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Abstract: Fuzzy clustering being focused on the discovery of structure in multivariable data is of relational nature in the sense of not distinguishing between the natures of the individual variables (features) encountered in the problem. In this study, we revisit the generic approach to clustering by studying situations in which there are families of features of descriptive and functional nature whose semantics needs to be incorporated into the clustering algorithm. While the structure is determined on the basis of all features taken en-block, it is anticipated that the topology revealed in this manner would aid the effectiveness of determining values of functional features given the vector of the corresponding descriptive features. We propose an augmented distance in which the families of descriptive and predictive features are distinguished through some weighted version of the distance between patterns. The optimization of this distance is guided by a reconstruction criterion, which helps minimize the reconstruction error between the original vector of functional features and their reconstruction realized by means of descriptive features. Experimental results are offered to demonstrate the performance of the clustering and quantify the effect of reaching balance between semantically distinct families of features. [ABSTRACT FROM AUTHOR]

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]