Abstract. Histograms are commonly used for representing summaries of observed data and they can be considered non parametric estimates of probability distributions. Symbolic Data Analysis formalized the concept of histogram symbolic variable, as a variable which allows to describe statistical units by histograms instead of single values. In this paper we present a linear regression model for mu...

Recent attempts to assess the performance of SSVM algorithms for unconstrained minimization problems differ in their evaluations from earlier assessments. Nevertheless, the new experiments confirm earlier observations that, on certain types of problems, the SSVM algorithms are far superior to other variable metric methods. This paper presents a critical review of these recent assessments and di...

We consider conceptual optimization methods combining two ideas: the Moreau-Yosida regularization in convex analysis, and quasi-Newton approximations of smooth functions. We outline several approaches based on this combination, and establish their global convergence. Then we study theoretically the local convergence properties of one of these approaches, which uses quasi-Newton updates of the o...

This paper introduces a new class of quasi-Newton algorithms for unconstrained minimization in which no line search is necessary and the inverse Hessian approximations are positive definite. These algorithms are based on a two-parameter family of rank two, updating formulae used earlier with line search in self-scaling variable metric algorithms. It is proved that, in a quadratic case, the new ...

Machine-learning solutions to classification, clustering and matching problems critically depend on the adopted metric, which in the past was selected heuristically. In the last decade, it has been demonstrated that an appropriate metric can be learnt from data, resulting in superior performance as compared with traditional metrics. This has recently stimulated a considerable interest in the to...

A multiple regression method based on distance analysis and metric scaling is proposed and studied. This method allow us to predict a continuous response variable from several explanatory variables, is compatible with the general linear model and is found to be useful when the predictor variables are both continuous and categorical. Real data examples are given to illustrate the results obtained.

In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in Bock and Diday [1] and the parameters of the model are estimated using the classic Least Squares method. An appropriate metric is introduced in order to measure the error between the observed and the predicted distributions. In particula...