Zied Elouedi

Assessing sensor reliability for multisensor data fusion within the transferable belief model

This paper presents a method for assessing the reliability of a sensor in a classification problem based on the transferable belief model. First, we develop a method for the evaluation of the reliability of a sensor when considered alone. The method is based on finding the discounting factor minimizing the distance between the pignistic probabilities computed from the discounted beliefs and the actual values of data. Next, we develop a method for assessing the reliability of several sensors that are supposed to work jointly and their readings are aggregated. The discounting factors are computed on the basis of minimizing the distance between the pignistic probabilities computed from the combined discounted belief functions and the actual values of data.

Decision trees as possibilistic classifiers

This paper addresses the classification problem with imperfect data. More precisely, it extends standard decision trees to handle uncertainty in both building and classification procedures. Uncertainty here is represented by means of possibility distributions. The first part investigates the issue of building decision trees from data with uncertain class values by developing a non-specificity based gain ratio as the attribute selection measure which, in our case, is more appropriate than the standard gain ratio based on Shannon entropy. The proposed non-specificity based possibilistic decision tree (NS-PDT) approach is then extended by considering another kind of uncertainty inherent in the building procedure. The extended approach so-called non-specificity based possibilistic option decision tree (NS-PODT) offers a more flexible building procedure by allowing the selection of more than one attribute in each node. The second part addresses the classification phase. More specifically, it investigates the issue of predicting the class value of new instances presented with certain and/or uncertain attribute values. Finally, we have developed a possibilistic decision tree toolbox (PD2T) in order to show the feasibility of the proposed approach.

How to preserve the conflict as an alarm in the combination of belief functions

In the belief function framework, a unique function is induced from the use of a combination rule so allowing to synthesize all the knowledge of the initial belief functions. When information sources are reliable and independent, the conjunctive rule of combination, proposed by Smets, may be used. This rule is equivalent to the Dempster rule without the normalization process. The conjunctive combination provides interesting properties, as the commutativity and the associativity. However, it is characterized by having the empty set, called also the conflict, as an absorbing element. So, when we apply a significant number of conjunctive combinations, the mass assigned to the conflict tends to 1 which makes impossible returning the distinction between the problem arisen during the fusion and the effect due to the absorption power of the empty set.The objective of this paper is then to define a formalism preserving the initial role of the conflict as an alarm signal announcing that there is a kind of disagreement between sources. More exactly, that allows to preserve some conflict, after the fusion by keeping only the part of conflict reflecting the opposition between the belief functions. This approach is based on dissimilarity measures and on a normalization process between belief functions. Our proposed formalism is tested and compared with the conjunctive rule of combination on synthetic belief functions. In belief function theory, one of the main combination rules is the conjunctive rule.With this rule, a series of combinations results in mass equal to 1 on the conflict.In this case, it is impossible to identify a potential problem in the fusion process.The proposed method allows us to keep the real opposition between belief functions.Using this approach, the conflict regains its initial role of alarm.

Naïve possibilistic network classifiers

Naive Bayesian network classifiers have proved their effectiveness to accomplish the classification task, even if they work under the strong assumption of independence of attributes in the context of the class node. However, as all of them are based on probability theory, they run into problems when they are faced with imperfection. This paper proposes a new approach of classification under the possibilistic framework with naive classifiers. To output the naive possibilistic network classifier, two procedures are studied namely the building phase, which deals with imperfect (imprecise/uncertain) dataset attributes and classes, and the classification phase, which is used to classify new instances that may be characterized by imperfect attributes. To improve the performance of our classifier, we propose two extensions namely selective naive possibilistic classifier and semi-naive possibilistic classifier. Experimental study has shown naive Bayes style possibilistic classifier, and is efficient in the imperfect case.

Information Affinity: A New Similarity Measure for Possibilistic Uncertain Information

This paper addresses the issue of measuring similarity between pieces of uncertain information in the framework of possibility theory. In a first part, natural properties of such functions are proposed and a survey of the few existing measures is presented. Then, a new measure so-called Information Affinity is proposed to overcome the limits of the existing ones. The proposed function is based on two measures, namely, a classical informative distance, e.g. Manhattan distance which evaluates the difference, degree by degree, between two normalized possibility distributions and the well known inconsistency measure which assesses the conflict between the two possibility distributions. Some potential applications of the proposed measure are also mentioned in this paper.

DBSCAN-GM: An improved clustering method based on Gaussian Means and DBSCAN techniques

Clustering is one of the most useful methods of intelligent engineering domain, in which a set of similar objects are categorized into clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, the majority is not robust enough towards noisy data. This paper presents an efficient and effective clustering technique, named DBSCAN-GM that combines Gaussian-Means and DBSCAN algorithms. The idea of DBSCAN-GM is to cover the limitations of DBSCAN, by exploring the benefits of Gaussian-Means: it runs Gaussian-Means to generate small clusters with determined cluster centers, in purpose to estimate the values of DBSANs parameters. The results of our method show that it is efficient even for large data sets especially data with large dimension and capable to handle noises, contrary to partitioning algorithms such as K-Means or Gaussian-Means. Additionally, DBSCAN-GM does not necessitate any priori information, in contrast to the density clustering DBSCAN obliging two input parameters which are hard to guess, namely Eps (the radius that bounds the neighborhood region of an object) and MinPts (the minimum number of objects that must exist in the objects neighborhood region). Simulative experiments are carried out on a variety of datasets, which highlight the DBSCAN-GMs effectiveness and cluster validity to check the good quality of clustering results.

Pruning belief decision tree methods in averaging and conjunctive approaches

The belief decision tree (BDT) approach is a decision tree in an uncertain environment where the uncertainty is represented through the Transferable Belief Model (TBM), one interpretation of the belief function theory. The uncertainty can appear either in the actual class of training objects or attribute values of objects to classify. From the procedures of building BDT, we mention the averaging and the conjunctive approaches. In this paper, we develop pruning methods of belief decision trees induced within averaging and conjunctive approaches where the objective is to cope with the problem of overfitting the data in BDT in order to improve its comprehension and to increase its quality of the classification.

Classification systems based on rough sets under the belief function framework

In this paper, we present two classification approaches based on Rough Sets (RS) that are able to learn decision rules from uncertain data. We assume that the uncertainty exists only in the decision attribute values of the Decision Table (DT) and is represented by the belief functions. The first technique, named Belief Rough Set Classifier (BRSC), is based only on the basic concepts of the Rough Sets (RS). The second, called Belief Rough Set Classifier, is more sophisticated. It is based on Generalization Distribution Table (BRSC-GDT), which is a hybridization of the Generalization Distribution Table and the Rough Sets (GDT-RS). The two classifiers aim at simplifying the Uncertain Decision Table (UDT) in order to generate significant decision rules for classification process. Furthermore, to improve the time complexity of the construction procedure of the two classifiers, we apply a heuristic method of attribute selection based on rough sets. To evaluate the performance of each classification approach, we carry experiments on a number of standard real-world databases by artificially introducing uncertainty in the decision attribute values. In addition, we test our classifiers on a naturally uncertain web usage database. We compare our belief rough set classifiers with traditional classification methods only for the certain case. Besides, we compare the results relative to the uncertain case with those given by another similar classifier, called the Belief Decision Tree (BDT), which also deals with uncertain decision attribute values.

FDCM: A Fuzzy Dendritic Cell Method

An immune-inspired danger theory model based on dendritic cells (DCs) within the framework of fuzzy set theory is proposed in this paper. Our objective is to smooth the abrupt separation between normality (semi-mature) and abnormality (mature) using fuzzy set theory since we can neither identify a clear boundary between the two contexts nor quantify exactly what is meant by “semi-mature” or “mature”. In this model, the context of each object (DC) is described using linguistic variables. Fuzzy subsets and the corresponding membership functions describe these variables. A knowledge base, comprising rules, is built to support the fuzzy inference. The induction of the context of each object is diagnosed using a compositional rule of fuzzy inference. Experiments on real data sets show that by alleviating the crisp separation between the two contexts, our new approach which focuses on binary classification problems produces more accurate results.

Iterative meta-clustering through granular hierarchy of supermarket customers and products

This paper proposes a novel iterative meta-clustering technique that uses clustering results from one set of objects to dynamically change the representation of another set of objects. The proposal evolves two clustering schemes in parallel influencing each other through indirect recursion. The proposal is based on the emerging area of granular computing, where each object is represented as an information granule and an information granule can hierarchically include other information granules. The paper describes the theoretical and algorithmic formulation of the iterative meta-clustering algorithm followed by its implementation. The proposal is demonstrated with the help of a retail store dataset consisting of transactions involving customers and products. A customer granule is represented by static information obtained from the database and dynamic information obtained from clustering of products bought by the customer. Similarly, the product granule augments the static representation from the database with clustering profiles of customers who buy these products. The algorithm is tested for a synthetic dataset to explore various nuances of the proposal, followed by an extensive experimentation with a real-world retail dataset.