34867589
Modeling temporal functions with granular regression and fuzzy rules
Modeling of temporal functions has been studied extensively in last few decades. Temporal functions or time series are found practically in the gamut of applications, ranging from engineering analysis to financial and commercial transactions.Numerous time series models been proposed, and they can be found in the relevant time series literature. Deterministic and stochastic models have dominated much of the research in this area. Nonetheless, these models have their limitations, and particularly specific models solve specific problem domains. Therefore, there is no general mechanism that can address the issues of modeling of temporal functions.Granular information is now being used to address a few of the problems in the theory of time series. This paper proposes two models that use the concepts of regression and interleaved information granules-intervals and fuzzy sets to identify the structure existing in a given time series. In brevity, we are attempting to combine regression and fuzzy rules to model temporal systems.
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.
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.
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.
9555956
Face recognition using fuzzy Integral and wavelet decomposition method
In this paper, we develop a method for recognizing face images by combining wavelet decomposition, Fisherface method, and fuzzy integral. The proposed approach is comprised of four main stages. The first stage uses the wavelet decomposition that helps extract intrinsic features of face images. As a result of this decomposition, we obtain four subimages (namely approximation, horizontal, vertical, and diagonal detailed images). The second stage of the approach concerns the application of the Fisherface method to these four decompositions. The choice of the Fisherface method in this setting is motivated by its insensitivity to large variation in light direction, face pose, and facial expression. The two last phases are concerned with the aggregation of the individual classifiers by means of the fuzzy integral. Both Sugeno and Choquet type of fuzzy integral are considered as the aggregation method. In the experiments we use n-fold cross-validation to assure high consistency of the produced classification outcomes. The experimental results obtained for the Chungbuk National University (CNU) and Yale University face databases reveal that the approach presented in this paper yields better classification performance in comparison to the results obtained by other classifiers.
9853981
Face recognition: A study in information fusion using fuzzy integral
We study two approaches to fuzzy information fusion for face recognition involving aggregation of local and global face information and a wavelet decomposition approach. The former is concerned with a fuzzy information fusion involving both feature-based (e.g., eye, nose, and mouth) and template-based (global face) approaches to face recognition. The latter is associated with fuzzy information fusion based on four subimages (that is approximation, horizontal, vertical, and diagonal detailed images) using wavelet decomposition method. Making use of these two approaches, we design classifiers based on the well-known fisherface method. We demonstrate that the proposed method comes with better performance when compared with other template-based techniques and shows substantial insensitivity to large variation in light direction and facial expression. The fusion of the individual classifiers is realized by means of the Choquet fuzzy integral. The experimental results produced for FERET face database with 600 frontal face images corresponding to 200 subjects quantifies the performance of the classifier and contrast it with some other approaches existing in the literature.
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.
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.