Search

Abstract: Given the rapidly growing diversity of techniques and applications of fuzzy clustering, an interpretation of grouping results becomes of paramount relevance. Fuzzy clusters offer a lot of detailed information about the structure in data by allocating patterns to clusters with numeric degrees of membership. While this information could be highly beneficial, its level of detail could be too overwhelming and in some sense somewhat detrimental to the formation of the global view of the structure. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. With the shadowed sets of clusters in place, discussed is a taxonomy of patterns leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure. [Copyright &y& Elsevier]

In this study, we introduce a new clustering architecture in which several subsets of patterns can be processed together with an objective of finding a structure that is common to all of them. To reveal this structure, the clustering algorithms operating on the separate subsets of data collaborate by exchanging information about local partition matrices. In this sense, the required communication links are established at the level of information granules (more specifically, fuzzy sets forming the partition matrices) rather than patterns that are directly available in the databases. We discuss how this form of collaboration helps meet requirements of data confidentiality. A detailed clustering algorithm is developed on a basis of the standard FCM method and illustrated by means of numeric examples. [Copyright &y& Elsevier]

The paper is concerned with a logic-based expansion of the standard FCM clustering. The proposed algorithm captures the logic fabric of the structure in a dataset by describing it in the form of a union of the clusters (that is fuzzy relations) determined by the clustering algorithm. In contrast to the standard FCM, the elements (clusters) are combined together as a union of such fuzzy relations—clusters and this form of combination arises as a constraint in the clustering method. In this sense, the introduced clustering environment gives rise to the clustering that is regarded as a logic-driven data decomposition. A detailed algorithm is presented along with some illustrative examples. [Copyright &y& Elsevier]