Kohonen s Self-Organizing Map

An observation of the results of cross-validation revealed that all but one of the compounds in the dataset had been modeled pretty well. The last (31st) compound behaved weirdly. When we looked at its chemical structure, we saw that it was the only compound in the dataset which contained a fluorine atom. What would happen if we removed the compound from the dataset The quahty ofleaming became essentially improved. It is sufficient to say that the cross-vahdation coefficient in-CTeased from 0.82 to 0.92, while the error decreased from 0.65 to 0.44. Another learning method, the Kohonen s Self-Organizing Map, also failed to classify this 31st compound correctly. Hence, we had to conclude that the compound containing a fluorine atom was an obvious outlier of the dataset. 

Now, one may ask, what if we are going to use Feed-Forward Neural Networks with the Back-Propagation learning rule Then, obviously, SVD can be used as a data transformation technique. PCA and SVD are often used as synonyms. Below we shall use PCA in the classical context and SVD in the case when it is applied to the data matrix before training any neural network, i.e., Kohonen s Self-Organizing Maps, or Counter-Propagation Neural Networks. 

Arrigo, P., Giuliano, F., Scalia, F., Rapallo, A., and Damiani, G. (1991). Identification of a new motif on nucleic acid sequence data using Kohonen s self-organizing map. Comput. Appl. Biosci. 7, 353-357. 

Unsupervised multivariate statistical methods [CA, principal components analysis, Kohonen s self-organizing maps (SOMs), nonlinear mapping, etc.], which perform spontaneous data analysis without the need for special training (learning), levels of knowledge, or preliminary conditions. 

Figure 10.1-4. Distribution of compounds from two data sets in the same KNN (Kohonen s self-organizing neural network) map by using 18 topological descriptors as input descriptors, where 1 represents the 1588 compounds in the Merck data set (excluding those compounds that are also in the Huuskonen data set) 2 represents the 799 compounds in the Huuskonen data set (excluding those compounds that are also in the Merck data set), and 3 represents the overlapping part of the Huuskonen data set and the Merck data set.

Kohonen, T. A Simple Paradigm For The Self-Organized Formatiom Of Structured Feature Maps In Competition And Cooperation In Neural Nets (Lecture notes in biomathematics vol 45, Amari, S. Arbib, M. A. Eds.) ISBN 0387115749 Springer-Verlag Berlin, 1982. 

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