Stability of continuous value discretisation: an application within rough set theory Original Research Article

Continuous value discretisation (CVD) is the process of partitioning a set of continuous values into a finite number of intervals (categories). This paper introduces a number of stability measures associated with the resultant CVD. The stability measures are constructed from a series of estimated probability distributions for the individual ‘partitioning’ intervals found using the method of Parzen windows. These measures enable comparisons between the results of alternative methods of CVD on their ability to effectively partition the continuous values. A further utilisation of these measures is exposited within rough set theory (RST). RST is a modern approach to the generation of sets of rules enabling the classification of objects to categories based on sets (reducts) of related characteristics. To avoid rules of poor quality (from RST analysis) induced directly from continuous valued characteristics, CVD methods can be used to reduce the associated granularity and allow higher rule quality. The notion of stability introduced enables the further introduction of novel measures particular to reduct and rule set stability within RST.