From data to models: synergies of a joint data mining and similarity theory approach
Peter Hertkorn, Stephan Rudolph · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1999
Successful model building techniques in the natural sciences can usually be classified into the two categories of inductive and deductive methods. If numerical data is the only source of available knowledge in a certain problem, then it is obvious that inductive techniques seem to be the method of choice. Recently, data mining has received much attention to extract hidden knowledge from very large databases, and is, therefore, in this framework considered to be an inductive approach. Deductive methods, on the contrary, rely on a rigorous application and the explicit knowledge of the underlying domain, using first principles to establish a mathematical model of the problem, typically yielding governing equations. This paper focuses on the establishment of an intermediate knowledge representation level, between inductive and deductive knowledge identification techniques. This intermediate knowledge representation level is based on the notion of group transforms, and can be shown to be a mathematically necessary condition in the existence of any correct model representation. The synergy effect of using group transforms in both the inductive data mining and the deductive similarity theory approach can be demonstrated to be conceptually advantageous and is observed to be numerically superior to conventional techniques. The limitations and underlying assumptions of the approach are identified and discussed using example.