MembershipMap: A data transformation for knowledge discovery based on granulation and fuzzy membership aggregation

Abstract

In this chapter, we describe a new data-driven transformation that facilitates many data mining, interpretation, and analysis tasks. This approach, called MembershipMap, strives to granulate and extract the underlying sub-concepts of each raw attribute. The orthogonal union of these sub-concepts are then used to define a new membership space. The sub-concept soft labels of each point in the original space determine the position of that point in the new space. Since sub-concept labels are prone to uncertainty inherent in the original data and in the initial extraction process, a combination of labeling schemes that are based on different measures of uncertainty will be presented. In particular, we introduce the CrispMap, the FuzzyMap, and the PossibilisticMap. We outline the advantages and disadvantages of each mapping scheme, and we show that the three transformed spaces are complementary. We also show that in addition to improving the performance of clustering by taking advantage of the richer information content, the MembershipMap can be used as a flexible pre-processing tool to support such tasks as: sampling, data cleaning, and outlier detection. © 2008 Springer-Verlag Berlin Heidelberg.