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A one-way ANOVA test for functional data with graphical interpretation

Tomáš Mrkvička, Mari Myllymäki, Milan Jílek, Ute Hahn (2020)

Kybernetika

A new functional ANOVA test, with a graphical interpretation of the result, is presented. The test is an extension of the global envelope test introduced by Myllymäki et al. (2017, Global envelope tests for spatial processes, J. R. Statist. Soc. B 79, 381-404, doi: 10.1111/rssb.12172). The graphical interpretation is realized by a global envelope which is drawn jointly for all samples of functions. If a mean function computed from the empirical data is out of the given envelope, the null hypothesis...

A practical application of kernel-based fuzzy discriminant analysis

Jian-Qiang Gao, Li-Ya Fan, Li Li, Li-Zhong Xu (2013)

International Journal of Applied Mathematics and Computer Science

A novel method for feature extraction and recognition called Kernel Fuzzy Discriminant Analysis (KFDA) is proposed in this paper to deal with recognition problems, e.g., for images. The KFDA method is obtained by combining the advantages of fuzzy methods and a kernel trick. Based on the orthogonal-triangular decomposition of a matrix and Singular Value Decomposition (SVD), two different variants, KFDA/QR and KFDA/SVD, of KFDA are obtained. In the proposed method, the membership degree is incorporated...

A proximity based macro stress testing framework

Boris Waelchli (2016)

Dependence Modeling

In this a paper a non-linear macro stress testing methodology with focus on early warning is developed. The methodology builds on a variant of Random Forests and its proximity measures. It is embedded in a framework, in which naturally defined contagion and feedback effects transfer the impact of stressing a relatively small part of the observations on the whole dataset, allowing to estimate a stressed future state. It will be shown that contagion can be directly derived from the proximities while...

A review of canonical coordinates and an alternative to correspondence analysis using Hellinger distance.

C. Radhakrishna Rao (1995)

Qüestiió

In this paper a general theory of canonical coordinates is developed for reduction of dimensionality in multivariate data, assessing the loss of information and plotting higher dimensional data in two or three dimensions for visual displays. The theory is applied to data in two way tables with variables in one category and samples (individual or populations) in the other. Two types of data are considered, one with continuous measurements on the variables and another with frequencies of attributes....

A scratch removal method

Michal Haindl, Stanislava Šimberová (1998)

Kybernetika

We present a new type of scratch removal algorithm based on a causal adaptive multidimensional prediction. The predictor use available information from the failed pixel surrounding due to spectral and spatial correlation of multispectral data but not any information from failed pixel itself. Predictor parameters cannot be directly identified so a special approximation is introduced.

A short note on multivariate dependence modeling

Vladislav Bína, Radim Jiroušek (2013)

Kybernetika

As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled...

A simple upper bound to the Bayes error probability for feature selection

Lorenzo Bruzzone, Sebastiano B. Serpico (1998)

Kybernetika

In this paper, feature selection in multiclass cases for classification of remote-sensing images is addressed. A criterion based on a simple upper bound to the error probability of the Bayes classifier for the minimum error is proposed. This criterion has the advantage of selecting features having a link with the error probability with a low computational load. Experiments have been carried out in order to compare the performances provided by the proposed criterion with the ones of some of the widely...

A study of the tangent space model of the von Mises-Fisher distrubution.

A. Chakak, L. Imhali (2003)

RACSAM

For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.

A subcopula based dependence measure

Arturo Erdely (2017)

Kybernetika

A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.

A survey on continuous elliptical vector distributions.

Eusebio Gómez, Miguel A. Gómez-Villegas, J. Miguel Marín (2003)

Revista Matemática Complutense

In this paper it is taken up a revision and characterization of the class of absolutely continuous elliptical distributions upon a parameterization based on the density function. Their properties (probabilistic characteristics, affine transformations, marginal and conditional distributions and regression) are shown in a practical and easy to interpret way. Two examples are fully undertaken: the multivariate double exponential distribution and the multivariate uniform distribution.

A variant of gravitational classification

Tomasz Górecki, Maciej Luczak (2014)

Biometrical Letters

In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement...

A viscosity solution method for Shape-From-Shading without image boundary data

Emmanuel Prados, Fabio Camilli, Olivier Faugeras (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we propose a solution of the Lambertian shape-from-shading (SFS) problem by designing a new mathematical framework based on the notion of viscosity solution. The power of our approach is twofolds: (1) it defines a notion of weak solutions (in the viscosity sense) which does not necessarily require boundary data. Moreover, it allows to characterize the viscosity solutions by their “minimums”; and (2) it unifies the works of [Rouy and Tourin, SIAM J. Numer. Anal.29 (1992) 867–884],...

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