funsQandR: Functions for the number of shared NNs, shared NN vector, and the number of reflexive NNs

Description

Four functions: Qval, Qvec, sharedNN and Rval.

Qval returns the \(Q\) value, the number of points with shared nearest neighbors (NNs), which occurs when two or more points share a NN, for data in any dimension.

Qvec returns the Q-value and also yields the \(Qv\) vector \(Qv=(Q_0,Q_1,\ldots)\) as well for data in any dimension, where \(Q_j\) is the number of points shared as a NN by \(j\) other points.

sharedNN returns the vector of number of points with shared NNs, \(Q=(Q_0,Q_1,\ldots)\) where \(Q_i\) is the number of points that are NN to \(i\) points, and if a point is a NN of \(i\) points, then there are \(i(i-1)\) points that share a NN. So, \(Q=\sum_{i>1} i(i-1)Q_i\).

Rval returns the number of reflexive NNs, \(R\) (i.e., twice the number of reflexive NN pairs).

These quantities are used, e.g., in computing the variances and covariances of the entries of the nearest neighbor contingency tables used for Dixon's tests and other NNCT tests. The input must be the incidence matrix, \(W\), of the NN digraph.

Usage

Qval(W)
Qvec(W)
sharedNN(W)
Rval(W)

Value

The function Qval returns the \(Q\) value

The function Qvec returns a list with two elements

q: the \(Q\) value, the number of shared NNs
qvec: the vector of \(Q_j\) values

The function sharedNN returns a matrix with 2 rows, where first row is the \(j\) values and second row is the corresponding vector of \(Q_j\) values

The function Rval returns the \(R\) value, the number of reflexive NNs.

See the description above for the details of these quantities.

Arguments

W: The incidence matrix, \(W\), for the NN digraph

Author

Elvan Ceyhan

Examples

Run this code

#Examples for Qval
#3D data points
n<-10
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
Qval(W)

#1D data points
X<-as.matrix(runif(10)) # need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(10) would not work
ipd<-ipd.mat(X)
W<-Wmat(ipd)
Qval(W)

#with ties=TRUE in the data
Y<-matrix(round(runif(15)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
Qval(W)

#with ties=TRUE in the data
Y<-matrix(round(runif(15)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
Qval(W)

#Examples for Qvec
#3D data points
n<-10
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
Qvec(W)

#2D data points
n<-15
Y<-matrix(runif(2*n),ncol=2)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
Qvec(W)

#1D data points
X<-as.matrix(runif(15)) # need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(15) would not work
ipd<-ipd.mat(X)
W<-Wmat(ipd)
Qvec(W)

#with ties=TRUE in the data
Y<-matrix(round(runif(15)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
Qvec(W)

#Examples for sharedNN
#3D data points
n<-10
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
sharedNN(W)
Qvec(W)

#1D data points
X<-as.matrix(runif(15)) # need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(5) would not work
ipd<-ipd.mat(X)
W<-Wmat(ipd)
sharedNN(W)
Qvec(W)

#2D data points
n<-15
Y<-matrix(runif(2*n),ncol=2)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
sharedNN(W)
Qvec(W)

#with ties=TRUE in the data
Y<-matrix(round(runif(30)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
sharedNN(W)

#Examples for Rval
#3D data points
n<-10
Y<-matrix(runif(3*n),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd)
Rval(W)

#1D data points
X<-as.matrix(runif(15)) # need to be entered as a matrix with one column
#(i.e., a column vector), hence X<-runif(5) would not work
ipd<-ipd.mat(X)
W<-Wmat(ipd)
Rval(W)

#with ties=TRUE in the data
Y<-matrix(round(runif(30)*10),ncol=3)
ipd<-ipd.mat(Y)
W<-Wmat(ipd,ties=TRUE)
Rval(W)