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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: In this study, we develop a concept of dynamic data granulation realized in presence of incoming data organized in the form of so-called data snapshots. For each of these snapshots we reveal a structure by running fuzzy clustering. The proposed algorithm of adjustable fuzzy C-means (FCM) exhibits a number of useful features which directly associate with the dynamic nature of the underlying data: (a) the number of clusters is adjusted from one data snapshot to another in order to capture the varying structure of patterns and its complexity, (b) continuity between the consecutively discovered structures is retained, viz the clusters formed for a certain data snapshot are constructed as a result of evolving the clusters discovered in the predeceasing snapshot. We present a detailed clustering algorithm in which the mechanisms of adjustment of information granularity (the number of clusters) become the result of solutions to well-defined optimization tasks. The cluster splitting is guided by conditional fuzzy C-means (FCM) while cluster merging involves two neighboring prototypes. The criterion used to control the level of information granularity throughout the process is guided by a reconstruction criterion which quantifies an error resulting from pattern granulation and de-granulation. Numeric experiments provide a suitable illustration of the approach. [Copyright &y& Elsevier]

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]

Fuzzy clustering becomes a broadly accepted synonym of fundamental endeavors aimed at finding structures in multidimensional data. In essence, these methods operate in unsupervised mode. This means that they act upon data while being directed by some predefined objective function (criterion) for which they “discover” a structure (clusters) that yields a minimal value of this criterion. In this study, we discuss an issue of exploiting and effectively incorporating auxiliary problem dependent hints being available as a part of the domain knowledge associated with the pattern recognition problem at hand. As such hints are usually expressed by experts/data analysts at the level of clusters (information granules) rather than individual data (patterns), we refer to them as knowledge-based indicators and allude to a set of them as a knowledge-based guidance available to fuzzy clustering. The proposed paradigm shift in which fuzzy clustering incorporates this type of knowledge-based supervision is discussed and contrasted with the “pure” (that is data-driven) version of fuzzy clustering. Several fundamental categories of the guidance mechanisms are introduced and discussed, namely partial supervision, proximity-based guidance and uncertainty driven knowledge hints. The details on how the guidance machinery translates into updates of the partition matrices are presented. We also present a number of practical scenarios in which the role of knowledge hints becomes evident and highly justifiable. This concerns Web exploration, exploitation of labeled patterns, issues of incomplete feature spaces, and constraints of typicality of patterns, to name a few representative applications. [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]