Kohonen map

Reactions belonging to the same reaction type are projected into coherent areas on the Kohonen map this shows that the assignment of reaction types by a chemist is also perceived by the Kohonen network on the basis of the electronic descriptors. This attests to the power of this approach. 

There are finer details to be extracted from such Kohonen maps that directly reflect chemical information, and have chemical significance. A more extensive discussion of the chemical implications of the mapping of the entire dataset can be found in the original publication [28]. Gearly, such a map can now be used for the assignment of a reaction to a certain reaction type. Calculating the physicochemical descriptors of a reaction allows it to be input into this trained Kohonen network. If this reaction is mapped, say, in the area of Friedel-Crafts reactions, it can safely be classified as a feasible Friedel-Qafts reaction. 

As oversimplified cases of the criterion to be used for the clustering of datasets, we may consider some high-quality Kohonen maps, or PCA plots, or hierarchical clustering. 

Analyze the Kohonen map. The content of the neurons is given when clicking on the map. 

Figure 9-20. Left Kohonen map showing the projection ofthe olive oil samples. Middle Map of Italy showing the regions of origin for the olive oils, Right Key giving the regions and their codes,...

One application of clustering could, for example, be the comparison of compound libraries A training set is chosen which contains members of both libraries. After the structures are coded (cf. Chapter 8), a Kohonen network (cf. Section 9.5.3) is trained and arranges the structures within the Kohonen map in relation to their structural similarity. Thus, the overlap between the two different libraries of compounds can be determined. 

The reactions which have been observed arc well separated from the reactions which arc expected to have no or a low yield. The reaaions leading to the preferred regioisomer arc projected into the upper part of the Kohonen map, whereas the reactions of the non-preferred regioisomer arc projected into the lower part of the Kohonen map. 

Figure 10.4-S. Kohonen map (10 / 7) obtained from a data set of 112 dopamine and 60 benzodiazepine agonists.

Figure 10.4-9. Kohonen map (40 / 30) of a data set consisting of the dopamine and benzodiazepine agonists of Figure 10.4-8 and 8323 compounds in a chemical supplier s catalog.

Figure 10.4-10. Structures that were mapped into the neuron at position (4,10) of the Kohonen map in Figure 10.4-9.

Balakin KV, Ekins S, Bugrim A, Ivanenkov YA, Korolev D, Nikolsky YV, Skorenko AV, Ivashchenko AA, Savchuk NP, Nikolskaya T. Kohonen maps for prediction of binding to human cytochrome P450 3A4. Drug Metab Dispos 2004 32 1183-9. 

As described in the Introduction to this volume (Chapter 28), neural networks can be used to carry out certain tasks of supervised or unsupervised learning. In particular, Kohonen mapping is related to clustering. It will be explained in more detail in Chapter 44. 

The unit in the Kohonen map that is most similar to the input vector is declared as the winning unit and is activated (i.e. its output is set to 1). The output of a Kohonen unit is typically 0 (not activated) or 1 (activated). 

Due to the Kohonen learning algorithm, the individual weight vectors in the Kohonen map are arranged and oriented in such a way that the structure of the input space, i.e. the topology is preserved as well as possible in the resulting... 

In contrast to common ANNs, Kohonen networks produce self-organized topological feature maps (Kohonen [1982, 1984]). The basic idea of Kohonen mapping is that information in data usually contains not only an algebraic but also a topological aspect. These double aspect is shown schematically in Fig. 8.25 where the data and the structure of them are composed. 

Also known as a Self-Organizing Feature Map or SOFM, or a Kohonen map after its inventor. 

That the SOM is often called a Kohonen map indicates the degree to which Kohonen and his co-workers have helped to define the field. Papers by Kohonen provide a rapid route into work with SOMs, but Zupan and Gasteiger s book Neural Networks for Chemists An Introduction 1 2 3 6 offers a broader look at the techniques and should be helpful for anyone starting work in this area. 

Also nonlinear methods can be applied to represent the high-dimensional variable space in a smaller dimensional space (eventually in a two-dimensional plane) in general such data transformation is called a mapping. Widely used in chemometrics are Kohonen maps (Section 3.8.3) as well as latent variables based on artificial neural networks (Section 4.8.3.4). These methods may be necessary if linear methods fail, however, are more delicate to use properly and are less strictly defined than linear methods. 

The basic theory of Kohonen maps—and only this will be treated here—is mathematically simple. A typical Kohonen map consists of a rectangular (often quadratic) array of fields (squares, cells, nodes, neurons) with a typical size of 5 x 5 (25 fields) to 100 x 100 (10,000 fields). Each field k is characterized by a vector wk, containing the weights wki, wia, , with in being the number of variables of a multivariate data set X (Figure 3.18) the lengths of the weight vectors are, for instance,... 

Result of Kohonen Mapping for the Reduced Glass Vessels Data Containing Three Groups of Samples... 

FIGURE 3.25 Sammon s NLM with p— 1 (left) and Kohonen map (right) of fatty acid concentration data from mummies and reference samples. 

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