Maria Brigida Ferraro

A linear regression model for imprecise response

A linear regression model with imprecise response and p real explanatory variables is analyzed. The imprecision of the response variable is functionally described by means of certain kinds of fuzzy sets, the LR fuzzy sets. The LR fuzzy random variables are introduced to model usual random experiments when the characteristic observed on each result can be described with fuzzy numbers of a particular class, determined by 3 random values: the center, the left spread and the right spread. In fact, these constitute a natural generalization of the interval data. To deal with the estimation problem the space of the LR fuzzy numbers is proved to be isometric to a closed and convex cone of R^3 with respect to a generalization of the most used metric for LR fuzzy numbers. The expression of the estimators in terms of moments is established, their limit distribution and asymptotic properties are analyzed and applied to the determination of confidence regions and hypothesis testing procedures. The results are illustrated by means of some case-studies.

Cold adaptation shapes the robustness of metabolic networks in Drosophila melanogaster

When ectotherms are exposed to low temperatures, they enter a cold‐induced coma (chill coma) that prevents resource acquisition, mating, oviposition, and escape from predation. There is substantial variation in time taken to recover from chill coma both within and among species, and this variation is correlated with habitat temperatures such that insects from cold environments recover more quickly. This suggests an adaptive response, but the mechanisms underlying variation in recovery times are unknown, making it difficult to decisively test adaptive hypotheses. We use replicated lines of Drosophila melanogaster selected in the laboratory for fast (hardy) or slow (susceptible) chill‐coma recovery times to investigate modifications to metabolic profiles associated with cold adaptation. We measured metabolite concentrations of flies before, during, and after cold exposure using nuclear magnetic resonance (NMR) spectroscopy to test the hypotheses that hardy flies maintain metabolic homeostasis better during cold exposure and recovery, and that their metabolic networks are more robust to cold‐induced perturbations. The metabolites of cold‐hardy flies were less cold responsive and their metabolic networks during cold exposure were more robust, supporting our hypotheses. Metabolites involved in membrane lipid synthesis, tryptophan metabolism, oxidative stress, energy balance, and proline metabolism were altered by selection on cold tolerance. We discuss the potential significance of these alterations.

A toolbox for fuzzy clustering using the R programming language

Abstract Fuzzy 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

In 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.

A Linearity Test for a Simple Regression Model with LR Fuzzy Response

A linearity test for a simple regression model with an imprecise response is investigated. The values of the imprecise response are formalized through LR-fuzzy numbers, and the stochastic variability through probability spaces. The linear regression model and the least squares estimators of the regression parameters are briefly recalled. The nonparametric model to be employed as reference in the testing approach is also presented. The statistic compares the variability explained by the linear regression with the one explained by the nonparametric regression, since in case of linearity, both quantities should be similar. The problem is approached by bootstrapping. A simulation study has been carried out in order to check the performance of the procedure.

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

Abstract 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.

From Separating to Proximal Plane Classifiers: A Review

A review of parallel and proximal plane classifiers is proposed. We discuss separating plane classifier introduced in support vector machines and we describe different proposals to obtain two proximal planes representing the two classes in the binary classification case. In details, we deal with proximal SVM classification by means of a generalized eigenvalues problem. Furthermore, some regularization techniques are analyzed in order to solve the singularity of the matrices. For the same purpose, proximal support vector machine using local information is handled. In addition, a brief description of twin support vector machines and nonparallel plane proximal classifier is reported.

A Proposal of Robust Regression for Random Fuzzy Sets

In standard regression the Least Squares approach may fail to give valid estimates due to the presence of anomalous observations violating the method assumptions. A solution to this problem consists in considering robust variants of the parameter estimates, such as M-, S- and MM-estimators. In this paper, we deal with robustness in the field of regression analysis for imprecise information managed in terms of fuzzy sets. Although several proposals for regression analysis of fuzzy sets can be found in the literature, limited attention has been paid to the management of possible outliers in order to avoid inadequate results. After discussing the concept of outliers for fuzzy sets, a robust regression method is introduced on the basis of one of the proposals available in the literature. The robust regression method is applied to a synthetic data set and a comparison with the non-robust counterpart is given.

Prediction of Single-Nucleotide Polymorphisms Causative of Rare Diseases

The study of rare diseases uses next-generation sequencing (NGS) technology to detect causative mutations in the human genome. NGS is a new approach for biomedical research, useful for the genetic diagnosis in extremely heterogeneous conditions. Nevertheless, only few publications address the problem when pooled experiments are considered, and existing tools are often inaccurate. In this work we focus on rare diseases and we describe how data are generated by NGS.

Bootstrap Confidence Intervals for the Parameters of a Linear Regression Model with Fuzzy Random Variables

Confidence intervals for the parameters of a linear regression model with a fuzzy response variable and a set of real and/or fuzzy explanatory variables are investigated. The family of LR fuzzy random variables is considered and an appropriate metric is suggested for coping with this type of variables. A class of linear regression models is then proposed for the center and for suitable transformations of the spreads in order to satisfy the non-negativity conditions for the latter ones. Confidence intervals for the regression parameters are introduced and discussed. Since there are no suitable parametric sampling models for the imprecise variables, a bootstrap approach has been used. The empirical behavior of the procedure is analyzed by means of simulated data and a real-case study.