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**Skills and Expertise**

## Publications

Publications (78)

The Lilliefors test of normality is a popular and easy-to-explain method for testing whether a sample comes from a normal distribution. Unfortunately, since it relies on the sample mean and sample standard deviation for estimating the parameters of the normal distribution, the Lilliefors test is quite sensitive to the presence of outliers. Contrari...

The aim of a ranking aggregation problem is to combine several rankings into a single one that best represents them. A common method for solving this problem is due to Kemeny and selects as the aggregated ranking the one that minimizes the sum of the Kendall distances to the rankings to be aggregated. Unfortunately, the identification of the said r...

Most data analysis techniques, e.g. those faced in [15,16,17,18] usually require datasets without missing data, however, in the current age of large datasets it is becoming more and more common to deal with huge datasets for which some values are missing. For this reason, several techniques for the imputation of missing values have been developed....

The present paper focuses on the study of the conditions under which the covariance matrix of a multivariate Gaussian distribution is totally positive, paying particular attention to multivariate Gaussian distributions that are Gaussian Markov Random Fields. More specifically, it is proven that, if the graph over which the Gaussian Markov Random Fi...

Gaussian Markov Random Fields over graphs have been widely used in many fields of application. Here, we address the matrix construction problem that arises in the study of Gaussian Markov Random Fields with uniform correlation, i.e., those in which all correlations between adjacent nodes in the graph are equal. We provide a characterization of the...

Ordered Weighted Averaging (OWA) functions are a popular tool for the aggregation of real values and have been used successfully in several fields of application. The extension of these OWA functions to the multivariate setting is not unique and has been addressed separately by different disciplines. In this paper, we introduce a unifying perspecti...

The amount of labelled data (referred to as absolute information) obtained from experts has an obvious effect on the performance of an ordinal classifier. In order to make up for a lack of sufficient labelled data, a possibility is to access other sources of information. Inspired by the popularity of public crowdsourcing platforms, an effective way...

The study of Gaussian Markov Random Fields has attracted the attention of a large number of scientific areas due to its increasing usage in several fields of application. Here, we consider the construction of Gaussian Markov Random Fields from a graph and a positive-definite matrix, which is closely related to the problem of finding the Maximum Lik...

Aggregation functions on bounded partially ordered sets have been extensively studied for more than thirty years. In this paper, we study aggregation functions on a specific type of bounded partially ordered set: a Cartesian product of several bounded partially ordered sets. In particular, we position this type of aggregation into the recently-intr...

Stochastic dominance is a popular stochastic order for the comparison of random variables. Even though it carries many intuitive properties, stochastic dominance does not result in a complete order relation, even when restricted to certain parametric families of probability distributions. In this paper, we explore a graded version of stochastic dom...

The performance of an ordinal classifier is highly affected by the amount of absolute information (labelled data) available for training. In order to make up for a lack of sufficient absolute information, an effective way out is to consider additional types of information. In this work, we focus on ordinal classification problems that are provided...

A pesar de que Matemáticas y Música son dos asignaturas claramente diferenciadas en el currículo de la Educación Secundaria Obligatoria (12-16 años) en España, es innegable que existe una relación inherente entre ellas y que gran parte de sus contenidos pueden reforzarse simultáneamente. Desafortunadamente, ambas asignaturas suelen polarizar los gu...

Preference aggregation and in particular ranking aggregation are mainly studied by the field of social choice theory but extensively applied in a variety of contexts. Among the most prominent methods for ranking aggregation, the Kemeny method has been proved to be the only one that satisfies some desirable properties such as neutrality, consistency...

Compositional data naturally appear in many fields of application. For instance, in chemistry, the relative contributions of different chemical substances to a product are typically described in terms of a compositional data vector. Although the aggregation of compositional data frequently arises in practice, the functions formalizing this process...

The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the ch...

Probabilistic topic modelling is frequently used in machine learning and statistical analysis for extracting latent information from complex datasets. Despite being closely associated with natural language processing and text mining, these methods possess several properties that make them particularly attractive in metabolomics applications where t...

The aim of a clustering method is to create groups (clusters) of objects that are similar to each other. This similarity is usually measured by means of a distance, thus, the choice of distance function plays a crucial role in the clustering process. In this work, we propose a variant of the classical clustering method kmeans that combines the info...

PISA for Schools is an OECD (Organization for Economic Cooperation and Development) program designed to provide results on students’ performance in Mathematics, Reading and Science at school level. In order to achieve this purpose, participants are asked to answer a content-based test together with a background questionnaire. Answers are next evalu...

Although the order-based definition of the univariate median is ubiquitous in statistics, the same order-based definition is typically abandoned when extending the univariate median to higher dimensions. In this paper, an example of order-based multivariate median based on the use of a linear extension of the product order is brought to the attenti...

The performance of a classifier is often limited by the amount of labeled data (absolute information) available. In order to overcome this limitation, the incorporation of side information into the classification process has become a popular research topic in the field of machine learning. In this work, we propose a new method for ordinal classific...

In the paper "An inherent difficulty in the aggregation of multidimensional data" recently accepted for publication in this very journal, the property of orthomonotonicity is introduced. This property is proved to be weaker than monotonicity and orthogonal equivariance together and to reduce the family of idempotent functions to the family of weigh...

OWA operators have been ubiquitous in many disciplines since they were introduced by Yager in 1988. Aside of some other intuitive properties (e.g. monotonicity and idempotence), OWA operators are known to be continuous and, for some carefully constructed weighing vectors, very robust in the presence of outliers. In a recent paper, a natural extensi...

A large amount of labelled data (absolute information) is usually needed for an ordinal classifier to attain a good performance. As shown in a recent paper by the present authors, the lack of a large amount of absolute information can be overcome by additionally considering some side information in the form of relative information, thus augmenting...

Fuzzy relations and, in particular, fuzzy order relations, have been largely studied since Zadeh first introduced the concept back in 1971. Bearing in mind that betweenness relations and their relationship with order relations have historically attracted the attention of mathematicians, it is very surprising that the study of fuzzy betweenness rela...

A classical problem in the field of food science concerns the consensus evaluation of food samples. Typically, several panelists are asked to provide scores describing the perceived quality of the samples, and subsequently, the overall (consensus) scores are determined. Unfortunately, gathering a large number of panelists is a challenging and very...

In voting theory, two different settings are commonplace: either voters express a preference ordering on the set of candidates or they express an individual evaluation of each candidate. In either case, the aim may be to obtain a global ranking of the candidates and, in particular, to determine the winner of the election. We introduce a probabilist...

We consider the problem of constructing a fuzzy betweenness relation from a metric. More precisely, given a continuous Archimedean triangular norm, we present two construction methods for a fuzzy betweenness relation from a metric by making use of the pseudo-inverse of either a continuous additive generator or a continuous multiplicative generator...

The field of aggregation theory aims at formalizing in a mathematical way the process of combining several inputs into a single output, typically both the inputs and the output being elements of a poset. Although the field in itself only dates from the second half of the last century, one could easily trace back further in time prominent examples o...

The ability to learn an accurate classification process is often limited by the amount of labeled data. Incorporating additional information into the learning process for overcoming this limitation has been a popular research topic. In this work, we focus on ordinal classification problems that are provided with limited absolute information and add...

Ordinal classification is a special case of multiclass classification in which there exists a natural order on the set of class labels. Due to the nature of the problem, datasets for ordinal classification are typically rather small, having a negative impact on performance. A possible way out is to look for additional information. In this paper, fi...

The problem of ranking different candidates or alternatives according to the preferences of different voters or experts is a common study subject in the fields of social choice theory and preference modelling. Whereas the former field normally restricts its attention to preferences given in the form of rankings (with ties), the latter field embrace...

Whereas the field of aggregation theory has historically studied aggregation on bounded posets (mainly the aggregation of real numbers), different aggregation processes have been analysed in different fields of application. In particular, the aggregation of strings has been a popular topic in many fields featuring computer science and bioinformatic...

The property of monotonicity, which requires a function to preserve a given order, has been considered the standard in the aggregation of real numbers for decades. In this paper, we argue that, for the case of multidimensional data, an order-based definition of monotonicity is far too restrictive. We propose several meaningful alternatives to this...

The development of quality monitoring systems for perishable food products like seafood requires extensive data collection under specified packaging and storage conditions, followed by advanced data analysis and interpretation. Even though the benefits of using volatile organic compounds as food quality indices have been recognized, few studies hav...

In the field of information fusion, the problem of data aggregation has been formalized as an order-preserving process that builds upon the property of monotonicity. However, fields such as computational statistics, data analysis and geometry, usually emphasize the role of equivariances to various geometrical transformations in aggregation processe...

Betweenness relations are the mathematical formalization of the geometrical notion of an element being in between other two elements. In this paper, we exploit a well-known result representing a betweenness relation as a family of order relations and analyse the corresponding family of induced (Alexandrov) topologies. In particular, the intersectio...

The study of conditions, under which the existence of an “absolute” best winner can be assured, is a hot topic in the field of social choice. Unanimity is an evident example of a condition under which the winner is obvious. However, many more properties weaker than unanimity have been analysed in literature: the presence of a Condorcet winner, stro...

The notions of (sample) mean, median and mode are common tools for describing the central tendency of a given probability distribution. In this article, we propose a new measure of central tendency, the sample monomode, which is related to the notion of sample mode. We also illustrate the computation of the sample monomode and propose a statistical...

After more than half a year of elections (yielding three voting stages and nine voting rounds), the 2017 Rector election at Ghent University (Belgium) resulted in a victory for the duo leading all nine voting rounds, and in a resounding defeat for the electoral system. Significant regulation changes were needed in order to break the institutional d...

The field of social choice dates back to the eighteenth century, when Borda and Condorcet started a never-ending discussion about the use of either positional or pairwise information. Three centuries later, after countless axiomatic characterizations of voting rules, impossibility theorems and many other study subjects, researchers still debate whe...

Penalty functions have been a common tool in data aggregation for decades. Unfortunately, although the definition of a penalty function has evolved over the years, the use of penalty functions has been reduced to the aggregation of real numbers. However, in this 'era of aggregation', the need of generalizing the current definition in order to compl...

We consider a predictive modelling problem, where the goal is to predict the absolute evaluation of an object on an ordinal scale, traditionally known as an ordinal regression problem. We present a framework that is capable of learning such a model while combining different types of information: absolute evaluations by experts and relative evaluati...

The problem of obtaining the consensus evaluation of food samples is commonly considered by researchers in food science. Typically, trained panellists provide scores describing the overall quality of the samples. However, due to the fact that trained panellists are limited in number and very expensive, it is common to recruit untrained panellists t...

A common problem in food science concerns the assessment of the quality of food samples. Typically, a group of panellists is trained exhaustively on how to identify different quality indicators in order to provide absolute information, in the form of scores, for each given food sample. Unfortunately, this training is expensive and time-consuming. F...

A common problem in social choice theory concerns the aggregation of the rankings expressed by several voters. Two different settings are often discussed depending on whether the aggregate is assumed to be a latent true ranking that voters try to identify or a compromise ranking that (partially) satisfies most of the voters. In a previous work, we...

In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be “clones” if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clon...

Among all existing paradoxes of voting, the one pointed out by Condorcet has managed to become known as ‘the’ voting paradox. This relevant paradox states that the transitivity of the voters’ preferences does not imply the transitivity of the collective preference. However, this collective preference disregards a considerable part of the informatio...

The field of aggregation theory addresses the mathematical formalization of aggregation processes. Historically, the developed mathematical framework has been largely confined to the aggregation of real numbers, while the aggregation of other types of structures, such as rankings, has been independently considered in different fields of application...

Aggregating the preferences of several voters on a set of candidates is a classical problem in several fields of application. In previous work, we have addressed this problem in the case where each voter expresses his/her preferences in the form of a ranking on the set of candidates, by searching for monotonicity of three different types of represe...

In this paper, we consider the problem of obtaining the consensus evaluation of multiple objects based on the evaluations expressed by several experts. This problem is of relevance to several fields, in particular to the field of sensory evaluation, such as in food quality appraisal, and to the field of recommender systems, such as in movie recomme...

Back in the eighteenth century, the works of Borda and Condorcet laid the foundations of social choice theory. On the one hand, Borda proposed to exploit the positions at which each candidate is ranked. On the other hand, Condorcet proposed to exploit the relative positions of each pair of candidates. Both proposals have equally called the attentio...

Representations of votes, such as the scorix, the votrix or the beatpath matrix, are common tools in social choice theory. They gather the most relevant information given by the voters and are key elements in most of the existing ranking rules. The goal of this paper is twofold. First, the most relevant representations of votes based on pairwise in...

The choice of the ranking that best captures the preferences of several voters on a set of candidates has been a matter of study for centuries. An interesting point of view on this problem is centred on the notion of monotonicity. In this paper, we deal with an aspect of monotonicity that has not been addressed before: if there is a true ranking on...

In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterizati...

The aggregation of rankings is a recurrent task in several fields of application. In a recent work by Rademaker and De Baets, a ranking rule based on a natural monotonicity property was proposed in the context of social choice theory. This rule is built on the premise that, for a ranking to represent a group's opinion, it would be natural that the...

In earlier work, some of the present authors have advocated that the search for monotonicity of the votrix, a well-known representation of votes, leads to natural ranking rules. In order to exploit hitherto unconsidered information, we introduced a new representation of votes, the votex, and the search for monotonicity was extended to this represen...

The aggregation of rankings is a long-standing problem that consists of, given a profile of rankings, obtaining the single ranking that best represents the nature of this given profile. Under the name of metric rationalisation of ranking rules, it has been proven that most ranking rules can be characterized as minimizing the distance to a consensus...

We propose a new point of view of the long-standing problem where several voters have expressed a (strict) linear order (or ranking) over a set of candidates. For a ranking to represent a group's opinion, it would be natural that the strength with which is supported should not be less than both the strength with which and the strength with which ar...

Ordering sets is a long-standing open problem due to its remarkable importance in many areas such as decision making, image processing or human reliability. This work is focused on introducing methods for ordering finitely generated sets as a generalization of those methods previously defined for ordering intervals. In addition, these orders betwee...

We propose a new point of view in the long-standing problem where several voters have expressed a linear order relation (or ranking) over a set of candidates. For a ranking a > b > c to represent a group's opinion, it would be logical that the strength with which a > c is supported should not be less than the strength with which either a > b or b >...

The main purpose of this paper is to develop a new method to aggregate the information given by several experts or criteria about different alternatives in order to obtain the preferred alternative or alternatives. This method has to take into account the interaction of the different alternatives and a parameter modelling the flexibility of this me...