22511023
Fuzzy clustering with partial supervision
Presented here is a problem of fuzzy clustering with partial supervision, i.e., unsupervised learning completed in the presence of some labeled patterns. The classification information is incorporated additively as a part of an objective function utilized in the standard FUZZY ISODATA. The algorithms proposed in the paper embrace two specific learning scenarios of complete and incomplete class assignment of the labeled patterns. Numerical examples including both synthetic and real-world data arising in the realm of software engineering are also provided.
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.
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.
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.
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.
12910860
Multi-layer hybrid fuzzy polynomial neural networks: a design in the framework of computational intelligence
We introduce a new architecture of hybrid fuzzy polynomial neural networks (HFPNN) that is based on a genetically optimized multi-layer perceptron and develop their comprehensive design methodology involving mechanisms of genetic optimization. The construction of HFPNN exploits fundamental technologies of computational intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the resulting genetically optimized HFPNN (namely gHFPNN) results from a synergistic usage of the hybrid system generated by combining fuzzy polynomial neurons (FPNs)-based fuzzy neural networks (FNN) with polynomial neurons (PNs)-based polynomial neural networks (PNN). The design of the conventional HFPNN exploits the extended group method of data handling (GMDH) with some essential parameters of the network being provided by the designer and kept fixed throughout the overall development process. This restriction may hamper a possibility of producing an optimal architecture of the model. The augmented gHFPNN results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of HFPNN leads to the selection of preferred nodes (FPNs or PNs) available within the HFPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFPNN is quantified through experimentation where we exploit data coming from processes of pH neutralization and NOx emission. These datasets have already been used quite intensively in fuzzy and neurofuzzy modeling. The obtained results demonstrate superiority of the proposed networks over the existing fuzzy and neural models.
1991956
Noninvasive data analysis: a web of information granules
The study is concerned with a development of information granules and their use in data analysis. The design of information granules exploits a concept of “overshadowing” meaning that, we retain a given level of membership to a given concept unless faced with a contrary evidence. A detailed algorithm is provided and illustrated through a number of numerical studies. The idea of noninvasive data analysis is then introduced and discussed from a standpoint of a minimal level of structural dependencies to be used in the model.
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.