MembershipMap: Data Transformation Based on Granulation and Fuzzy Membership Aggregation

We propose a new data-driven transformation that facilitates many data mining, interpretation, and analysis tasks. Our approach, called MembershipMap, strives to granulate and extract the underlying subconcepts of each raw attribute. The orthogonal union of these subconcepts are then used to define a new membership space. The subconcept soft labels of each point in the original space determine the position of that point in the new space. Since subconcept 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 preprocessing tool to support such tasks as: sampling, data cleaning, and outlier detection