Alpha generalised correlations between two compositional datasets
\(\alpha\) generalised correlations between two compositional datasets
Tuning of the alpha generalised correlations between two compositional datasets
Tuning of the alpha generalised correlations between two compositional datasets
Contour plot of the alpha multivariate normal in S^2
Contour plot of the \(\alpha\) multivariate normal in \(S^2\)
The alpha-k-NN regression with compositional predictor variables
The \(\alpha\)-k-NN regression with compositional predictor variables
Regularised and flexible discriminant analysis for compositional data using the alpha-transformation
Regularised and flexible discriminant analysis for compositional data using the \(\alpha\)-transformation
Energy test of equality of distributions using the alpha-transformation
Energy test of equality of distributions using the \(\alpha\)-transformation
The alpha-k-NN regression for compositional response data
The \(\alpha\)-k-NN regression for compositional response data
Cross validation for the alpha-kernel regression with compositional response data
Cross validation for the \(\alpha\)-kernel regression with compositional response data
The alpha-IT transformation
The \(\alpha\)-IT transformation
Principal coordinate analysis using the alpha-distance
Principal coordinate analysis using the \(\alpha\)-distance
Cross validation for the alpha-k-NN regression with compositional response data
Cross validation for the \(\alpha\)-k-NN regression with compositional response data
Cross validation for the regularised and flexible discriminant analysis with compositional data using the alpha-transformation
Cross validation for the regularised and flexible discriminant analysis with compositional data using the \(\alpha\)-transformation
Gaussian mixture models for compositional data using the alpha-transformation
Gaussian mixture models for compositional data using the \(\alpha\)-transformation
Cross-validation for the naive Bayes classifiers for compositional data using the alpha-transformation
Cross-validation for the naive Bayes classifiers for compositional data using the \(\alpha\)-transformation
Regression with compositional data using the alpha-transformation
Regression with compositional data using the \(\alpha\)-transformation
Cross validation for the alpha-k-NN regression with compositional predictor variables
Cross validation for the \(\alpha\)-k-NN regression with compositional predictor variables
Choose the number of principal components via reconstruction error
Choose the number of principal components via reconstruction error
Tuning of the k-NN algorithm for compositional data
Tuning of the k-NN algorithm for compositional data
Tuning the value of alpha in the alpha-regression
Tuning the value of \(\alpha\) in the \(\alpha\)-regression
Contour plot of the t distribution in S^2
Contour plot of the t distribution in \(S^2\)
The \(\alpha\)-transformation
Multivariate kernel density estimation for compositional data
Multivariate kernel density estimation for compositional data
Contour plot of the normal distribution in S^2
Contour plot of the normal distribution in \(S^2\)
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Exponential empirical likelihood hypothesis testing for two mean vectors
Exponential empirical likelihood hypothesis testing for two mean vectors
Contour plot of the Dirichlet distribution in S^2
Contour plot of the Dirichlet distribution in \(S^2\)
Contour plot of the kernel density estimate in S^2
Contour plot of the kernel density estimate in \(S^2\)
MLE of the Dirichlet distribution
MLE of the a Dirichlet distribution
Naive Bayes classifiers for compositional data using the alpha-transformation
Naive Bayes classifiers for compositional data using the \(\alpha\)-transformation
Ridge regression with compositional data in the covariates side using the alpha-transformation
Ridge regression with compositional data in the covariates side using the \(\alpha\)-transformation
Greenacre's power transformation
Greenacre's power transformation
Compositional Data Analysis
Principal component analysis using the alpha-transformation
Principal component analysis using the \(\alpha\)-transformation
Helper Frechet mean for compositional data
Helper Frechet mean for compositional data
Fast estimation of the value of alpha
Fast estimation of the value of \(\alpha\)
The Frechet mean for compositional data
The Frechet mean for compositional data
Two-sample test of high-dimensional means for compositional data
Two-sample test of high-dimensional means for compositional data
All pairwise additive log-ratio transformations
All pairwise additive log-ratio transformations
The k-nearest neighbours using the alpha-distance
The k-nearest neighbours using the \(\alpha\)-distance
LASSO log-ratio regression with compositional response
LASSO log-ratio regression with compositional response
Estimation of the value of alpha in the folded model
Estimation of the value of \(\alpha\) in the folded model
Tuning the number of PCs in the PCR with compositional data using the alpha-transformation
Tuning the number of PCs in the PCR with compositional data using the \(\alpha\)-transformation
ANOVA for the log-contrast regression versus the uncostrained log-contrast regression
ANOVA for the log-contrast regression versus the uncostrained log-contrast regression
Principal component analysis
Principal component analysis
Perturbation operation
LASSO Kullback-Leibler divergence based regression
LASSO Kullback-Leibler divergence based regression
Ridge regression with the alpha-transformation plot
Ridge regression plot
The Box-Cox transformation applied to ratios of components
The Box-Cox transformation applied to ratios of components
The \(\alpha\)-IT-distance
Beta regression
MLE of distributions defined in the (0, 1) interval
MLE of distributions defined in the (0, 1) interval
The k-NN algorithm for compositional data
The k-NN algorithm for compositional data
Cross-validation for the naive Bayes classifiers for compositional data
Cross-validation for the naive Bayes classifiers for compositional data
Cross-validation for the Dirichlet discriminant analysis
Cross-validation for the Dirichlet discriminant analysis
Cross-validation for the constrained linear least squares for compositional responses and predictors
Cross-validation for the constrained linear least squares for compositional
responses and predictors
Dirichlet discriminant analysis
Dirichlet discriminant analysis
Power operation
The pivot coordinate transformation and its inverse
The pivot coordinate transformation and its inverse
Naive Bayes classifiers for compositional data
Naive Bayes classifiers for compositional data
Tuning of the projection pursuit regression for compositional data
Tuning of the projection pursuit regression for compositional data
The alpha-kernel regression with compositional response data
The \(\alpha\)-kernel regression with compositional response data
Column-wise MLE of some univariate distributions
Column-wise MLE of some univariate distributions
Density of the folded normal distribution
Density of the folded model normal distribution
Bayesian network learning with compositional data
Bayesian network learning with compositional data
Density of the Flexible Dirichlet distribution
Density of the Flexible Dirichlet distribution
Estimating location and scatter parameters for compositional data
Estimating location and scatter parameters for compositional data
Cross validation for the ridge regression with compositional data as predictor using the alpha-transformation
Cross validation for the ridge regression with compositional data as predictor using the \(\alpha\)-transformation
Hypothesis testing for two or more compositional mean vectors
Hypothesis testing for two or more compositional mean vectors
Dirichlet regression
Contour plot of the alpha-folded model in S^2
Contour plot of the \(\alpha\)-folded model in \(S^2\)
MLE of the Dirichlet distribution via Newton-Rapshon
MLE of the Dirichlet distribution via Newton-Rapshon
Multivariate or univariate regression with compositional data in the covariates side using the alpha-transformation
Multivariate or univariate regression with compositional data in the covariates side using the \(\alpha\)-transformation
The folded power transformation
The folded power transformation
Projection pursuit regression with compositional predictor variables
Projection pursuit regression with compositional predictor variables
The Helmert sub-matrix
Density values of a mixture of Dirichlet distributions
Density values of a mixture of Dirichlet distributions
Principal component generalised linear models
Principal component generalised linear models
Cross validation for the transformation-free linear regression for compositional responses and predictors
Cross validation for the transformation-free linear regression for compositional
responses and predictors
Density of compositional data from Gaussian mixture models
Simulation of compositional data from Gaussian mixture models
Tuning the principal components with GLMs
Tuning the principal components with GLMs
Density values of a Dirichlet distribution
Density values of a Dirichlet distribution
Cross validation for the ridge regression
Cross validation for the ridge regression
Fitting a Flexible Dirichlet distribution
Fitting a Flexible Dirichlet distribution
Contour plot of the Flexible Dirichlet distribution in S^2
Contour plot of the Flexible Dirichlet distribution in \(S^2\)
Cross validation for the kernel regression with Euclidean response data
Cross validation for the kernel regression with Euclidean response data
Random values generation from some univariate distributions defined on the (0,1) interval
Random values generation from some univariate distributions defined on the \((0,1)\) interval
Divergence based regression for compositional data with compositional data in the covariates side using the alpha-transformation
Divergence based regression for compositional data with compositional data in the covariates side using the \(\alpha\)-transformation
Quasi binomial regression for proportions
Quasi binomial regression for proportions
Estimation of the value of alpha via the profile log-likelihood
Estimation of the value of \(\alpha\) via the alfa profile log-likelihood
Ridge regression plot
Hotelling's multivariate version of the 1 sample t-test for Euclidean data
Hotelling's multivariate version of the 1 sample t-test for Euclidean data
Ternary diagram
Ternary diagram of regression models
Ternary diagram of regression models
Ridge regression
Simulation of compositional data from Gaussian mixture models
Simulation of compositional data from Gaussian mixture models
MLE of the folded model for a given value of alpha
MLE of the folded model for a given value of \(\alpha\)
Inverse of the alpha-transformation
Inverse of the \(\alpha\)-transformation
Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions
Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions
Contour plot of the Kent distribution in S^2
Contour plot of the Kent distribution in \(S^2\)
The \(\alpha\)-distance
Cross validation for some compositional regression models
Cross validation for some compositional regression models
Kernel regression with a numerical response vector or matrix
Kernel regression with a numerical response vector or matrix
Empirical likelihood for a one sample mean vector hypothesis testing
Empirical likelihood for a one sample mean vector hypothesis testing
Empirical likelihood hypothesis testing for two mean vectors
Empirical likelihood hypothesis testing for two mean vectors
Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the alpha-transformation
Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the \(\alpha\)-transformation
Unconstrained log-contrast regression with multiple compositional predictors
Unconstrained log-contrast regression with multiple compositional predictors
Contour plot of mixtures of Dirichlet distributions in S^2
Contour plot of mixtures of Dirichlet distributions in \(S^2\)
Contour plot of the Gaussian mixture model in S^2
Contour plot of the Gaussian mixture model in \(S^2\)
Constrained linear least squares for compositional responses and predictors
Constrained linear least squares for compositional responses and predictors
MLE of the zero adjusted Dirichlet distribution
MLE of the zero adjusted Dirichlet distribution
Unit-Weibull regression models for proportions
Unit-Weibull regression models for proportions
Zero adjusted Dirichlet regression
Zero adjusted Dirichlet regression
Non linear least squares regression for compositional data
Non linear least squares regression for compositional data
Multivariate normal random values simulation on the simplex
Multivariate normal random values simulation on the simplex
Multivariate skew normal random values simulation on the simplex
Multivariate skew normal random values simulation on the simplex
Hotelling's multivariate version of the 2 sample t-test for Euclidean data
Hotelling's multivariate version of the 2 sample t-test for Euclidean data
ICE plot for univariate kernel regression
ICE plot for univariate kernel regression
Tuning the parameters of the regularised discriminant analysis
Tuning the parameters of the regularised discriminant analysis
Non parametric zero replacement strategies
Non parametric zero replacement strategies
The additive log-ratio transformation and its inverse
The additive log-ratio transformation and its inverse
Divergence based regression for compositional data
Divergence based regression for compositional data
Helper functions for the Kullback-Leibler regression
Helper functions for the Kullback-Leibler regression
Dirichlet random values simulation
Dirichlet random values simulation
Plot of the LASSO coefficients
Plot of the LASSO coefficients
Log-contrast regression with compositional predictor variables
Log-contrast regression with compositional predictor variables
Log-contrast logistic or Poisson regression with compositional predictor variables
Log-contrast logistic or Poisson regression with compositional predictor variables
Generate random folds for cross-validation
Generate random folds for cross-validation
Mixture model selection via BIC
Mixture model selection via BIC
Mixture model selection with the alpha-transformation using BIC
Mixture model selection with the \(\alpha\)-transformation using BIC
Projection pursuit regression for compositional data
Projection pursuit regression for compositional data
Multivariate linear regression
Multivariate linear regression
MLE for the multivariate t distribution
MLE for the multivariate t distribution
Total variability
Transformation-free linear regression for compositional responses and predictors
Transformation-free linear regression for compositional responses and predictors
Multivariate analysis of variance
Multivariate analysis of variance
Log-contrast regression with multiple compositional predictors
Log-contrast regression with multiple compositional predictors
Multivariate regression with compositional data
Multivariate regression with compositional data
Cross-validation for the LASSO Kullback-Leibler divergence based regression
Cross-validation for the LASSO Kullback-Leibler divergence based regression
Cross-validation for the LASSO log-ratio regression with compositional response
Cross-validation for the LASSO log-ratio regression with compositional response
Log-likelihood ratio test for a Dirichlet mean vector
Log-likelihood ratio test for a Dirichlet mean vector
Tuning of the bandwidth h of the kernel using the maximum likelihood cross validation
Tuning of the bandwidth h of the kernel using the maximum likelihood cross validation
Multivariate kernel density estimation
Multivariate kernel density estimation
Divergence matrix of compositional data
Divergence matrix of compositional data
The ESOV-distance
Estimation of the probability left outside the simplex when using the alpha-transformation
Estimation of the probability left outside the simplex when using the alpha-transformation
Tuning of the projection pursuit regression with compositional predictor variables
Tuning of the projection pursuit regression with compositional predictor variables
Simulation of compositional data from the Flexible Dirichlet distribution
Simulation of compositional data from the Flexible Dirichlet distribution
Unconstrained log-contrast logistic or Poisson regression with compositional predictor variables
Unconstrained log-contrast logistic or Poisson regression with compositional predictor variables
Simulation of compositional data from the folded normal distribution
Simulation of compositional data from the folded model normal distribution
Unconstrained log-contrast regression with compositional predictor variables
Unconstrained log-contrast regression with compositional predictor variables
Principal coordinate analysis using the Jensen-Shannon divergence
Principal coordinate analysis using the Jensen-Shannon divergence
ICE plot for projection pursuit regression with compositional predictor variables
ICE plot for projection pursuit regression with compositional predictor variables
James multivariate version of the t-test
James multivariate version of the t-test
Multivariate analysis of variance (James test)
Multivariate analysis of variance (James test)
Gaussian mixture models for compositional data
Gaussian mixture models for compositional data
Distance based regression models for proportions
Distance based regression models for proportions
Proportionality correlation coefficient matrix
Proportionality correlation coefficient matrix
Regularised discriminant analysis for Euclidean data
Regularised discriminant analysis for Euclidean data
Simulation of compositional data from mixtures of Dirichlet distributions
Simulation of compositional data from mixtures of Dirichlet distributions
Multivariate t random values simulation on the simplex
Multivariate t random values simulation on the simplex
Contour plot of the skew skew-normal distribution in S^2
Contour plot of the skew skew-normal distribution in \(S^2\)
Spatial median regression
Spatial median regression
Log-likelihood ratio test for a symmetric Dirichlet distribution
Log-likelihood ratio test for a symmetric Dirichlet distribution