% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/BidimentionalPosetRepresentation.R
\name{BidimentionalPosetRepresentation}
\alias{BidimentionalPosetRepresentation}
\title{Bidimensional representation of multidimensional ordinal binary data generated by a specific
reversed pair of lexicographic linear extensions}
\usage{
BidimentionalPosetRepresentation(profile, weights, variablesPriority)
}
\arguments{
\item{profile}{Boolean matrix of dimension \eqn{m\times k} of the unique \eqn{m\leq n} different observed profiles.
Each observed profile is row of `profile`. Each observed profile is repeated only once in the matrix `profile`.}

\item{weights}{real vector of length \eqn{m} with the frequencies/weights of each observed profile. Element
of position \eqn{j} in vector `weights` is the frequency/weight of the profile in row \eqn{j} of `profile`.}

\item{variablesPriority}{integer vector of dimension \eqn{k} containing a permutation \eqn{i_1,...,i_k} of \eqn{1,...,k}.
This vector specifies the criterion to build the reversed pair of lexicographic linear extensions used to
approximate \eqn{B_k}. The first linear extension is built by ordering profiles first according to their
scores on \eqn{V_{i_1}}, then to the scores on \eqn{V_{i_{2}}} and so on, until \eqn{V_{i_{k}}}; the second linear extension
is built by ordering profiles first according to their scores on \eqn{V_{i_k}}, then to the scores on \eqn{V_{i_{k-1}}} and so on, until \eqn{V_{i_{1}}}.}
}
\value{
a list of 2 elements named `LossVAlue` and `Representation`.

`LossVAlue` real number indicating the value of the global error \eqn{L(D^{out}|D^{inp}, p)} corresponding to the representation induced by the chosen `variablesPriority`.

`Representation`  a data frame with \eqn{m} values (one value for each observed profile) of 5 variables named `profiles`, `x`, `y`, `weights` and `error`.
`$profile` is an integer vector containing the base-10 representation of the \eqn{k}-dimensional Boolean vectors representing observed profiles.
`$x` is an integer vector containing the x-coordinates of points representing observed profiles in the bidimensional representation.
`$y` is an integer vector containing the y-coordinates of points representing observed profiles in the bidimensional representation.
`$weights` is a real vector with the frequencies/weights of each observed profile.
`$error` is a real vector with the values of the approximation errors \eqn{L(b|D^{inp}, p)} associated to each observed profile
in the bidimensional representation.
}
\description{
Starting from a dataset related to \eqn{n} statistical units, scored against \eqn{k}
ordinal 0/1-indicators and partially ordered component-wise into a Boolean lattice \eqn{B_k=(\{0,1\}^k,\leq_{cmp})},
it finds the bidimensional data representation generated by a specific reversed pair of lexicographic linear extensions.
}
\examples{
#SIMULATING OBSERVED BINARY DATA
#number of binary variables
k <- 6
#building observed profiles matrix
profiles <- sapply((0:(2^k-1)) ,function(x){ as.integer(intToBits(x))})
profiles <- t(profiles[1:k, ])
#building the vector of observation frequencies
weights <- sample.int(100, nrow(profiles), replace=TRUE)
#Chosing (at random) a variable priority
vp <- sample.int(k, k, replace=FALSE)
result <- BidimentionalPosetRepresentation(profiles, weights, vp)

}
