Designing Gaussian Membership Functions for Fuzzy Classifier Generated by Heuristic Possibilistic Clustering

The paper deals with the problem of constructing Gaussian membership functions of fuzzy sets for fuzzy rules derived from the data by using heuristic algorithms of possibilistic clustering. Basic concepts of the heuristic approach to possibilistic clustering are reminded and the extended technique of constructing membership functions of fuzzy sets is proposed. An illustrative example is given and preliminary conclusions are made

Possibilistic and fuzzy clustering methods for robust analysis of non-precise data

This work focuses on robust clustering of data affected by imprecision. The imprecision is managed in terms of fuzzy sets. The clustering process is based on the fuzzy and possibilistic approaches. In both approaches the observations are assigned to the clusters by means of membership degrees. In fuzzy clustering the membership degrees express the degrees of sharing of the observations to the clusters. In contrast, in possibilistic clustering the membership degrees are degrees of typicality. These two sources of information are complementary because the former helps to discover the best fuzzy partition of the observations while the latter reflects how well the observations are described by the centroids and, therefore, is helpful to identify outliers. First, a fully possibilistic k-means clustering procedure is suggested. Then, in order to exploit the benefits of both the approaches, a joint possibilistic and fuzzy clustering method for fuzzy data is proposed. A selection procedure for choosing the parameters of the new clustering method is introduced. The effectiveness of the proposal is investigated by means of simulated and real-life data

Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise

A Heuristic Approach to Possibilistic Clustering for Fuzzy Data

The paper deals with the problem of the fuzzy data clustering. In other words, objects attributes can be represented by fuzzy numbers or fuzzy intervals. A direct algorithm of possibilistic clustering is the basis of an approach to the fuzzy data clustering. The paper provides the basic ideas of the method of clustering and a plan of the direct possibilistic clustering algorithm. Definitions of fuzzy intervals and fuzzy numbers are presented and distances for fuzzy numbers are considered. A concept of a vector of fuzzy numbers is introduced and the fuzzy data preprocessing methodology for constructing of a fuzzy tolerance matrix is described. A numerical example is given and results of application of the direct possibilistic clustering algorithm to a set of vectors of triangular fuzzy numbers are considered in the example. Some preliminary conclusions are stated

A Method for Estimating the Least Number of Objects in Fuzzy Clusters

The theoretical note deals with the problem of estimation of the value of the least number of objects in fuzzy clusters for following detection of the optimal number of objects in fuzzy clusters through heuristic possibilistic clustering. A technique for detecting the optimal maximal number of elements in the a priori unknown number of fuzzy clusters of the sought clustering structure is reminded and a procedure for finding the initial minimal value of the number of objects in fuzzy clusters is proposed. Numerical examples are considered and conclusions are formulated

Выявление аномального поведения системами обнаружения атак при интервально-значном представлении данных

В статье рассмотрен метод обнаружения аномального поведения пользователей распределенной компьютерной сети при интервально-значном представлении данных, основанный на построении устойчивой кластерной структуры с помощью эвристического метода возможностной кластеризации. Предложенный метод иллюстрируется результатами вычислительного эксперимента.У статті розглянуто метод виявлення аномальної поведінки користувачів розподіленої комп’ютерної мережі при інтервально-значному зображенні даних, що заснований на побудові стійкої кластерної структури за допомогою евристичного методу можливісної кластеризації. Запропонований метод ілюструється результатами обчислювального експерименту.A method of detecting anomalous user behavior in a distributed computational network for a case of interval-valued data is considered in the article. The method is based on constructing stable clustering structure using a heuristic method of possibilistic clustering. The proposed method is illustrated by the results of numerical experiment