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( h , Φ ) -entropy differential metric

María Luisa Menéndez, Domingo Morales, Leandro Pardo, Miquel Salicrú (1997)

Applications of Mathematics

Burbea and Rao (1982a, 1982b) gave some general methods for constructing quadratic differential metrics on probability spaces. Using these methods, they obtained the Fisher information metric as a particular case. In this paper we apply the method based on entropy measures to obtain a Riemannian metric based on ( h , Φ ) -entropy measures (Salicrú et al., 1993). The geodesic distances based on that information metric have been computed for a number of parametric families of distributions. The use of geodesic...

A Bayesian approach to cluster analysis.

José M. Bernardo, F.Javier Girón (1988)

Qüestiió

A general probabilistic model for describing the structure of statistical problems known under the generic name of cluster analysis, based on finite mixtures of distributions, is proposed. We analyse the theoretical and practical implications of this approach, and point out some open question on both the theoretical problem of determining the reference prior for models based on mixtures, and the practical problem of approximation that mixtures typically entail. Finally, models based on mixtures...

A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally, the map...

A Bimodality Test in High Dimensions

Palejev, Dean (2012)

Serdica Journal of Computing

We present a test for identifying clusters in high dimensional data based on the k-means algorithm when the null hypothesis is spherical normal. We show that projection techniques used for evaluating validity of clusters may be misleading for such data. In particular, we demonstrate that increasingly well-separated clusters are identified as the dimensionality increases, when no such clusters exist. Furthermore, in a case of true bimodality, increasing the dimensionality makes identifying the correct...

A blind definition of shape

J. L. Lisani, J. M. Morel, L. Rudin (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition” as a task which requires a “model” pattern which is searched in all images of a certain kind. We give instead a “blind” definition of shapes relying only on invariance and repetition arguments. Given a set of images ℐ , we call shape of this...

A blind definition of shape

J. L. Lisani, J. M. Morel, L. Rudin (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, we propose a general definition of shape which is both compatible with the one proposed in phenomenology (gestaltism) and with a computer vision implementation. We reverse the usual order in Computer Vision. We do not define “shape recognition" as a task which requires a “model" pattern which is searched in all images of a certain kind. We give instead a “blind" definition of shapes relying only on invariance and repetition arguments. Given a set of images ℐ , we call shape of this...

A comparative study of microaggregation methods.

Josep Maria Mateo Sanz, Josep Domingo Ferrer (1998)

Qüestiió

Microaggregation is a statistical disclosure control technique for microdata. Raw microdata (i.e. individual records) are grouped into small aggregates prior to publication. Each aggregate should contain at least k records to prevent disclosure of individual information. Fixed-size microaggregation consists of taking fixed-size microaggregates (size k). Data-oriented microaggregation (with variable group size) was introduced recently. Regardless of the group size, microaggregations on a multidimensional...

A comparison of evidential networks and compositional models

Jiřina Vejnarová (2014)

Kybernetika

Several counterparts of Bayesian networks based on different paradigms have been proposed in evidence theory. Nevertheless, none of them is completely satisfactory. In this paper we will present a new one, based on a recently introduced concept of conditional independence. We define a conditioning rule for variables, and the relationship between conditional independence and irrelevance is studied with the aim of constructing a Bayesian-network-like model. Then, through a simple example, we will...

A complete gradient clustering algorithm formed with kernel estimators

Piotr Kulczycki, Małgorzata Charytanowicz (2010)

International Journal of Applied Mathematics and Computer Science

The aim of this paper is to provide a gradient clustering algorithm in its complete form, suitable for direct use without requiring a deeper statistical knowledge. The values of all parameters are effectively calculated using optimizing procedures. Moreover, an illustrative analysis of the meaning of particular parameters is shown, followed by the effects resulting from possible modifications with respect to their primarily assigned optimal values. The proposed algorithm does not demand strict assumptions...

A copula test space model how to avoid the wrong copula choice

Frederik Michiels, Ann De Schepper (2008)

Kybernetika

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...

A depth-based modification of the k-nearest neighbour method

Ondřej Vencálek, Daniel Hlubinka (2021)

Kybernetika

We propose a new nonparametric procedure to solve the problem of classifying objects represented by d -dimensional vectors into K ≥ 2 groups. The newly proposed classifier was inspired by the k nearest neighbour (kNN) method. It is based on the idea of a depth-based distributional neighbourhood and is called k nearest depth neighbours (kNDN) classifier. The kNDN classifier has several desirable properties: in contrast to the classical kNN, it can utilize global properties of the considered distributions...

A dynamic model of classifier competence based on the local fuzzy confusion matrix and the random reference classifier

Pawel Trajdos, Marek Kurzynski (2016)

International Journal of Applied Mathematics and Computer Science

Nowadays, multiclassifier systems (MCSs) are being widely applied in various machine learning problems and in many different domains. Over the last two decades, a variety of ensemble systems have been developed, but there is still room for improvement. This paper focuses on developing competence and interclass cross-competence measures which can be applied as a method for classifiers combination. The cross-competence measure allows an ensemble to harness pieces of information obtained from incompetent...

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