Tucker3 Model for Compositional Data

Gallo, Michele

doi:10.1080/03610926.2013.798664

Cited by 21 publications

(13 citation statements)

References 19 publications

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“…A particular version of the Tucker models for CoDa was proposed to analyze the chemical composition of surficial waters pertaining to the Arno river. Gallo () has shown how it is possible to apply the Tucker3 model for CoDa by discussing the results obtained when different kinds of preprocessing are used. Here, this approach was proposed for wPCA model, and a full interpretation of the results is given.…”

Section: Discussionmentioning

confidence: 99%

“…Thus, it is easy to verify that these constraints are automatically respected. Gallo (2012a) has shown that the loadings matrices of clr, plr, and ilr transformed data are strongly linked. In detail, the loadings matrices for the first and third modes are equivalent for the three transformations.…”

Section: The Tucker3 Model For Compositional Datamentioning

confidence: 99%

“…Starting from Gallo's (, ) study, the aim of this paper was to analyze CoDa through a special version of the Tucker model that is known as weighted PCA (wPCA; Ten Berge et al ., ) and by using some graphical procedures such as one‐mode plots, clr ‐joint biplot, and trajectory plots to visualize data. To this purpose, an extensive matrix related to a sampling carried out along the Arno river (central‐northern Apennines, Italy) between May 2002 and October 2003 (Nisi et al ., ; Nisi et al ., ) was analyzed.…”

Section: Introductionmentioning

confidence: 99%

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Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

Gallo

Buccianti

2013

Environmetrics

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Data collected for the investigation of the environmental and ecological characteristics of a river basin are often in the form of a large three-way array; hence, a particular version of the Tucker model could be applied to gather more information contained in such complex geochemical systems. Indeed, when the data are in compositional form, more attention must be given to the analysis of the numerical data. Recently, the Tucker3 model has been proposed to analyze compositional data characterized by a three-way structure. In this work, a particular version of the Tucker model, known as the weighted\ud principal component analysis, was used to analyze water samples collected from the Arno river (Tuscany, central Italy)\ud in order to evaluate the method’s effectiveness. Several graphical displays have been developed to allow an accurate and complete interpretation of results

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Section: Discussionmentioning

confidence: 99%

Section: The Tucker3 Model For Compositional Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

Gallo

Buccianti

2013

Environmetrics

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“…Tucker3 is another multivariate deconvolution method for higher-order data also known as "3-way principal component analysis (PCA)" [25]. It decomposes the three-way data as follows [9]:…”

Section: Theorymentioning

confidence: 99%

“…Both PARAFAC and Tucker3 decompose the three-way data into factors containing scores (information pertaining to the sample's variability) and two different loadings, one for the 1 st mode (e.g., emission) and another for the 2 nd mode (e.g., excitation) profiles [6,8]. The difference between these techniques is that 4 the Tucker3 method also generates a core array containing the scores and loadings weights for each factor generated [7][8][9]. Both PARAFAC and Tucker3 significantly reduce the dataset, speeding up computational processing time, solving problems of ill-conditioned data and removing interference.…”

Section: Introductionmentioning

confidence: 99%

TTWD-DA: A MATLAB toolbox for discriminant analysis based on trilinear three-way data

Morais

Lima

Martin

2019

Chemometrics and Intelligent Laboratory Systems

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Three-way trilinear data is increasingly used in chemical and biochemical applications. This type of data is composed of three-way structures representing two different signal responses and one sample dimension distributed among a 3D structure, such as the data represented by fluorescence excitation emission matrices (EMMs), spectral-pH responses, spectral-kinetic responses, spectral-electric potential responses, among others. Herein, we describe a new MATLAB toolbox for classification of trilinear three-way data using discriminant analysis techniques (linear discriminant analysis [LDA], quadratic discriminant analysis [QDA], and partial least squares discriminant analysis [PLS-DA]), termed "TTWD-DA". These discrimination techniques were coupled to multivariate deconvolution techniques by means of parallel factor analysis (PARAFAC) and Tucker3 algorithm. The toolbox is based on a user-friendly graphical interface, where these algorithms can be easily applied. Also, as output, multiple figures of merit are automatically calculated, such as accuracy, sensitivity and specificity. This software is free available online.

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Multiple and multiway correspondence analysis

Beh

Lombardo²

2019

WIREs Computational Stats

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One of the most popular, and versatile, ways of visually analyzing the associating between categorical data is to perform a correspondence analysis on the contingency table that is formed from their cross‐classification. Traditionally the analysis of multiple categorical variables involves transforming such a table into a two‐way form through “flattening,” stacking or by some other means; doing so leads to simple or multiple correspondence analysis. Although such a transformation does not always preserve some of the truly multivariate nature of the association. Therefore one may instead adopt the less common multiway correspondence analysis. This paper will briefly explore the development, literature, and possible research opportunities of multiple and multiway correspondence analysis. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Multivariate Analysis Statistical and Graphical Methods of Data Analysis > Dimension Reduction Data: Types and Structures > Categorical Data

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Tucker3 Model for Compositional Data

Cited by 21 publications

References 19 publications

Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

Weighted principal component analysis for compositional data: application example for the water chemistry of the Arno river (Tuscany, central Italy)

TTWD-DA: A MATLAB toolbox for discriminant analysis based on trilinear three-way data

Multiple and multiway correspondence analysis

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