Dataset Information

Compositional cubes: a new concept for multi-factorial compositions.

ABSTRACT: Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature, there is still a need for a comprehensive approach to the analysis of multi-factorial relative-valued data. Therefore, this contribution builds around the current knowledge about compositional data a general theoretical framework for k-factorial compositional data. As a main finding it turns out that, similar to the case of compositional tables, also the multi-factorial structures can be orthogonally decomposed into an independent and several interactive parts and, moreover, a coordinate representation allowing for their separate analysis by standard analytical methods can be constructed. For the sake of simplicity, these features are explained in detail for the case of three-factorial compositions (compositional cubes), followed by an outline covering the general case. The three-dimensional structure is analyzed in depth in two practical examples, dealing with systems of spatial and time dependent compositional cubes. The methodology is implemented in the R package robCompositions.

SUBMITTER: Facevicova K

PROVIDER: S-EPMC9366844 | biostudies-literature | 2023

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Compositional cubes: a new concept for multi-factorial compositions.

Fačevicová Kamila K Filzmoser Peter P Hron Karel K

Statistical papers (Berlin, Germany) 20220811 3

Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature, there is still a need for a comprehensive approach to the analysis of multi-factorial relative-valued data. Therefore, this contribution builds around the current knowledge about compositional data a general theoretical framework for <i>k</i>-factorial compositi ...[more]

PMID: 35971537

Similar Datasets

Project description:The concept of univentricular heart moved from hearts with only one ventricle connected with atria [double inlet ventricle or absent atrioventricular (AV) connection] to hearts not amenable to biventricular repair, namely hearts with two ventricles unable to sustain separately pulmonary and systemic circulations in sequence. In the latter definition, even hearts with one hypoplastic ventricle are considered "functional" univentricular hearts. They include pulmonary/aortic atresia or severe stenosis with hypoplastic ventricle, and rare conditions like huge intramural cardiac tumors and Ebstein anomaly with extreme atrialization of right ventricular cavity. In this setting, the surgical repair is univentricular with "Fontan" operation, bypassing the ventricular mass. In other words, functionally univentricular heart is a condition in which, after surgery, only one ventricle sustain systemic circulation. Univentricular hearts (double inlet or absent AV connection) almost invariably show two ventricular chambers, one main and one accessory, which lacks an inlet portion. The latter is located posteriorly when morphologically left and anteriorly when morphologically right. As far as double inlet left ventricle, this is usually associated with discordant ventriculo-arterial (VA) connection (transposition of the great arteries) and all the blood flow to the aorta, which takes origin from the hypoplastic anterior right ventricle, is ventricular septal defect (bulbo-ventricular foramen) dependent. If restrictive, an aortic arch obstruction may be present. Double inlet left ventricle may be rarely associated with VA concordance (Holmes heart). As far as double inlet right ventricle with posterior hypoplastic left ventricular cavity, ventriculo-arterial connection is usually of double outlet type; thus the term double inlet-outlet right ventricle may be coined. Absent right or left AV connection may develop in the setting of both d- or l-loop, whatever the situs. In this condition, the contra-lateral patent AV valve may be either mitral or tricuspid in terms of morphology and the underlying ventricle (main chamber) either morphologically left or right. Establishing the loop, whatever right or left (also called right or left ventricular topology), is a fundamental step in the segmental-sequential analysis of congenital heart disease.

Dataset Information

Compositional cubes: a new concept for multi-factorial compositions.

Publications

Compositional cubes: a new concept for multi-factorial compositions.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets