In the symbolic data framework, probabilistic symbolic data are considered as those whose components are random variables with general probability distributions. Intervals (or uniform distributions), histograms (or empirical distributions), Gaussian distribution and Chi-squared distribution are...

This paper proposes threshold models to analyze and forecast interval-valued time series. A relatively simple algorithm is proposed to obtain least square estimates of the threshold and slope parameters. The construction of forecasts based on the proposed model and methods for the analysis of...

<Para ID="Par1">In this paper we present a new linear regression technique for distributional symbolic variables, i.e., variables whose realizations can be histograms, empirical distributions or empirical estimates of parametric distributions. Such data are known as numerical modal data according to the...</para>

In this paper, following a partitioning around medoids approach, a fuzzy clustering model for interval-valued data, i.e., FCMd-ID, is introduced. Successively, for avoiding the disruptive effects of possible outlier interval-valued data in the clustering process, a robust fuzzy clustering model...

<Para ID="Par1">Trachoma, caused by repeated ocular infections with Chlamydia trachomatis whose vector is a fly, is an important cause of blindness in the world. We are presenting here an application of the Symbolic Data Analysis approach to an interventional study on trachoma conducted in Mali. This study was...</para>

A new method of regression analysis for interval-valued data is proposed. The relationship between an interval-valued response variable and a set of interval-valued explanatory variables is investigated by considering two regression models, one for the midpoints and the other one for the radii....

Parameter estimation for model-based clustering using a finite mixture of normal inverse Gaussian (NIG) distributions is achieved through variational Bayes approximations. Univariate NIG mixtures and multivariate NIG mixtures are considered. The use of variational Bayes approximations here is a...

We introduce a method to minimize the mean square error (MSE) of an estimator which is derived from a classification. The method chooses an optimal discrimination threshold in the outcome of a classification algorithm and deals with the problem of unequal and unknown misclassification costs and...

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we consider the case of mixture of mixture models with...

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered, for example, when looking for common principal components. The Flury method is a popular approach but is not effective for higher dimensional problems. We obtain...