Analysis of processes and large data sets by a self-organizing method

Frequently one must deal with natural processes and data for which no known models can be derived from classical systems theory. A solution is that relationships between the elements are described by nonlinear functional expansions called "neural networks". The most familiar neural-network models make use of supervised learning, which means that the data used for identification must be verified, validated, and preclassified. Such data, however, is very expensive and sometimes even impossible to acquire. A different approach altogether is unsupervised learning that uses raw data, usually available on mass. In the article, the most widespread unsupervised-learning method, the self-organizing map (SOM) algorithm is described. The central idea in this algorithm and in self organization in general, is to use a large number of relatively simple and structurally similar, interacting, statistical submodels. Each submodel describes only a limited domain of observations, but since the submodels can communicate, they can mutually decide what and how large a domain belongs to each submodel. By virtue of such collective interactions it becomes possible to span the whole data space nonlinearly, thereby minimizing the average overall modeling error. As the SOM implements a characteristic nonlinear projection from the input space to a visual display, it can be used, e.g., to reveal process states that otherwise would escape notice. Applications to industry and "data mining" in general are surveyed. The mapping of all electronically available patent abstracts in the world onto a visual display is also reported.