Constructing Intermediate Concepts by Decomposition of Real Functions

Abstract

In learning from examples it is often useful to expand an attribute-vector representation by intermediate concepts. The usual advantage of such structuring of the learning problem is that it makes the learning easier and improves the comprehensibility of induced descriptions. In this paper, we develop a technique for discovering useful intermediate concepts when both the class and the attributes are real-valued. The technique is based on a decomposition method originally developed for the design of switching circuits and recently extended to handle incompletely specified multi-valued functions. It was also applied to machine learning tasks. In this paper, we introduce modifications, needed to decompose real functions and to present them in symbolic form. The method is evaluated on a number of test functions. The results show that the method correctly decomposes fairly complex functions. The decomposition hierarchy does not depend on a given repertoir of basic functions (background knowledge).