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Canonical non-symmetrical correspondence analysis: an alternative in constrained ordination.

Priscila Willems, M. Purificación Galindo Villardon (2008)

SORT

Canonical non-symmetrical correspondence analysis is developed as an alternative method for constrained ordination, relating external information (e.g., environmental variables) with ecological data, considering species abundance as dependant on sites. Ordination axes are restricted to be linear combinations of the environmental variables, based on the information of the most abundant species. This extension and its associated unconstrained ordination method are terms of a global model that permits...

Central limit theorems for eigenvalues in a spiked population model

Zhidong Bai, Jian-Feng Yao (2008)

Annales de l'I.H.P. Probabilités et statistiques

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). This model is proposed by Johnstone to cope with empirical findings on various data sets. The question is to quantify the effect of the perturbation caused by the spike eigenvalues. A recent work by Baik and Silverstein establishes the almost sure limits of the extreme sample eigenvalues associated to the spike eigenvalues when the population and the...

Construction d'un schéma d'implication entre variables issues d'une analyse des correspondances multiples. Développements. Application

E. Henri Riard, M. Tensaout (1996)

Mathématiques et Sciences Humaines

L'une des limites de l'analyse des correspondances multiples appliquée à de grands tableaux de données qualitatives est la difficulté d'analyse et d'interprétation des structures de relations entre variables. Afin de dépasser la frontière descriptive, il est proposé une méthodologie de recherche de schémas d'implication reposant sur les fréquences conditionnelles données par les tableaux de Burt. L'analyse des correspondances multiples y est utilisée comme filtre principal de variables à partir...

Construction of nonlinear discrimination function based on the MDL criterion

Manabu Sato, Mineichi Kudo, Jun Toyama, Masaru Shimbo (1998)

Kybernetika

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.

Correspondence analysis and two-way clustering.

Antonio Ciampi, Ana González Marcos, Manuel Castejón Limas (2005)

SORT

Correspondence analysis followed by clustering of both rows and columns of a data matrix is proposed as an approach to two-way clustering. The novelty of this contribution consists of: i) proposing a simple method for the selecting of the number of axes; ii) visualizing the data matrix as is done in micro-array analysis; iii) enhancing this representation by emphasizing those variables and those individuals which are 'well represented' in the subspace of the chosen axes. The approach is applied...

Covariance Structure of Principal Components for Three-Part Compositional Data

Klára Hrůzová, Karel Hron, Miroslav Rypka, Eva Fišerová (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....

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