From e7284babb05d1a2ea74dba27fff77ef843507288 Mon Sep 17 00:00:00 2001
From: Eric Coissac
Date: Wed, 21 Aug 2019 09:32:43 +0200
Subject: [PATCH] Adds some docs to the package

DESCRIPTION  5 ++++
NAMESPACE  1 +
R/corls_test.R  6 +++
R/covls.R  70 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++
R/procmod.R  3 +++
R/procmod_frame.R  10 ++++++
R/procuste.R  2 +
inst/REFERENCES.bib  406 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
man/getPermuteMatrix.Rd  9 ++++++++
man/internal.Trace.Rd  30 ++++++++++++++++++++++++++++++
man/internal.getPermuteMatrix.Rd  29 
man/protate.Rd  2 +
man/varls.Rd  65 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
manuscript/document.bib  398 
manuscript/figure/fig__r21.pdf  Bin 14208 > 0 bytes
manuscript/figure/fig__r2_vec1.pdf  Bin 13237 > 0 bytes
manuscript/figure/fig_h01.pdf  Bin 15696 > 0 bytes
manuscript/figure/fig_h0_111.pdf  Bin 11663 > 0 bytes
manuscript/figure/fig_nested_shared1.pdf  Bin 7609 > 0 bytes
manuscript/figure/fig_nested_shared_variation1.pdf  Bin 67986 > 0 bytes
manuscript/main.Rnw  22 +++++++++++++++++
manuscript/main.pdf  Bin 463576 > 0 bytes
manuscript/main.tex  32 ++++++++++++++++++++++
23 files changed, 615 insertions(+), 475 deletions()
create mode 100644 R/procmod.R
create mode 100755 inst/REFERENCES.bib
create mode 100644 man/internal.Trace.Rd
delete mode 100644 man/internal.getPermuteMatrix.Rd
delete mode 100755 manuscript/document.bib
diff git a/DESCRIPTION b/DESCRIPTION
index d4d9147..5577b12 100644
 a/DESCRIPTION
+++ b/DESCRIPTION
@@ 17,16 +17,19 @@ Imports: MASS,
mvtnorm,
stats,
doParallel,
 foreach
+ foreach,
+ Rdpack
Suggests: knitr,
rmarkdown,
roxygen2,
vegan
+RdMacros: Rdpack
VignetteBuilder: knitr
Collate:
'internals.R'
'procmod_frame.R'
'multivariate.R'
+ 'procmod.R'
'covls.R'
'corls_test.R'
'procuste.R'
diff git a/NAMESPACE b/NAMESPACE
index b28ed6b..c4d5721 100644
 a/NAMESPACE
+++ b/NAMESPACE
@@ 40,3 +40,4 @@ export(varls)
import(MASS)
import(doParallel)
import(foreach)
+importFrom(Rdpack,reprompt)
diff git a/R/corls_test.R b/R/corls_test.R
index 8def685..d241756 100644
 a/R/corls_test.R
+++ b/R/corls_test.R
@@ 6,9 +6,9 @@ NULL
#' Generate permutation matrix according to a schema.
#'
#' @param perm
#' @param n
#' @param strata
+#' @param perm xxx
+#' @param n zzz
+#' @param strata eeee
#'
#'
#' The permutation schema is defined using the `how` function.
diff git a/R/covls.R b/R/covls.R
index f16b683..f99b526 100644
 a/R/covls.R
+++ b/R/covls.R
@@ 1,3 +1,4 @@
+#' @include procmod.R
#' @include procmod_frame.R
#' @include multivariate.R
#' @import doParallel
@@ 12,6 +13,9 @@ registerDoParallel(1)
#' Compute the trace of a square matrix.
#'
+#' The trace of a square matrix is defined as the sum
+#' of its diagonal elements.
+#'
#' @param X a square matrix
#' @return the trace of X
#'
@@ 20,16 +24,12 @@ registerDoParallel(1)
#' ProcMod:::.Trace(m)
#' @note Internal function do not use.
#'
#' @rdname internal.getPermuteMatrix
+#' @rdname internal.Trace
#' @author Eric Coissac
#' @author Christelle GonindardMelodelima
#'
.Trace < function(X) sum(diag(X))
.estimate_mode < function(x) {
 d < density(x)
 d$x[which.max(d$y)]
}
.var2cor < function(c) {
v < sqrt(diag(c))
@@ 37,20 +37,62 @@ registerDoParallel(1)
c / vv
}
#' Compute the variance, covariance matrix of K coordinate matrices.
+#' Compute the procrustean variance, covariance matrix of K matrices.
#'
#' Covariance between two matrices is defined as the sum of the
#' sigular values of the X'Y matrix. All the matrices must have
+#' Procrustean covariance between two matrices X and Y, is defined as the sum
+#' of the singular values of the X'Y matrix
+#' \insertCite{Gower:71:00,Lingoes:74:00}{Rdpack}. Both the matrices must have
#' the same number of rows.
#'
#' @param ... the set of matrices
+#' \code{varls} computes the variance covariance matrix of a set of matrices
+#' following the above definition. The variances and covariances are corrected
+#' to avoid over fitting \insertCite{CoissacEric:19:00}{Rdpack}. .
+#'
+#' Before computing the covariances, matrices are projected into an
+#' orthogonal space using the \code{\link[ProcMod]{ortho}} function.
+#'
+#' @references{
+#' \insertRef{Gower:71:00}{ProcMod}
+#'
+#' \insertRef{Lingoes:74:00}{ProcMod}
+#'
+#' \insertRef{CoissacEric:19:00}{ProcMod}
+#' }
+#'
+#' @param ... the set of matrices or a \code{\link[ProcMod]{procmod.frame}}
+#' object.
#' @param nrand number of randomisation used to estimate the mean
#' covariance observed between two random matrix.
+#' If rand is \code{NULL} or equal to \code{0}, no correction
+#' is estimated and the raw procrustean covariances are
+#' estimated.
#' @param p.adjust.method the multiple test correction method used
#' to adjust p values. \code{p.adjust.method} belongs
#' one of the folowing values: "holm", "hochberg", "hommel",
#' "bonferroni", "BH", "BY", "fdr", "none". The default is
#' set to "holm".
+#' to adjust p values. \code{\link[stats]{p.adjust.method}}
+#' belongsone of the folowing values: \code{"holm"},
+#' \code{"hochberg"}, \code{"hommel"}, \code{"bonferroni"},
+#' \code{"BH"}, \code{"BY"}, \code{"fdr"}, \code{"none"}.
+#' The default is,set to \code{"holm"}.
+#'
+#' @return a \code{procmod.varls} object which corresponds to a numeric
+#' matrix annotated by several attributes.
+#'
+#' The following attribute is always added:
+#'
+#'  \code{nrand} an integer value indicating the number of
+#' randomisations used to estimate the mean of the random
+#' covariance.
+#'
+#' When \code{nrand} is greater than 0 a couple of attributes
+#' is added:
+#'
+#'  \code{rcovls} a numeric matrix containing the estimation
+#' of the mean of the random covariance.
+#'
+#'  \code{p.value} a numeric matrix containing the estimations
+#' of the p.values of tests checking that the observed
+#' covariance is larger than the mean of the random covariance.
+#' p.values are corrected for multiple tests according to the
+#' method specified by the \code{p.adjust.method} parameter.
#'
#' @examples
#' # Build Three matrices of 3 rows.
@@ 60,6 +102,8 @@ registerDoParallel(1)
#' # compute the variance covariance matrix
#' varls(A, B, C)
#' varls(A = A, B = B, C = C)
+#' data = procmod.frame(A = A, B = B, C = C)
+#' varls(data)
#' @author Eric Coissac
#' @author Christelle GonindardMelodelima
#' @export
diff git a/R/procmod.R b/R/procmod.R
new file mode 100644
index 0000000..d21412e
 /dev/null
+++ b/R/procmod.R
@@ 0,0 +1,3 @@
+#' @docType package
+#' @importFrom Rdpack reprompt
+NULL
diff git a/R/procmod_frame.R b/R/procmod_frame.R
index 82dd13c..268a823 100644
 a/R/procmod_frame.R
+++ b/R/procmod_frame.R
@@ 238,7 +238,7 @@ procmod.frame < function(...,
.siteNames(value[[i]]) < NULL
}
 return(make_subS3Class(value, "procmod.frame"))
+ make_subS3Class(value, "procmod.frame")
}
#'
@@ 386,7 +386,8 @@ dim.procmod.frame < function(x)
#' @export
`$<.procmod.frame` < function(x, name, value) {
x[[name]] < value
 return(x)
+
+ x
}
#' @author Eric Coissac
@@ 437,7 +438,7 @@ dim.procmod.frame < function(x)
attr(y, "row.names") < rownames(y[[1]])
}
 return(y)
+ y
}
#' @author Eric Coissac
@@ 469,5 +470,6 @@ subset.procmod.frame < function(x, subset, select, drop = FALSE, ...) {
#' @export
as.list.procmod.frame < function(x, ...) {
class(x) < "list"
 return(x)
+
+ x
}
diff git a/R/procuste.R b/R/procuste.R
index 994bcb2..74ad3e1 100644
 a/R/procuste.R
+++ b/R/procuste.R
@@ 11,7 +11,7 @@ NULL
#'
#' The optimal rotation is computed according to the procruste methode.
#' Rotation is based on singular value decomposition (SVD).
#' No scaling is done, only the rotation.
+#' No scaling and no centrering are done, before computing the SVD.
#'
#' @param src a numeric matrix to be rotated
#' @param dest a numeric matrix used as reference space
diff git a/inst/REFERENCES.bib b/inst/REFERENCES.bib
new file mode 100755
index 0000000..27b9cee
 /dev/null
+++ b/inst/REFERENCES.bib
@@ 0,0 +1,406 @@
+%% This BibTeX bibliography file was created using BibDesk.
+%% http://bibdesk.sourceforge.net/
+
+
+%% Created for Eric Coissac at 20190819 09:13:32 +0200
+
+
+%% Saved with string encoding Unicode (UTF8)
+
+
+@comment{jabrefmeta: selector_publisher:}
+@comment{jabrefmeta: selector_author:}
+@comment{jabrefmeta: selector_journal:}
+@comment{jabrefmeta: selector_keywords:}
+
+
+
+@article{CoissacEric:19:00,
+ Author = {Coissac, Eric and GonindardMelodelima, Christelle},
+ DateAdded = {20190819 09:07:57 +0200},
+ DateModified = {20190819 09:12:35 +0200},
+ Journal = {in prep},
+ Title = {Assessing the shared variation among highdimensional data matrices: a modified version of the Procrustean correlation coefficient},
+ Year = {2019}}
+
+@book{Theil:58:00,
+ Address = {Amsterdam},
+ Annote = {Le R2 ajuster de R
+
+http://www.sudoc.abes.fr/xslt/DB=2.1//SRCH?IKT=12&TRM=005519756
+
+},
+ Author = {Theil, Henri, and Cramer, Jan Salomon, and Moerman, H. and Russchen, A.},
+ DateAdded = {20190711 15:10:21 +0200},
+ DateModified = {20190819 09:13:20 +0200},
+ Keywords = {Economics, Mathematical; Forecasting; Business},
+ Language = {en},
+ Pages = {213},
+ Publisher = {NorthHolland Publishing Company},
+ Title = {Economic forecasts and policy},
+ Year = 1958}
+
+@misc{CSoRgo:96:00,
+ Author = {Cs{\"o}rg{\H o}, S{\'a}ndor and Faraway, Julian J},
+ DateAdded = {20190520 11:28:37 +0200},
+ DateModified = {20190520 11:32:25 +0200},
+ Journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
+ Number = 1,
+ Pages = {221234},
+ Title = {The Exact and Asymptotic Distributions of {Cram{\'e}rVon} Mises Statistics},
+ Volume = 58,
+ Year = 1996}
+
+@article{Robert:76:00,
+ Abstract = {[Consider two data matrices on the same sample of n individuals,
+ X(p $\times$ n), Y(q $\times$ n). From these matrices,
+ geometrical representations of the sample are obtained as two
+ configurations of n points, in Rp and Rq. It is shown that the
+ RVcoefficient (Escoufier, 1970, 1973) can be used as a measure
+ of similarity of the two configurations, taking into account the
+ possibly distinct metrics to be used on them to measure the
+ distances between points. The purpose of this paper is to show
+ that most classical methods of linear multivariate statistical
+ analysis can be interpreted as the search for optimal linear
+ transformations or, equivalently, the search for optimal metrics
+ to apply on two data matrices on the same sample; the optimality
+ is defined in terms of the similarity of the corresponing
+ configurations of points. which, in turn, calls for the
+ maximization of the associated RVcoefficient. The methods
+ studied are principal components, principal components of
+ instrumental variables, multivariate regression, canonical
+ variables, discriminant analysis; they are differentiated by the
+ possible relationships existing between the two data matrices
+ involved and by additional constraints under which the maximum
+ of RV is to be obtained. It is also shown that the
+ RVcoefficient can be used as a measure of goodness of a
+ solution to the problem of discarding variables.]},
+ Author = {Robert, P and Escoufier, Y},
+ DateAdded = {20190517 10:53:50 +0200},
+ DateModified = {20190517 10:54:04 +0200},
+ Journal = {J. R. Stat. Soc. Ser. C Appl. Stat.},
+ Number = 3,
+ Pages = {257265},
+ Publisher = {[Wiley, Royal Statistical Society]},
+ Title = {A Unifying Tool for Linear Multivariate Statistical Methods: The {RV} Coefficient},
+ Volume = 25,
+ Year = 1976}
+
+@article{Mayer:11:00,
+ Abstract = {The integration of multiple highdimensional data sets (omics
+ data) has been a very active but challenging area of
+ bioinformatics research in recent years. Various adaptations of
+ nonstandard multivariate statistical tools have been suggested
+ that allow to analyze and visualize such data sets
+ simultaneously. However, these methods typically can deal with
+ two data sets only, whereas systems biology experiments often
+ generate larger numbers of highdimensional data sets. For this
+ reason, we suggest an explorative analysis of similarity between
+ data sets as an initial analysis steps. This analysis is based on
+ the RV coefficient, a matrix correlation, that can be interpreted
+ as a generalization of the squared correlation from two single
+ variables to two sets of variables. It has been shown before
+ however that the highdimensionality of the data introduces
+ substantial bias to the RV. We therefore introduce an alternative
+ version, the adjusted RV, which is unbiased in the case of
+ independent data sets. We can also show that in many situations,
+ particularly for very highdimensional data sets, the adjusted RV
+ is a better estimator than previously RV versions in terms of the
+ mean square error and the power of the independence test based on
+ it. We demonstrate the usefulness of the adjusted RV by applying
+ it to data set of 19 different multivariate data sets from a
+ systems biology experiment. The pairwise RV values between the
+ data sets define a similarity matrix that we can use as an input
+ to a hierarchical clustering or a multidimensional scaling. We
+ show that this reveals biological meaningful subgroups of data
+ sets in our study.},
+ Author = {Mayer, ClausDieter and Lorent, Julie and Horgan, Graham W},
+ DateAdded = {20190517 10:52:46 +0200},
+ DateModified = {20190517 10:52:51 +0200},
+ Journal = {Stat. Appl. Genet. Mol. Biol.},
+ Language = {en},
+ Pages = {Article 14},
+ Title = {Exploratory analysis of multiple omics datasets using the adjusted {RV} coefficient},
+ Volume = 10,
+ Year = 2011}
+
+@article{ElGhaziri:15:00,
+ Abstract = {We review three measures of association between two datasets in
+ view of their use in sensory data. The aim is threefold: (i) to
+ show in which situations each measure of association is
+ appropriate, (ii) to show their properties and how they can be
+ applied efficiently to sensory data, (iii) to compare them. The
+ three measures of association are multivariate correlation
+ coefficient, RV coefficient and Procrustes similarity index. A
+ particular emphasis is put on RV coefficient since it is very
+ popular among sensory scientists. We stress the properties and
+ shortcomings of this coefficient and propose an adjusted RV
+ coefficient to be used instead of RV coefficient, particularly in
+ situations where the number of samples is small or/and the number
+ of variables is large.},
+ Author = {El Ghaziri, Ang{\'e}lina and Qannari, El Mostafa},
+ DateAdded = {20190517 10:52:46 +0200},
+ DateModified = {20190517 10:52:51 +0200},
+ Journal = {Food Qual. Prefer.},
+ Keywords = {Multivariate correlation coefficient; Procrustes similarity index; RV coefficient; Permutation test; Adjusted RV coefficient},
+ Month = mar,
+ Pages = {116124},
+ Title = {Measures of association between two datasets; Application to sensory data},
+ Volume = 40,
+ Year = 2015}
+
+@article{Jackson:95:00,
+ Abstract = {Abstract:A multivariate measure of the concordance or
+ association between matrices of species abundances and
+ environmental variables was generally lacking in ecology until
+ recently. Traditional statistical procedures comparing such
+ relationships are often unsuitable because of nonlinearity
+ among species and/or environmental data. To address these
+ problems, I propose a randomization test based on Procrustes
+ analysis. One matrix is subject to reflection, rigid rotation,
+ translation, and dilation to minimize the sum of the squared
+ residual deviations between points for each observation and the
+ identical observation in the target matrix. This is a classical
+ Procrustes approach to matrix analysis. To assess the
+ significance of this measure of matrix concordance, I use a
+ randomization test to determine whether the sum of residual
+ deviations is less than that expected by chance. The PROcrustean
+ randomization TEST (PROTEST) may be used with either raw data
+ matrices or with multivariate summaries of the original data
+ (i.e. both direct or indirect gradient analysis). I provide
+ examples of PROTEST analyses with benthic invertebrate
+ communities, lakewater chemistry, lake morphology, and lake
+ geographic position. Significant concordance between the benthic
+ community and both lakewater chemistry and geographic position
+ were found. PROTEST results differed from Mantel test results as
+ the choice of distance measure with Mantel tests will influence
+ the level of significance obtained.},
+ Author = {Jackson, Donald A},
+ DateAdded = {20190514 18:22:51 +0200},
+ DateModified = {20190514 18:22:54 +0200},
+ Journal = {{\'E}coscience},
+ Month = jan,
+ Number = 3,
+ Pages = {297303},
+ Publisher = {Taylor \& Francis},
+ Title = {{PROTEST}: A {PROcrustean} Randomization {TEST} of community environment concordance},
+ Volume = 2,
+ Year = 1995}
+
+@article{Dray:07:00,
+ Abstract = {Multivariate analyses are well known and widely used to identify
+ and understand structures of ecological communities. The ade4
+ package for the R statistical environment proposes a great number
+ of multivariate methods. Its implementation follows the tradition
+ of the French school of ``Analyse des Donnees'' and is based on
+ the use of the duality diagram. We present the theory of the
+ duality diagram and discuss its implementation in ade4. Classes
+ and main functions are presented. An example is given to
+ illustrate the ade4 philosophy.},
+ Author = {Dray, St{\'e}phane and Dufour, AnneB{\'e}atrice},
+ DateAdded = {20190513 19:18:23 +0200},
+ DateModified = {20190513 19:18:25 +0200},
+ Journal = {Journal of Statistical Software, Articles},
+ Number = 4,
+ Pages = {120},
+ Title = {The ade4 Package: Implementing the Duality Diagram for Ecologists},
+ Volume = 22,
+ Year = 2007}
+
+@article{Dixon:03:00,
+ Abstract = {Abstract. VEGAN adds vegetation analysis functions to the
+ generalpurpose statistical program R. Both R and VEGAN can be
+ downloaded for free. VEGAN implements several ordination methods,
+ including Canonical Correspondence Analysis and Nonmetric
+ Multidimensional Scaling, vector fitting of environmental
+ variables, randomization tests, and various other analyses of
+ vegetation data. It can be used for large data. Graphical output
+ can be customized using the R language's extensive graphics
+ capabilities. VEGAN is appropriate for routine and research use,
+ if you are willing to learn some R.},
+ Author = {Dixon, Philip},
+ DateAdded = {20190513 19:15:06 +0200},
+ DateModified = {20190513 19:15:09 +0200},
+ Journal = {J. Veg. Sci.},
+ Month = dec,
+ Number = 6,
+ Pages = {927930},
+ Title = {{VEGAN}, a package of {R} functions for community ecology},
+ Volume = 14,
+ Year = 2003}
+
+@book{Bravais:44:00,
+ Author = {Bravais, A},
+ DateAdded = {20190510 13:28:14 +0200},
+ DateModified = {20190510 13:28:16 +0200},
+ Language = {fr},
+ Publisher = {Impr. Royale},
+ Title = {Analyse math{\'e}matique sur les probabilit{\'e}s des erreurs de situation d'un point},
+ Year = 1844}
+
+@article{PeresNeto:01:00,
+ Abstract = {The Mantel test provides a means to test the association between
+ distance matrices and has been widely used in ecological and
+ evolutionary studies. Recently, another permutation test based on
+ a Procrustes statistic (PROTEST) was developed to compare
+ multivariate data sets. Our study contrasts the effectiveness, in
+ terms of power and type I error rates, of the Mantel test and
+ PROTEST. We illustrate the application of Procrustes
+ superimposition to visually examine the concordance of
+ observations for each dimension separately and how to conduct
+ hypothesis testing in which the association between two data sets
+ is tested while controlling for the variation related to other
+ sources of data. Our simulation results show that PROTEST is as
+ powerful or more powerful than the Mantel test for detecting
+ matrix association under a variety of possible scenarios. As a
+ result of the increased power of PROTEST and the ability to
+ assess the match for individual observations (not available with
+ the Mantel test), biologists now have an additional and powerful
+ analytical tool to study ecological and evolutionary
+ relationships.},
+ Author = {PeresNeto, Pedro R and Jackson, Donald A},
+ DateAdded = {20190510 12:59:02 +0200},
+ DateModified = {20190510 12:59:05 +0200},
+ Journal = {Oecologia},
+ Keywords = {Mantel test; Matrix association; Multivariate analysis; Procrustes analysis; Randomization test},
+ Language = {en},
+ Month = oct,
+ Number = 2,
+ Pages = {169178},
+ Title = {How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test},
+ Volume = 129,
+ Year = 2001}
+
+@article{Gower:71:00,
+ Author = {Gower, J C},
+ DateAdded = {20190419 12:11:20 +0200},
+ DateModified = {20190419 12:11:23 +0200},
+ Journal = {Mathematics in the archaeological and historical sciences},
+ Pages = {138149},
+ Publisher = {Edinburgh University Press Edinburgh},
+ Title = {Statistical methods of comparing different multivariate analyses of the same data},
+ Year = 1971}
+
+@article{Lingoes:74:00,
+ Abstract = {In connection with a leastsquares solution for fitting one
+ matrix,A, to another,B, under optimal choice of a rigid motion
+ and a dilation, Sch{\"o}nemann and Carroll suggested two measures
+ of fit: a raw measure,e, and a refined similarity measure,es,
+ which is symmetric. Both measures share the weakness of depending
+ upon the norm of the target matrix,B,e.g.,e(A,kB) $\neq$e(A,B)
+ fork $\neq$ 1. Therefore, both measures are useless for answering
+ questions of the type: ``DoesA fitB better thanA fitsC?''. In
+ this note two new measures of fit are suggested which do not
+ depend upon the norms ofA andB, which are (0, 1)bounded, and
+ which, therefore, provide meaningful answers for comparative
+ analyses.},
+ Author = {Lingoes, James C and Sch{\"o}nemann, Peter H},
+ DateAdded = {20190419 12:07:12 +0200},
+ DateModified = {20190419 12:07:17 +0200},
+ Journal = {Psychometrika},
+ Month = dec,
+ Number = 4,
+ Pages = {423427},
+ Title = {Alternative measures of fit for the Sch{\"o}nemanncarroll matrix fitting algorithm},
+ Volume = 39,
+ Year = 1974}
+
+@article{SzeKely:13:00,
+ Address = {Orlando, FL, USA},
+ Author = {Sz{\'e}Kely, G{\'a}bor J and Rizzo, Maria L},
+ DateAdded = {20190419 00:38:28 +0200},
+ DateModified = {20190419 00:38:39 +0200},
+ Journal = {J. Multivar. Anal.},
+ Keywords = {Distance correlation, Distance covariance, High dimension, Multivariate independence, dCor, dCov, primary, secondary},
+ Month = may,
+ Pages = {193213},
+ Publisher = {Academic Press, Inc.},
+ Title = {The Distance Correlation Ttest of Independence in High Dimension},
+ Volume = 117,
+ Year = 2013}
+
+@article{Szekely:07:00,
+ Abstract = {Project Euclid  mathematics and statistics online},
+ Author = {Sz{\'e}kely, G{\'a}bor J and Rizzo, Maria L and Bakirov, Nail K},
+ DateAdded = {20190419 00:25:31 +0200},
+ DateModified = {20190419 00:25:35 +0200},
+ Journal = {Ann. Stat.},
+ Keywords = {Distance correlation; distance covariance; multivariate independence},
+ Language = {en},
+ Month = dec,
+ Number = 6,
+ Pages = {27692794},
+ Publisher = {Institute of Mathematical Statistics},
+ Title = {Measuring and testing dependence by correlation of distances},
+ Volume = 35,
+ Year = 2007}
+
+@article{Escoufier:73:00,
+ Author = {Escoufier, Yves},
+ DateAdded = {20190419 00:11:19 +0200},
+ DateModified = {20190419 00:11:23 +0200},
+ Journal = {Biometrics},
+ Pages = {751760},
+ Publisher = {JSTOR},
+ Title = {Le traitement des variables vectorielles},
+ Year = 1973}
+
+@article{Smilde:09:00,
+ Abstract = {MOTIVATION: Modern functional genomics generates highdimensional
+ datasets. It is often convenient to have a single simple number
+ characterizing the relationship between pairs of such
+ highdimensional datasets in a comprehensive way. Matrix
+ correlations are such numbers and are appealing since they can be
+ interpreted in the same way as Pearson's correlations familiar to
+ biologists. The highdimensionality of functional genomics data
+ is, however, problematic for existing matrix correlations. The
+ motivation of this article is 2fold: (i) we introduce the idea
+ of matrix correlations to the bioinformatics community and (ii)
+ we give an improvement of the most promising matrix correlation
+ coefficient (the RVcoefficient) circumventing the problems of
+ highdimensional data. RESULTS: The modified RVcoefficient can
+ be used in highdimensional data analysis studies as an easy
+ measure of common information of two datasets. This is shown by
+ theoretical arguments, simulations and applications to two
+ reallife examples from functional genomics, i.e. a
+ transcriptomics and metabolomics example. AVAILABILITY: The
+ Matlab mfiles of the methods presented can be downloaded from
+ http://www.bdagroup.nl.},
+ Author = {Smilde, A K and Kiers, H A L and Bijlsma, S and Rubingh, C M and van Erk, M J},
+ DateAdded = {20190419 00:08:07 +0200},
+ DateModified = {20190419 00:08:17 +0200},
+ Journal = {Bioinformatics},
+ Language = {en},
+ Month = feb,
+ Number = 3,
+ Pages = {401405},
+ Title = {Matrix correlations for highdimensional data: the modified {RVcoefficient}},
+ Volume = 25,
+ Year = 2009}
+
+@article{Ramsay:84:00,
+ Abstract = {A correlational measure for ann byp matrixX and ann byq matrixY
+ assesses their relation without specifying either as a fixed
+ target. This paper discusses a number of useful measures of
+ correlation, with emphasis on measures which are invariant with
+ respect to rotations or changes in singular values of either
+ matrix. The maximization of matrix correlation with respect to
+ transformationsXL andYM is discussed where one or both
+ transformations are constrained to be orthogonal. Special
+ attention is focussed on transformations which causeXL andYM to
+ ben bys, wheres may be any number between 1 and min (p, q). An
+ efficient algorithm is described for maximizing the correlation
+ betweenXL andYM where analytic solutions do not exist. A factor
+ analytic example is presented illustrating the advantages of
+ various coefficients and of varying the number of columns of the
+ transformed matrices.},
+ Author = {Ramsay, J O and ten Berge, Jos and Styan, G P H},
+ DateAdded = {20190418 23:38:55 +0200},
+ DateModified = {20190418 23:39:01 +0200},
+ Journal = {Psychometrika},
+ Month = sep,
+ Number = 3,
+ Pages = {403423},
+ Title = {Matrix correlation},
+ Volume = 49,
+ Year = 1984}
diff git a/man/getPermuteMatrix.Rd b/man/getPermuteMatrix.Rd
index dcc665f..aa7d29b 100644
 a/man/getPermuteMatrix.Rd
+++ b/man/getPermuteMatrix.Rd
@@ 7,7 +7,14 @@
getPermuteMatrix(perm, n, strata = NULL)
}
\arguments{
\item{strata}{The permutation schema is defined using the `how` function.
+\item{perm}{xxx}
+
+\item{n}{zzz}
+
+\item{strata}{eeee
+
+
+The permutation schema is defined using the `how` function.
The implementation of this function is inspired
from the VEGAN package and reproduced here to avoid an extra
dependency on an hidden vegan function.}
diff git a/man/internal.Trace.Rd b/man/internal.Trace.Rd
new file mode 100644
index 0000000..621c6ef
 /dev/null
+++ b/man/internal.Trace.Rd
@@ 0,0 +1,30 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/covls.R
+\name{.Trace}
+\alias{.Trace}
+\title{Compute the trace of a square matrix.}
+\usage{
+.Trace(X)
+}
+\arguments{
+\item{X}{a square matrix}
+}
+\value{
+the trace of X
+}
+\description{
+The trace of a square matrix is defined as the sum
+of its diagonal elements.
+}
+\note{
+Internal function do not use.
+}
+\examples{
+m < matrix(1:16, nrow = 4)
+ProcMod:::.Trace(m)
+}
+\author{
+Eric Coissac
+
+Christelle GonindardMelodelima
+}
diff git a/man/internal.getPermuteMatrix.Rd b/man/internal.getPermuteMatrix.Rd
deleted file mode 100644
index fd60210..0000000
 a/man/internal.getPermuteMatrix.Rd
+++ /dev/null
@@ 1,29 +0,0 @@
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/covls.R
\name{.Trace}
\alias{.Trace}
\title{Compute the trace of a square matrix.}
\usage{
.Trace(X)
}
\arguments{
\item{X}{a square matrix}
}
\value{
the trace of X
}
\description{
Compute the trace of a square matrix.
}
\note{
Internal function do not use.
}
\examples{
m < matrix(1:16, nrow = 4)
ProcMod:::.Trace(m)
}
\author{
Eric Coissac

Christelle GonindardMelodelima
}
diff git a/man/protate.Rd b/man/protate.Rd
index 856d82d..2dec9ea 100644
 a/man/protate.Rd
+++ b/man/protate.Rd
@@ 17,7 +17,7 @@ a numeric matrix
\description{
The optimal rotation is computed according to the procruste methode.
Rotation is based on singular value decomposition (SVD).
No scaling is done, only the rotation.
+No scaling and no centrering are done, before computing the SVD.
}
\examples{
# Renerate a random matrix of size 10 x 15
diff git a/man/varls.Rd b/man/varls.Rd
index 33ba786..0f3ac26 100644
 a/man/varls.Rd
+++ b/man/varls.Rd
@@ 2,27 +2,63 @@
% Please edit documentation in R/covls.R
\name{varls}
\alias{varls}
\title{Compute the variance, covariance matrix of K coordinate matrices.}
+\title{Compute the procrustean variance, covariance matrix of K matrices.}
\usage{
varls(..., nrand = 100, p.adjust.method = "holm")
}
\arguments{
\item{...}{the set of matrices}
+\item{...}{the set of matrices or a \code{\link[ProcMod]{procmod.frame}}
+object.}
\item{nrand}{number of randomisation used to estimate the mean
covariance observed between two random matrix.}
+covariance observed between two random matrix.
+If rand is \code{NULL} or equal to \code{0}, no correction
+is estimated and the raw procrustean covariances are
+estimated.}
\item{p.adjust.method}{the multiple test correction method used
to adjust p values. \code{p.adjust.method} belongs
one of the folowing values: "holm", "hochberg", "hommel",
"bonferroni", "BH", "BY", "fdr", "none". The default is
set to "holm".}
+to adjust p values. \code{\link[stats]{p.adjust.method}}
+belongsone of the folowing values: \code{"holm"},
+\code{"hochberg"}, \code{"hommel"}, \code{"bonferroni"},
+\code{"BH"}, \code{"BY"}, \code{"fdr"}, \code{"none"}.
+The default is,set to \code{"holm"}.}
+}
+\value{
+a \code{procmod.varls} object which corresponds to a numeric
+ matrix annotated by several attributes.
+
+ The following attribute is always added:
+
+  \code{nrand} an integer value indicating the number of
+ randomisations used to estimate the mean of the random
+ covariance.
+
+ When \code{nrand} is greater than 0 a couple of attributes
+ is added:
+
+  \code{rcovls} a numeric matrix containing the estimation
+ of the mean of the random covariance.
+
+  \code{p.value} a numeric matrix containing the estimations
+ of the p.values of tests checking that the observed
+ covariance is larger than the mean of the random covariance.
+ p.values are corrected for multiple tests according to the
+ method specified by the \code{p.adjust.method} parameter.
}
\description{
Covariance between two matrices is defined as the sum of the
sigular values of the X'Y matrix. All the matrices must have
+Procrustean covariance between two matrices X and Y, is defined as the sum
+of the singular values of the X'Y matrix
+\insertCite{Gower:71:00,Lingoes:74:00}{Rdpack}. Both the matrices must have
the same number of rows.
}
+\details{
+\code{varls} computes the variance covariance matrix of a set of matrices
+following the above definition. The variances and covariances are corrected
+to avoid over fitting \insertCite{CoissacEric:19:00}{Rdpack}. .
+
+Before computing the covariances, matrices are projected into an
+orthogonal space using the \code{\link[ProcMod]{ortho}} function.
+}
\examples{
# Build Three matrices of 3 rows.
A < matrix(1:9, nrow = 3)
@@ 31,6 +67,17 @@ C < matrix(20:31, nrow = 3)
# compute the variance covariance matrix
varls(A, B, C)
varls(A = A, B = B, C = C)
+data = procmod.frame(A = A, B = B, C = C)
+varls(data)
+}
+\references{
+{
+ \insertRef{Gower:71:00}{ProcMod}
+
+ \insertRef{Lingoes:74:00}{ProcMod}
+
+ \insertRef{CoissacEric:19:00}{ProcMod}
+}
}
\author{
Eric Coissac
diff git a/manuscript/document.bib b/manuscript/document.bib
deleted file mode 100755
index 189a95e..0000000
 a/manuscript/document.bib
+++ /dev/null
@@ 1,398 +0,0 @@
%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/


%% Created for Eric Coissac at 20190712 16:37:23 +0200


%% Saved with string encoding Unicode (UTF8)


@comment{jabrefmeta: selector_publisher:}
@comment{jabrefmeta: selector_author:}
@comment{jabrefmeta: selector_journal:}
@comment{jabrefmeta: selector_keywords:}



@inbook{Theil:58:00,
 Address = {Amsterdam},
 Annote = {Le R2 ajuster de R

http://www.sudoc.abes.fr/xslt/DB=2.1//SRCH?IKT=12&TRM=005519756

},
 Author = {Theil, Henri, and Cramer, Jan Salomon, and Moerman, H. and Russchen, A.},
 DateAdded = {20190711 15:10:21 +0200},
 DateModified = {20190712 16:37:23 +0200},
 Keywords = {Economics, Mathematical; Forecasting; Business},
 Language = {en},
 Pages = {213},
 Publisher = {NorthHolland Publishing Company},
 Title = {Economic forecasts and policy},
 Year = 1958}

@misc{CSoRgo:96:00,
 Author = {Cs{\"o}rg{\H o}, S{\'a}ndor and Faraway, Julian J},
 DateAdded = {20190520 11:28:37 +0200},
 DateModified = {20190520 11:32:25 +0200},
 Journal = {Journal of the Royal Statistical Society: Series B (Methodological)},
 Number = 1,
 Pages = {221234},
 Title = {The Exact and Asymptotic Distributions of {Cram{\'e}rVon} Mises Statistics},
 Volume = 58,
 Year = 1996}

@article{Robert:76:00,
 Abstract = {[Consider two data matrices on the same sample of n individuals,
 X(p $\times$ n), Y(q $\times$ n). From these matrices,
 geometrical representations of the sample are obtained as two
 configurations of n points, in Rp and Rq. It is shown that the
 RVcoefficient (Escoufier, 1970, 1973) can be used as a measure
 of similarity of the two configurations, taking into account the
 possibly distinct metrics to be used on them to measure the
 distances between points. The purpose of this paper is to show
 that most classical methods of linear multivariate statistical
 analysis can be interpreted as the search for optimal linear
 transformations or, equivalently, the search for optimal metrics
 to apply on two data matrices on the same sample; the optimality
 is defined in terms of the similarity of the corresponing
 configurations of points. which, in turn, calls for the
 maximization of the associated RVcoefficient. The methods
 studied are principal components, principal components of
 instrumental variables, multivariate regression, canonical
 variables, discriminant analysis; they are differentiated by the
 possible relationships existing between the two data matrices
 involved and by additional constraints under which the maximum
 of RV is to be obtained. It is also shown that the
 RVcoefficient can be used as a measure of goodness of a
 solution to the problem of discarding variables.]},
 Author = {Robert, P and Escoufier, Y},
 DateAdded = {20190517 10:53:50 +0200},
 DateModified = {20190517 10:54:04 +0200},
 Journal = {J. R. Stat. Soc. Ser. C Appl. Stat.},
 Number = 3,
 Pages = {257265},
 Publisher = {[Wiley, Royal Statistical Society]},
 Title = {A Unifying Tool for Linear Multivariate Statistical Methods: The {RV} Coefficient},
 Volume = 25,
 Year = 1976}

@article{Mayer:11:00,
 Abstract = {The integration of multiple highdimensional data sets (omics
 data) has been a very active but challenging area of
 bioinformatics research in recent years. Various adaptations of
 nonstandard multivariate statistical tools have been suggested
 that allow to analyze and visualize such data sets
 simultaneously. However, these methods typically can deal with
 two data sets only, whereas systems biology experiments often
 generate larger numbers of highdimensional data sets. For this
 reason, we suggest an explorative analysis of similarity between
 data sets as an initial analysis steps. This analysis is based on
 the RV coefficient, a matrix correlation, that can be interpreted
 as a generalization of the squared correlation from two single
 variables to two sets of variables. It has been shown before
 however that the highdimensionality of the data introduces
 substantial bias to the RV. We therefore introduce an alternative
 version, the adjusted RV, which is unbiased in the case of
 independent data sets. We can also show that in many situations,
 particularly for very highdimensional data sets, the adjusted RV
 is a better estimator than previously RV versions in terms of the
 mean square error and the power of the independence test based on
 it. We demonstrate the usefulness of the adjusted RV by applying
 it to data set of 19 different multivariate data sets from a
 systems biology experiment. The pairwise RV values between the
 data sets define a similarity matrix that we can use as an input
 to a hierarchical clustering or a multidimensional scaling. We
 show that this reveals biological meaningful subgroups of data
 sets in our study.},
 Author = {Mayer, ClausDieter and Lorent, Julie and Horgan, Graham W},
 DateAdded = {20190517 10:52:46 +0200},
 DateModified = {20190517 10:52:51 +0200},
 Journal = {Stat. Appl. Genet. Mol. Biol.},
 Language = {en},
 Pages = {Article 14},
 Title = {Exploratory analysis of multiple omics datasets using the adjusted {RV} coefficient},
 Volume = 10,
 Year = 2011}

@article{ElGhaziri:15:00,
 Abstract = {We review three measures of association between two datasets in
 view of their use in sensory data. The aim is threefold: (i) to
 show in which situations each measure of association is
 appropriate, (ii) to show their properties and how they can be
 applied efficiently to sensory data, (iii) to compare them. The
 three measures of association are multivariate correlation
 coefficient, RV coefficient and Procrustes similarity index. A
 particular emphasis is put on RV coefficient since it is very
 popular among sensory scientists. We stress the properties and
 shortcomings of this coefficient and propose an adjusted RV
 coefficient to be used instead of RV coefficient, particularly in
 situations where the number of samples is small or/and the number
 of variables is large.},
 Author = {El Ghaziri, Ang{\'e}lina and Qannari, El Mostafa},
 DateAdded = {20190517 10:52:46 +0200},
 DateModified = {20190517 10:52:51 +0200},
 Journal = {Food Qual. Prefer.},
 Keywords = {Multivariate correlation coefficient; Procrustes similarity index; RV coefficient; Permutation test; Adjusted RV coefficient},
 Month = mar,
 Pages = {116124},
 Title = {Measures of association between two datasets; Application to sensory data},
 Volume = 40,
 Year = 2015}

@article{Jackson:95:00,
 Abstract = {Abstract:A multivariate measure of the concordance or
 association between matrices of species abundances and
 environmental variables was generally lacking in ecology until
 recently. Traditional statistical procedures comparing such
 relationships are often unsuitable because of nonlinearity
 among species and/or environmental data. To address these
 problems, I propose a randomization test based on Procrustes
 analysis. One matrix is subject to reflection, rigid rotation,
 translation, and dilation to minimize the sum of the squared
 residual deviations between points for each observation and the
 identical observation in the target matrix. This is a classical
 Procrustes approach to matrix analysis. To assess the
 significance of this measure of matrix concordance, I use a
 randomization test to determine whether the sum of residual
 deviations is less than that expected by chance. The PROcrustean
 randomization TEST (PROTEST) may be used with either raw data
 matrices or with multivariate summaries of the original data
 (i.e. both direct or indirect gradient analysis). I provide
 examples of PROTEST analyses with benthic invertebrate
 communities, lakewater chemistry, lake morphology, and lake
 geographic position. Significant concordance between the benthic
 community and both lakewater chemistry and geographic position
 were found. PROTEST results differed from Mantel test results as
 the choice of distance measure with Mantel tests will influence
 the level of significance obtained.},
 Author = {Jackson, Donald A},
 DateAdded = {20190514 18:22:51 +0200},
 DateModified = {20190514 18:22:54 +0200},
 Journal = {{\'E}coscience},
 Month = jan,
 Number = 3,
 Pages = {297303},
 Publisher = {Taylor \& Francis},
 Title = {{PROTEST}: A {PROcrustean} Randomization {TEST} of community environment concordance},
 Volume = 2,
 Year = 1995}

@article{Dray:07:00,
 Abstract = {Multivariate analyses are well known and widely used to identify
 and understand structures of ecological communities. The ade4
 package for the R statistical environment proposes a great number
 of multivariate methods. Its implementation follows the tradition
 of the French school of ``Analyse des Donnees'' and is based on
 the use of the duality diagram. We present the theory of the
 duality diagram and discuss its implementation in ade4. Classes
 and main functions are presented. An example is given to
 illustrate the ade4 philosophy.},
 Author = {Dray, St{\'e}phane and Dufour, AnneB{\'e}atrice},
 DateAdded = {20190513 19:18:23 +0200},
 DateModified = {20190513 19:18:25 +0200},
 Journal = {Journal of Statistical Software, Articles},
 Number = 4,
 Pages = {120},
 Title = {The ade4 Package: Implementing the Duality Diagram for Ecologists},
 Volume = 22,
 Year = 2007}

@article{Dixon:03:00,
 Abstract = {Abstract. VEGAN adds vegetation analysis functions to the
 generalpurpose statistical program R. Both R and VEGAN can be
 downloaded for free. VEGAN implements several ordination methods,
 including Canonical Correspondence Analysis and Nonmetric
 Multidimensional Scaling, vector fitting of environmental
 variables, randomization tests, and various other analyses of
 vegetation data. It can be used for large data. Graphical output
 can be customized using the R language's extensive graphics
 capabilities. VEGAN is appropriate for routine and research use,
 if you are willing to learn some R.},
 Author = {Dixon, Philip},
 DateAdded = {20190513 19:15:06 +0200},
 DateModified = {20190513 19:15:09 +0200},
 Journal = {J. Veg. Sci.},
 Month = dec,
 Number = 6,
 Pages = {927930},
 Title = {{VEGAN}, a package of {R} functions for community ecology},
 Volume = 14,
 Year = 2003}

@book{Bravais:44:00,
 Author = {Bravais, A},
 DateAdded = {20190510 13:28:14 +0200},
 DateModified = {20190510 13:28:16 +0200},
 Language = {fr},
 Publisher = {Impr. Royale},
 Title = {Analyse math{\'e}matique sur les probabilit{\'e}s des erreurs de situation d'un point},
 Year = 1844}

@article{PeresNeto:01:00,
 Abstract = {The Mantel test provides a means to test the association between
 distance matrices and has been widely used in ecological and
 evolutionary studies. Recently, another permutation test based on
 a Procrustes statistic (PROTEST) was developed to compare
 multivariate data sets. Our study contrasts the effectiveness, in
 terms of power and type I error rates, of the Mantel test and
 PROTEST. We illustrate the application of Procrustes
 superimposition to visually examine the concordance of
 observations for each dimension separately and how to conduct
 hypothesis testing in which the association between two data sets
 is tested while controlling for the variation related to other
 sources of data. Our simulation results show that PROTEST is as
 powerful or more powerful than the Mantel test for detecting
 matrix association under a variety of possible scenarios. As a
 result of the increased power of PROTEST and the ability to
 assess the match for individual observations (not available with
 the Mantel test), biologists now have an additional and powerful
 analytical tool to study ecological and evolutionary
 relationships.},
 Author = {PeresNeto, Pedro R and Jackson, Donald A},
 DateAdded = {20190510 12:59:02 +0200},
 DateModified = {20190510 12:59:05 +0200},
 Journal = {Oecologia},
 Keywords = {Mantel test; Matrix association; Multivariate analysis; Procrustes analysis; Randomization test},
 Language = {en},
 Month = oct,
 Number = 2,
 Pages = {169178},
 Title = {How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test},
 Volume = 129,
 Year = 2001}

@article{Gower:71:00,
 Author = {Gower, J C},
 DateAdded = {20190419 12:11:20 +0200},
 DateModified = {20190419 12:11:23 +0200},
 Journal = {Mathematics in the archaeological and historical sciences},
 Pages = {138149},
 Publisher = {Edinburgh University Press Edinburgh},
 Title = {Statistical methods of comparing different multivariate analyses of the same data},
 Year = 1971}

@article{Lingoes:74:00,
 Abstract = {In connection with a leastsquares solution for fitting one
 matrix,A, to another,B, under optimal choice of a rigid motion
 and a dilation, Sch{\"o}nemann and Carroll suggested two measures
 of fit: a raw measure,e, and a refined similarity measure,es,
 which is symmetric. Both measures share the weakness of depending
 upon the norm of the target matrix,B,e.g.,e(A,kB) $\neq$e(A,B)
 fork $\neq$ 1. Therefore, both measures are useless for answering
 questions of the type: ``DoesA fitB better thanA fitsC?''. In
 this note two new measures of fit are suggested which do not
 depend upon the norms ofA andB, which are (0, 1)bounded, and
 which, therefore, provide meaningful answers for comparative
 analyses.},
 Author = {Lingoes, James C and Sch{\"o}nemann, Peter H},
 DateAdded = {20190419 12:07:12 +0200},
 DateModified = {20190419 12:07:17 +0200},
 Journal = {Psychometrika},
 Month = dec,
 Number = 4,
 Pages = {423427},
 Title = {Alternative measures of fit for the Sch{\"o}nemanncarroll matrix fitting algorithm},
 Volume = 39,
 Year = 1974}

@article{SzeKely:13:00,
 Address = {Orlando, FL, USA},
 Author = {Sz{\'e}Kely, G{\'a}bor J and Rizzo, Maria L},
 DateAdded = {20190419 00:38:28 +0200},
 DateModified = {20190419 00:38:39 +0200},
 Journal = {J. Multivar. Anal.},
 Keywords = {Distance correlation, Distance covariance, High dimension, Multivariate independence, dCor, dCov, primary, secondary},
 Month = may,
 Pages = {193213},
 Publisher = {Academic Press, Inc.},
 Title = {The Distance Correlation Ttest of Independence in High Dimension},
 Volume = 117,
 Year = 2013}

@article{Szekely:07:00,
 Abstract = {Project Euclid  mathematics and statistics online},
 Author = {Sz{\'e}kely, G{\'a}bor J and Rizzo, Maria L and Bakirov, Nail K},
 DateAdded = {20190419 00:25:31 +0200},
 DateModified = {20190419 00:25:35 +0200},
 Journal = {Ann. Stat.},
 Keywords = {Distance correlation; distance covariance; multivariate independence},
 Language = {en},
 Month = dec,
 Number = 6,
 Pages = {27692794},
 Publisher = {Institute of Mathematical Statistics},
 Title = {Measuring and testing dependence by correlation of distances},
 Volume = 35,
 Year = 2007}

@article{Escoufier:73:00,
 Author = {Escoufier, Yves},
 DateAdded = {20190419 00:11:19 +0200},
 DateModified = {20190419 00:11:23 +0200},
 Journal = {Biometrics},
 Pages = {751760},
 Publisher = {JSTOR},
 Title = {Le traitement des variables vectorielles},
 Year = 1973}

@article{Smilde:09:00,
 Abstract = {MOTIVATION: Modern functional genomics generates highdimensional
 datasets. It is often convenient to have a single simple number
 characterizing the relationship between pairs of such
 highdimensional datasets in a comprehensive way. Matrix
 correlations are such numbers and are appealing since they can be
 interpreted in the same way as Pearson's correlations familiar to
 biologists. The highdimensionality of functional genomics data
 is, however, problematic for existing matrix correlations. The
 motivation of this article is 2fold: (i) we introduce the idea
 of matrix correlations to the bioinformatics community and (ii)
 we give an improvement of the most promising matrix correlation
 coefficient (the RVcoefficient) circumventing the problems of
 highdimensional data. RESULTS: The modified RVcoefficient can
 be used in highdimensional data analysis studies as an easy
 measure of common information of two datasets. This is shown by
 theoretical arguments, simulations and applications to two
 reallife examples from functional genomics, i.e. a
 transcriptomics and metabolomics example. AVAILABILITY: The
 Matlab mfiles of the methods presented can be downloaded from
 http://www.bdagroup.nl.},
 Author = {Smilde, A K and Kiers, H A L and Bijlsma, S and Rubingh, C M and van Erk, M J},
 DateAdded = {20190419 00:08:07 +0200},
 DateModified = {20190419 00:08:17 +0200},
 Journal = {Bioinformatics},
 Language = {en},
 Month = feb,
 Number = 3,
 Pages = {401405},
 Title = {Matrix correlations for highdimensional data: the modified {RVcoefficient}},
 Volume = 25,
 Year = 2009}

@article{Ramsay:84:00,
 Abstract = {A correlational measure for ann byp matrixX and ann byq matrixY
 assesses their relation without specifying either as a fixed
 target. This paper discusses a number of useful measures of
 correlation, with emphasis on measures which are invariant with
 respect to rotations or changes in singular values of either
 matrix. The maximization of matrix correlation with respect to
 transformationsXL andYM is discussed where one or both
 transformations are constrained to be orthogonal. Special
 attention is focussed on transformations which causeXL andYM to
 ben bys, wheres may be any number between 1 and min (p, q). An
 efficient algorithm is described for maximizing the correlation
 betweenXL andYM where analytic solutions do not exist. A factor
 analytic example is presented illustrating the advantages of
 various coefficients and of varying the number of columns of the
 transformed matrices.},
 Author = {Ramsay, J O and ten Berge, Jos and Styan, G P H},
 DateAdded = {20190418 23:38:55 +0200},
 DateModified = {20190418 23:39:01 +0200},
 Journal = {Psychometrika},
 Month = sep,
 Number = 3,
 Pages = {403423},
 Title = {Matrix correlation},
 Volume = 49,
 Year = 1984}
diff git a/manuscript/figure/fig__r21.pdf b/manuscript/figure/fig__r21.pdf
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index ae28fc7..7a0b597 100644
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diff git a/manuscript/figure/fig_nested_shared1.pdf b/manuscript/figure/fig_nested_shared1.pdf
index 083e826..1e37205 100644
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diff git a/manuscript/figure/fig_nested_shared_variation1.pdf b/manuscript/figure/fig_nested_shared_variation1.pdf
index 28bfe1e..c9e4d32 100644
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diff git a/manuscript/main.Rnw b/manuscript/main.Rnw
index 54f40fb..ef69547 100755
 a/manuscript/main.Rnw
+++ b/manuscript/main.Rnw
@@ 1,8 +1,19 @@
\documentclass{bioinfo}
\copyrightyear{2015} \pubyear{2015}
+\IfFileExists{bioinfo.cls}{%
+ \def\mode{0}%
+ }{%
+ \def\mode{1}%
+}
\access{Advance Access Publication Date: Day Month Year}
\appnotes{Manuscript Category}
+\if 0\mode
+ \documentclass{bioinfo}%
+ \copyrightyear{2015} \pubyear{2015}%
+ \access{Advance Access Publication Date: Day Month Year}%
+ \appnotes{Manuscript Category}%
+\else
+ \documentclass{article}%
+ \newcommand\firstpage[1]{}
+ \newcommand\subtitle[1]{}
+\fi
\usepackage{amsmath}
\usepackage{multirow}
@@ 29,6 +40,7 @@
\newcommand{\Y}{\mathbf{Y}}
\begin{document}
+
\firstpage{1}
\subtitle{Data and text mining}
@@ 1304,7 +1316,7 @@ This work has been supported by the... Text Text Text Text.
%
%\bibliographystyle{plain}
%
\bibliography{Document}
+\bibliography{../inst/REFERENCES}
\renewcommand\thesubsection{\Alph{subsection}}
diff git a/manuscript/main.pdf b/manuscript/main.pdf
index 4940bb4..b9b70e7 100644
Binary files a/manuscript/main.pdf and b/manuscript/main.pdf differ
diff git a/manuscript/main.tex b/manuscript/main.tex
index 8bb5696..77d90c2 100644
 a/manuscript/main.tex
+++ b/manuscript/main.tex
@@ 1,4 +1,11 @@
\documentclass{bioinfo}\usepackage[]{graphicx}\usepackage[]{color}
+\IfFileExists{bioinfo.cls}{%
+ \def\mode{0}%
+ }{%
+ \def\mode{1}%
+}
+
+\if 0\mode
+ \documentclass{bioinfo}\usepackage[]{graphicx}\usepackage[]{color}
% maxwidth is the original width if it is less than linewidth
% otherwise use linewidth (to make sure the graphics do not exceed the margin)
\makeatletter
@@ 48,11 +55,15 @@
\definecolor{errorcolor}{rgb}{1, 0, 0}
\newenvironment{knitrout}{}{} % an empty environment to be redefined in TeX
\usepackage{alltt}
\copyrightyear{2015} \pubyear{2015}

\access{Advance Access Publication Date: Day Month Year}
\appnotes{Manuscript Category}
+\usepackage{alltt}%
+ \copyrightyear{2015} \pubyear{2015}%
+ \access{Advance Access Publication Date: Day Month Year}%
+ \appnotes{Manuscript Category}%
+\else
+ \documentclass{article}%
+ \newcommand\firstpage[1]{}
+ \newcommand\subtitle[1]{}
+\fi
\usepackage{amsmath}
\usepackage{multirow}
@@ 79,6 +90,7 @@
\newcommand{\Y}{\mathbf{Y}}
\IfFileExists{upquote.sty}{\usepackage{upquote}}{}
\begin{document}
+
\firstpage{1}
\subtitle{Data and text mining}
@@ 341,7 +353,7 @@ To evaluate relative power of the three considered tests, pairs of to random mat
\begin{table}[!t]
\processtable{Estimation of $\overline{\rcovls(\X,\Y)}$ according to the number of random matrices (k) aligned.\label{tab:mrcovls}}{
% latex table generated in R 3.5.2 by xtable 1.84 package
% Fri Jul 12 17:51:46 2019
+% Wed Aug 21 09:31:39 2019
\begin{tabular}{rrrrrrr}
\hline
& & \multicolumn{2}{c}{normal} & & \multicolumn{2}{c}{exponential}\\ \cline{34} \cline{67}p & k &\multicolumn{1}{c}{mean} & \multicolumn{1}{c}{sd} & \multicolumn{1}{c}{ } &\multicolumn{1}{c}{mean} & \multicolumn{1}{c}{sd}\\\hline\multirow{3}{*}{10} & 10 & 0.5746 & $1.3687 \times 10^{2}$ & & 0.5705 & $1.1714 \times 10^{2}$ \\
@@ 443,7 +455,7 @@ whatever the $p$ tested (Table~\ref{tab:alpha_pvalue}). This ensure that the pro
of the distribution of $P_{values}$ correlation test to $\mathcal{U}(0,1)$
under the null hypothesis.\label{tab:alpha_pvalue}} {
% latex table generated in R 3.5.2 by xtable 1.84 package
% Fri Jul 12 17:51:49 2019
+% Wed Aug 21 09:31:44 2019
\begin{tabular*}{0.98\linewidth}{@{\extracolsep{\fill}}crrr}
\hline
& \multicolumn{3}{c}{CramerVon Mises p.value} \\
@@ 465,7 +477,7 @@ Power of the $CovLs$ test based on the estimation of $\overline{RCovLs(X,Y)}$ is
\begin{table}[!t]
\processtable{Power estimation of the procruste tests for two low level of shared variations $5\%$ and $10\%$.\label{tab:power}} {
% latex table generated in R 3.5.2 by xtable 1.84 package
% Fri Jul 12 17:51:49 2019
+% Wed Aug 21 09:31:44 2019
\begin{tabular}{lcrrrrrrrrr}
\hline
& $R^2$ & \multicolumn{4}{c}{5\%} & &\multicolumn{4}{c}{10\%} \\
@@ 550,7 +562,7 @@ This work has been supported by the... Text Text Text Text.
%
%\bibliographystyle{plain}
%
\bibliography{Document}
+\bibliography{../inst/REFERENCES}
\renewcommand\thesubsection{\Alph{subsection}}

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