17239140
Granular clustering: a granular signature of data
The study is devoted to a granular analysis of data. We develop a new clustering algorithm that organizes findings about data in the form of a collection of information granules-hyperboxes. The clustering carried out here is an example of a granulation mechanism. We discuss a compatibility measure guiding a construction (growth) of the clusters and explain a rationale behind their development. The clustering promotes a data mining way of problem solving by emphasizing the transparency of the results (hyperboxes). We discuss a number of indexes describing hyperboxes and expressing relationships between such information granules. It is also shown how the resulting family of the information granules is a concise descriptor of the structure of the data-a granular signature of the data. We examine the properties of features (variables) occurring of the problem as they manifest in the setting of the information granules. Numerical experiments are carried out based on two-dimensional (2-D) synthetic data as well as multivariable Boston data available on the WWW.
5269666
Conditional Fuzzy C-Means
A Fuzzy C-Means-based clustering method guided by an auxiliary (conditional) variable is introduced. The method reveals a structure within a family of patterns by considering their vicinity in a feature space along with the similarity of the values assumed by a certain conditional variable. The usefulness of the algorithm is exemplified in the problems of data mining.
37179983
Granular Regression
We augment a linear regression procedure by a thruth-functional method in order to identify a highly informative regression line. The idea is to use statistical methods to identify a confidence region for the line and exploit the structure of the sample data falling in this region for identifying the most fitting line. The fitness function is related to the fuzziness of the sampled points as a natural extension of the statistical criterion ruling the identification of the confidence region within the Algorithmic Inference approach. We tested the method on three well known benchmarks.
19471846
Fuzzy clustering with a knowledge-based guidance
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.
44496446
THE GENETIC DESIGN OF HYBRID FUZZY CONTROLLERS
In this study, we introduce a comprehensive design methodology of hybrid fuzzy controllers (HFCs). The hybrid facet of the proposed architecture of the controller manifests in the form of a convex combination of a standard proportional integral derivative (PID) controller and a fuzzy controller. The design procedure dwells on the use of evolutionary computing (genetic algorithms) and an autotuning algorithm based on estimation modes. The tuning of the scaling factors of the HFC is an essential component of the entire optimization process. Numerical studies are presented and a detailed comparative analysis is included as well.
2312456
Two iterative methods of decomposition of a fuzzy relation for image compression/decompression processing
A decomposition problem of max–min type for a fuzzy relation is proposed. A fast method is derived by transforming slightly the derivatives in the traditional gradient algorithm and by updating simultaneously the prototype relation. The complexities of the proposed algorithm, with respect to the traditional gradient one, are decreased to approximately 1/c, where “c” denotes the Schein rank of the fuzzy relation involved. A dual decomposition problem of max–min type is also formulated and a similar fast method is presented. Both methods are applied to image compression/decompression processing.
125593703
Associations and rules in data mining: A link analysis
We discuss a problem of synthesis and analysis of rules based on experimental numeric data. Two descriptors of the rules that are viewed individually and en block are introduced. The coverage of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing in the rule. Although this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed compared with other rules. It expresses how much the rule “interacts” with others in the sense that its conclusion is affected (distorted) by the conclusion parts coming from other rules. We propose a synthetic index of rule relevance that combines the two already introduced descriptors. We show how the rules are formed by means of fuzzy clustering and their quality is evaluated by means of the aforementioned indexes. Global characteristics of a set of rules also are discussed and related to the number of information granules formed in the space of antecedents and conclusions. Finally, we discuss the rules in the setting of granular modeling and express their performance in the design of numeric models. © 2004 Wiley Periodicals, Inc.