Self Organizing Maps SOMs

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. 

The relationships between the molecular structure of environmental pollutants, such as polychlorinated biphenyls (PCBs), and their rate of biodegradation are still not well understood, though some empirical relationships have been established. Self-organizing maps (SOMs) have been used to rationalize the resistance of PCBs to biodegradation and to predict the susceptibility to degradation of those compounds for which experimental data are lacking.3 The same technique has been used to analyze the behavior of lipid bilayers, following a... 

As we saw in the previous chapter, self-organizing maps (SOMs) are a powerful way to reveal the clustering of multidimensional samples. The two-dimensional SOM is often able to provide an informative separation of samples into classes and the learning in which it engages requires no input from the user, beyond the initial selection of parameters that define the scale of the mapping and the way that the algorithm operates. 

Self-organizing maps (SOMs) are gaining popularity due to their enhanced... 

Another type of ANNs widely employed is represented by the Kohonen self organizing maps (SOMs), used for unsupervised exploratory analysis, and by the counterpropagation (CP) neural networks, used for nonlinear regression and classification (Marini, 2009). Also, these tools require a considerable number of objects to build reliable models and a severe validation. 

For many problems, rather different solutions of similar fitness exist. To obtain a quick overview of the structure of the underlying high-dimensional fitness landscape, we used a self-organizing map (SOM) that was developed originally by Kohonen [14] in this study. Figure 10.1 shows a nonlinear mapping of a seven-... 

Fig. 10.1. Analysis of die fitness landscape for a basic amino acid dope (30% Arg, 30% Lys, 40% His), (a) Nonlinear projection of die seven-dimensional solution space onto two dimensions by a self-organizing map (SOM) [14]. The seven dimensions are (Tl, Cl, Al, T2, C2, A2, C3), encoding fractions of nucleoddes for each NN(G/C) codon position. The mean squared error between die computed and desired amino acid concentrations are indicated by shades of grey here and by color in die copy of diis figure on die CD diat accompanies diis book.

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. 

Steiner, F.M., Schilck-Steiner, B.C., Nikiforov, A., Kalb, R. and Mistrik, R. (2002). Cuticular hydrocarbons of Tetramorium ants from Central Europe Analysis of GC-MS data with self-organizing maps (SOM) and implications for systematics. 

Another approach for solving the problem of representing data points in an -dimensional measurement space involves using an iterative technique known as the Kohonen neural network [41, 42] or self-organizing map (SOM). A Kohonen neural network consists of a layer of neurons arranged in a two-dimensional grid or... 

The evaluation of the measurements, the correlation between the medium components and the various ranges of the 2D-fluorescence spectrum was performed by Principal Component Analysis (PCA), Self Organized Map (SOM) and Discrete Wavelet Transformation (DWT), respectively. Back Propagation Network (BPN) was used for the estimation of the process variables [62]. By means of the SOM the courses of several process variables and the CPC concentration were determined. 

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. 

An intermediate between similarity searching and descriptor-selection based QSAR, self-organizing maps (SOM), will be mentioned first. SOMs try to classify a population of individuals (each described by a fingerprint) into a fixed number of final categories, by assigning to each such category (or neuron ) a... 

Some historically important artificial neural networks are Hopfield Networks, Per-ceptron Networks and Adaline Networks, while the most well-known are Backpropa-gation Artificial Neural Networks (BP-ANN), Kohonen Networks (K-ANN, or Self-Organizing Maps, SOM), Radial Basis Function Networks (RBFN), Probabilistic Neural Networks (PNN), Generalized Regression Neural Networks (GRNN), Learning Vector Quantization Networks (LVQ), and Adaptive Bidirectional Associative Memory (ABAM). 

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