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Displaying 81 –
100 of
258
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...
La représentation visuelle d'une hiérarchie induit un ordre sur les singletons. Si l'on désire représenter la même hiérarchie en tenant compte de contraintes extérieures (ordre des singletons induit par une autre hiérarchie, une partition, un indice de dissimilarité, par exemple) des croisements peuvent apparaître. Il y a un croisement dans la représentation visuelle d'une hiérarchie quand une branche horizontale (associée à un palier) est coupée par une branche verticale associée à un singleton....
We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility...
The paper presents data mining methods applied to gene selection for recognition of a particular type of prostate cancer on the basis of gene expression arrays. Several chosen methods of gene selection, including the Fisher method, correlation of gene with a class, application of the support vector machine and statistical hypotheses, are compared on the basis of clustering measures. The results of applying these individual selection methods are combined together to identify the most often selected...
In the companion paper [C. Maugis and B. Michel, A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: P&S 15 (2011) 41–68] , a penalized likelihood criterion is proposed to select a Gaussian mixture model among a specific model collection. This criterion depends on unknown constants which have to be calibrated in practical situations. A “slope heuristics” method is described and experimented to deal with this practical problem. In a model-based clustering context,...
In the companion paper [C. Maugis and B. Michel,
A non asymptotic penalized criterion for Gaussian mixture model selection. ESAIM: P&S15 (2011) 41–68] , a penalized likelihood
criterion is proposed to select a Gaussian mixture model among a
specific model collection. This criterion depends on unknown
constants which have to be calibrated in practical situations. A
“slope heuristics” method is described and experimented to deal
with this practical problem. In a model-based clustering context,
the...
2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.Locally Linear Embedding (LLE) has gained prominence as a tool in unsupervised non-linear dimensional reduction. While the algorithm aims to preserve certain proximity relations between the observed points, this may not always be desirable if the shape in higher dimensions that we are trying to capture is observed with noise. This note suggests that a desirable first step is to remove or at least reduce the noise in the observations before...
Detecting a cluster structure is considered. This means solving either the problem of discovering a natural decomposition of data points into groups (clusters) or the problem of detecting clouds of data points of a specific form. In this paper both these problems are considered. To discover a cluster structure of a specific arrangement or a cloud of data of a specific form a class of nonlinear projections is introduced. Fitness functions that estimate to what extent a given subset of data points...
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