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.
20379804
Hybrid Fuzzy Polynomial Neural Networks
We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x)" where A is a fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data.
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.
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.
31716066
The genetic development of ordinal sums
Abstract The aim of this study is to develop an operational model of an ordinal sum of triangular norms. The essence of this construct lies in the use of different t-norms (and/or t-conorms) defined over disjoint subintervals of the unit interval. The result of such aggregation is a highly versatile logic operator that can be easily adapted to the existing experimental evidence. We propose a genetic optimisation environment (Genetic Algorithms, GAs, in particular) to construct ordinal sums and show how the GA mechanism helps optimize subintervals and to allocate individual local t-norms. The application of the genetically designed ordinal sums is shown in case of Zimmermann–Zysno logic operator data. We also demonstrate the use of the ordinal sum to the construction of neuro-fuzzy systems; in this case we quantify the performance of ordinal sums to “standard” logic operators used in such models.
2982088
Fuzzy Aggregation Method Using Fisherface and Wavelet Decomposition for Face Recognition
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.
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.