Self-Organizing Map method

TAMAYO, P., SLONIM, D MESIROV, J., ZHU, Q., KITAREEWAN, S., DMITROVSKY, E., LANDER, E.S., GOLUB, T.R., Interpreting patterns of gene expression with self-organizing maps methods and application to hematopoietic differentiation, Proc. Natl. Acad. Sci. USA, 1999,96,2907-2912. 

P. Tamayo, D. Slonim, J. Mesirov, Q. Zhu, S. Kitareewan, E. Dmitrovsky, E. S. Lander, and T. R. Golub, Interpreting patterns of gene expression with self-organizing maps methods and apphcation to hematopoietic differentiation. Proc Natl Acad Sci USA 96(6) 2907-2912 (1999). 

Tamayo, P., et al. (1999). Interpreting patterns of gene expression with self-organizing maps Methods and application to hemotopoietic differentiation. PNAS, 96 2907-2912. 

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. 

Kohonen networks, also known as self-organizing maps (SOMs), belong to the large group of methods called artificial neural networks. Artificial neural networks (ANNs) are techniques which process information in a way that is motivated by the functionality of biological nervous systems. For a more detailed description see Section 9.5. 

The Kohonen network or self-organizing map (SOM) was developed by Teuvo Kohonen [11]. It can be used to classify a set of input vectors according to their similarity. The result of such a network is usually a two-dimensional map. Thus, the Kohonen network is a method for projecting objects from a multidimensional space into a two-dimensional space. This projection keeps the topology of the multidimensional space, i.e., points which are close to one another in the multidimensional space are neighbors in the two-dimensional space as well. An advantage of this method is that the results of such a mapping can easily be visualized. 

However, the method suffers from two notable disadvantages. First, a self-organizing map is slow to train. During each epoch, every data point in every sample pattern in the database must be compared in turn with the corresponding weight in the vector at every node. Table 4.1 shows how quickly the total number of comparisons required in the training of a SOM grows as the scale of a problem increases. 

Another group has evaluated self-organizing maps [63] and shape/ pharmacophore models [64]. They developed a new method termed SQUIRREL to compare molecules in terms of both shape and pharmacophore points. Thus from a commercial library of 199,272 compounds, 1926 were selected based on self-organizing maps trained on peroxisome proliferator-activated receptor a (PPARa) "activity islands." The compounds were further evaluated with SQUIRREL and 7 out of 21 molecules selected were found to be active in PPARa. Furthermore, a new virtual screening technique (PhAST) was developed based on representation of molecules as text strings that describe their pharmacophores [65]. 

It can be shown that the unsupervised learning methodology based on Kohonen self-organizing maps algorithm can be effectively used for differentiation between various receptor-specific groups of GPCR ligands. The method is similar to that described in Section 12.2.6. 

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. 

Prediction-set samples were then passed to the network and assigned to the nearest neuron. They are represented as superscripts in Figure 9.18. All 19 prediction-set samples were assigned to neurons that had spectra with the same class label. The validation of the self-organizing maps using these 19 prediction-set samples implies that information is contained in the Raman spectra of the plastics characteristic of sample type. Classification of the plastics by the self-organizing map was as reliable as that obtained by other methods, and more importantly, the classification was obtained without any preassumptions about the data. 

Not all neural networks are the same their connections, elemental functions, training methods and applications may differ in significant ways. The types of elements in a network and the connections between them are referred to as the network architecture. Commonly used elements in artificial neural networks will be presented in Chapter 2. The multilayer perception, one of the most commonly used architectures, is described in Chapter 3. Other architectures, such as radial basis function networks and self organizing maps (SOM) or Kohonen architectures, will be described in Chapter 4. 

Kohonen self-organizing map An unsupervised learning method of clustering, based on the k-means algorithm, similar to the first stage of radial basis function networks. Self-organized maps are used for classification and clustering. 

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