nnspat (version 0.1.2)

Qsym.ct: \(Q\)-symmetry Contingency Table (QCT)

Description

Returns the \(k \times 3\) contingency table for \(Q\)-symmetry (i.e., \(Q\)-symmetry contingency table (QCT)) given the IPD matrix or data set x where \(k\) is the number of classes in the data set. Each row in the QCT is the vector of number of points with shared NNs, \(Q_i=(Q_{i0},Q_{i1},Q_{i2})\) where \(Q_{ij}\) is the number of class \(i\) points that are NN to class \(j\) points for \(j=0,1\) and \(Q_{i2}\) is the number of class \(i\) points that are NN to class \(j\) or more points. That is, this function pools the cells 3 or larger together for \(k\) classes, so, \(Q_2\), \(Q_3\) etc. are pooled, so, the column labels are \(Q_0\), \(Q_1\) and \(Q_2\) with the last one is actually sum of \(Q_j\) for \(j \ge 2\). Rows the QCT are labeled with the corresponding class labels.

\(Q\)-symmetry is also equivalent to Pielou's second type of NN symmetry or the symmetry in the shared NN structure for all classes.

The argument is.ipd is a logical argument (default=TRUE) to determine the structure of the argument x. If TRUE, x is taken to be the inter-point distance (IPD) matrix, and if FALSE, x is taken to be the data set with rows representing the data points.

See also (pielou:1961,ceyhan:SWJ-spat-sym2014;textualnnspat) and the references therein.

Usage

Qsym.ct(x, lab, is.ipd = TRUE, ...)

Value

Returns the \(k \times 3\) QCT where \(k\) is the number of classes in the data set.

Arguments

x

The IPD matrix (if is.ipd=TRUE) or a data set of points in matrix or data frame form where points correspond to the rows (if is.ipd = FALSE).

lab

The vector of class labels (numerical or categorical)

is.ipd

A logical parameter (default=TRUE). If TRUE, x is taken as the inter-point distance matrix, otherwise, x is taken as the data set with rows representing the data points.

...

are for further arguments, such as method and p, passed to the dist function.

Author

Elvan Ceyhan

References

See Also

sharedNNmc, Qsym.test and scct

Examples

n<-20  #or try sample(1:20,1)
Y<-matrix(runif(n*3),ncol=3)
cls<-sample(1:2,n,replace = TRUE)  #or try cls<-rep(1:2,c(10,10))
ipd<-ipd.mat(Y)

Qsym.ct(ipd,cls)
Qsym.ct(Y,cls,is.ipd = FALSE)
Qsym.ct(Y,cls,is.ipd = FALSE,method="max")

#cls as a factor
na<-floor(n/2); nb<-n-na
fcls<-rep(c("a","b"),c(na,nb))
Qsym.ct(ipd,fcls)

#############
n<-40
Y<-matrix(runif(3*n),ncol=3)
cls<-sample(1:4,n,replace = TRUE)  #or try cls<-rep(1:2,c(10,10))
ipd<-ipd.mat(Y)

Qsym.ct(ipd,cls)