This paper is concerned with the clustering of objects whose properties cannot be described by exact data. These can only be described by fuzzy sets or by linguistic values of previously defined linguistic variables. To cluster these objects we use a generalization of classic clustering methods in which instead of similarity (dissimilarity) of objects, used fuzzy similarity (fuzzy dissimilarity) to define the clustering of fuzzy objects.
Les concepts d'éléments R-ressemblants à un prototype X et de R-regroupement d'objets introduits dans cet article, sont basés sur la notion de relation de S-comparaison R définie au moyen d'un indice scalaire de similarité défini entre sous-ensembles flous. Cette relation tient compte du fait que la similarité et la non-dissimilarité des sous-ensembles flous ne sont pas en général des synonymes. Une technique de coalescence floue basée sur des R-regroupements maximaux est également introduite.
Prototype Selection (PS) techniques have traditionally been applied prior to Nearest Neighbour (NN) classification rules both to improve its accuracy (editing) and to alleviate its computational burden (condensing). Methods based on selecting/discarding prototypes and methods based on adapting prototypes have been separately introduced to deal with this problem. Different approaches to this problem are considered in this paper and their main advantages and drawbacks are pointed out along with some...
Comparing q-ary relations on a set of elementary objects is one of the most fundamental problems of classification and combinatorial data analysis. In this paper the specific comparison task that involves classification tree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches to tree comparison are discussed in the context...
Comparing q-ary relations on a set of elementary objects is one of the most fundamental problems of classification and combinatorial data analysis. In this paper the specific comparison task that involves classification tree structures (binary or not) is considered in this context. Two mathematical representations are proposed. One is defined in terms of a weighted binary relation; the second uses a 4-ary relation. The most classical approaches to tree comparison are discussed in the context...
Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem.
Consensus clustering algorithms are used to improve properties of traditional clustering methods, especially their accuracy and robustness. In this article, we introduce our approach that is based on a refinement of the set of initial partitions and uses differential evolution algorithm in order to find the most valid solution. Properties of the algorithm are demonstrated on four benchmark datasets.
With the rapid increase in the number of mobile devices connected to the Internet in recent years, the network load is increasing. As a result, there are significant delays in the delivery of cloud resources to mobile users. Edge computing technologies (edge, cloudlet, fog computing, etc.) have been widely used in recent years to eliminate network delays. This problem can be solved by allocating cloud resources to the cloudlets that are close to users. The article proposes a clustering-based model...
Although a nonlinear discrimination function may be superior to linear or quadratic classifiers, it is difficult to construct such a function. In this paper, we propose a method to construct a nonlinear discrimination function using Legendre polynomials. The selection of an optimal set of Legendre polynomials is determined by the MDL (Minimum Description Length) criterion. Results using many real data show the effectiveness of this method.
In classification problems, the issue of high dimensionality, of data is often considered important. To lower data dimensionality, feature selection methods are often employed. To select a set of features that will span a representation space that is as good as possible for the classification task, one must take into consideration possible interdependencies between the features. As a trade-off between the complexity of the selection process and the quality of the selected feature set, a pairwise...