The instinct of survival of man has driven him to investigate his surroundings. Intelligence and the ability to reason and to adapt have been crucial to the survival of man. Models can be thought of as explicit expressions of the surrounding world. Models can help us to understand our surroundings and to answer questions about it. A general definition of a model could be presented: ``Model is an object (or an abstraction) that facilitates the processing of another object''.
Kohonen states in his book [20]: Model, especially an analytical one, usually consists of a finite set variables and their quantitative interactions that are supposed to describe, e.g., states and signals in a real system, often assumed to behave according to known, simplified laws of nature.
Many kinds of models exist. The model that is best suited for a specific purpose must be chosen carefully taking into account the following considerations:
First, view-point must be decided. It is impossible to create a model that could answer all the questions. An accurate model has a restricted view on the problem. A more general model can exist on higher abstraction levels. Generality and the level of detail are contradictory: a detailed model cannot be general and a general model can not contain small details.
Secondly, scale of the model must be chosen. The problem itself does not contain any information on the scale in which the observer considers relevant, so the scale selection remains a problem of the observer. Some heuristics can be developed to pick a suitable scale, but these always contain assumptions of the observer.
Thirdly, the domain of applicability must be understood. Every model has its limitations and the model is not valid outside its scope. This restricts the use of a model.
Numerous modeling techniques have been used. These tend to be specific to a certain discipline and constrained by tradition. All model-making seem to suffer from the previously named problems.
Neural networks have been quite promising in modeling complex real-life phenomena. As mentioned earlier, they are data-rich and theory-poor [8] models in a sense that a few assumptions must be made to form such a model.
In the next two sections, we study ways of modeling with the SOM. First, a way to create regression models is presented. Secondly, a method is described to expand this kind of model to fit local models directly to the data.