1,721,155 research outputs found
Fitting parametric link functions in a regression model with imprecise random variables
Full text linkA regression model for imprecise random variables has been introduced in our previous works. The imprecision of a random element has been
formalized by means of the fuzzy random variable (FRV). In detail, a particular case of FRVs characterized by a center, a left and a right spread, the
LR family (LR FRV), has been considered. The idea is to jointly consider three regression models in which the response variables are the center, and
two transformations of the left and the right spreads in order to overcome the non-negativity conditions of the spreads. Response transformations
could be fixed, as we have done so far, but all inferential procedures, such as estimation, hypothesis tests on the regression parameters, linearity
test etc., are affected by this choice. For this reason we consider a family of parametric link functions, the Box-Cox transformation model, and by
means of a computational procedure we will look for the transformation parameters that maximize the goodness of fit of the model
Fuzzy k-Means: history and applications
Full text linkThe fuzzy approach to clustering arises to cope with situations where objects have not a clear assignment. Unlike the hard/standard approach where each object can only belong to exactly one cluster, in a fuzzy setting, the assignment is soft; that is, each object is assigned to all clusters with certain membership degrees varying in the unit interval. The best known fuzzy clustering algorithm is the fuzzy k-means (FkM), or fuzzy c-means. It is a generalization of the classical k-means method. Starting from the FkM algorithm, and in more than 40 years, several variants have been proposed. The peculiarity of such different proposals depends on the type of data to deal with, and on the cluster shape. The aim is to show fuzzy clustering alternatives to manage different kinds of data, ranging from numeric, categorical or mixed data to more complex data structures, such as interval-valued, fuzzy-valued or functional data, together with some robust methods. Furthermore, the case of two-mode clustering is illustrated in a fuzzy setting
Seconda edizione in lingua italiana dell'opera “The Basic Practice of Statistics”, 3rd edition . Di MOORE D S
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fclust: Fuzzy clustering
No full textAlgorithms for fuzzy clustering, cluster validity indices and plots for cluster validity and visualizing fuzzy clustering results
A linear regression model with LR fuzzy random variables
Full text linkIn standard regression analysis the relationship between one (response) variable and a set of (explanatory) variables is investigated.
In a classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random
variable. However, the data can be also subjected to other kinds of uncertainty, such as imprecision, vagueness, etc. A possible
way to manage all of these uncertainties is represented by the concept of fuzzy random variable (FRV). The most common class
of FRVs is the LR family, which allows us to express every FRV in terms of three random variables, namely, the center, the left
and the right spread. In this work, limiting our attention to the LR FRVs, we address the linear regression problem in presence
of one or more imprecise random elements. The procedure for estimating the model parameters is discussed, and the statistical
properties of the estimates are analyzed. Furthermore, in order to illustrate how the proposed model works in practice, the results
of some case-studies are given
A toolbox for fuzzy clustering using the R programming language
No full textFuzzy clustering is used extensively in several domains of research. In the literature, starting from the well-known fuzzy k-means (fkm) clustering algorithm, an increasing number of papers devoted to fkm and its extensions can be found. Nevertheless, a lack of the related software for implementing these algorithms can be observed preventing their use in practice. Even the standard fkm is not necessarily available in the most common software. For this purpose, a new toolbox for fuzzy clustering using the R programming language is presented by examples. The toolbox, called fclust, contains a suit of fuzzy clustering algorithms, fuzzy cluster validity indices and visualization tools for fuzzy clustering results
On possibilistic clustering with repulsion constraints for imprecise data
No full textIn possibilistic clustering objects are assigned to clusters according to the so-called membership degrees taking values in the unit interval. Differently from fuzzy clustering, it is not required that the sum of the membership degrees of an object to all clusters is equal to one. This is very helpful in the presence of outliers, which are usually assigned to the clusters with membership degrees close to zero. Unfortunately, a drawback of the possibilistic approach is the tendency to produce coincident clusters. A remedy is to add a repulsion term among prototypes in the loss function forcing the prototypes to be far 'enough' from each other. Here, a possibilistic clustering algorithm with repulsion constraints for imprecise data, managed in terms of fuzzy sets, is introduced. Applications to synthetic and real fuzzy data are considered in order to analyze how the proposed clustering algorithm works in practice. (C) 2013 Published by Elsevier Inc
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