodology named SOMM (Self-Organized Manifold Mapping) that can be useful to discover structures and clusters of input dataset using the SOM map as a representation of data distribution structure.
KeywordsManifold Learning Self Organizing Maps Dimensionality Reduction
Unable to display preview. Download preview PDF.
- 3.Pölzbauer, G., Rauber, A., Dittenbach, M.: Graph projection techniques for self-organizing maps. In: ESANN 2005 European Symposium on Artificial Neural Networks, Bruges, pp. 533–538 (2005)Google Scholar
- 4.Ultsch, A.: Maps for the visualization of high-dimensional data spaces. In: Proc. of Workshop of Self Organizing Maps, pp. 225–228 (2003)Google Scholar
- 5.Sammon Jr., J.W.: A nonlinear mapping for data structure analysis. IEEE Transaction on Computers, 401–409 (1969)Google Scholar
- 6.Tenenbaum, J.B., Silva, V.D., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science Magazine 290, 2319–2323 (2000)Google Scholar
- 7.Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by local linear embedding. Science Magazine 290, 2323–2326 (2000)Google Scholar
- 8.Kitani, E.C., Del-Moral-Hernandez, E., Giraldi, A.G., Thomaz, C.E.: Exploring and understanding the high dimensional and sparse image face space: A self or-ganized manifold mapping. New approaches to characterization and recognition of faces, pp. 225–238. Intech Open Access Publisher (2011)Google Scholar
- 11.Kiviluoto, K.: Topology preservation in self-organizing maps. In: IEEE International Conference on Neural Networks, vol. 1, pp. 294–299 (1996)Google Scholar
- 12.Kitani, E.C., Del-Moral-Hernandez, E., Thomaz, C.E., Silva, L.A.: Visual inter-pretation of Self Organizing Maps. In: IEEE-CS 11th Brazilian Symposium on Neural Networks (SBRN), pp. 37–42. São Bernardo do Campo (2010)Google Scholar
- 13.Cormen, T.H., et al.: Introduction to algorithms, 2nd edn. MIT Press (2001)Google Scholar
- 14.Vesanto, J., et al.: SOM Toolbox for Matlab 5. Helsinki University of Technology, Helsinki, pp. 1-60. Report A57 (2000)Google Scholar