poseticDataAnalysis (version 1.0.0)

BidimentionalPosetRepresentation: Bidimensional representation of multidimensional ordinal binary data generated by a specific reversed pair of lexicographic linear extensions

Description

Starting from a dataset related to \(n\) statistical units, scored against \(k\) ordinal 0/1-indicators and partially ordered component-wise into a Boolean lattice \(B_k=(\{0,1\}^k,\leq_{cmp})\), it finds the bidimensional data representation generated by a specific reversed pair of lexicographic linear extensions.

Usage

BidimentionalPosetRepresentation(profile, weights, variablesPriority)

Value

a list of 2 elements named LossVAlue and Representation.

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

Representation a data frame with \(m\) 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 \(k\)-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 \(L(b|D^{inp}, p)\) associated to each observed profile in the bidimensional representation.

Arguments

profile

Boolean matrix of dimension \(m\times k\) of the unique \(m\leq n\) different observed profiles. Each observed profile is row of profile. Each observed profile is repeated only once in the matrix profile.

weights

real vector of length \(m\) with the frequencies/weights of each observed profile. Element of position \(j\) in vector weights is the frequency/weight of the profile in row \(j\) of profile.

variablesPriority

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

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)