arcsCS1D: The arcs of Central Similarity Proximity Catch Digraph...

In pcds: Proximity Catch Digraphs and Their Applications

The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - multiple interval case

Description

An object of class "PCDs". Returns arcs as tails (or sources) and heads (or arrow ends) for 1D data set Xp as the vertices of CS-PCD and related parameters and the quantities of the digraph. Yp determines the end points of the intervals.

For this function, CS proximity regions are constructed data points inside or outside the intervals based on Yp points with expansion parameter t>0 and centrality parameter c \in (0,1). That is, for this function, arcs may exist for points in the middle or end intervals. It also provides various descriptions and quantities about the arcs of the CS-PCD such as number of arcs, arc density, etc.

Equivalent to function arcsCS1D.

See also (\insertCiteceyhan:revstat-2016;textualpcds).

Usage

arcsCS1D(Xp, Yp, t, c = 0.5)

Arguments

Xp	A set or vector of 1D points which constitute the vertices of the CS-PCD.
Yp	A set or vector of 1D points which constitute the end points of the intervals.
t	A positive real number which serves as the expansion parameter in CS proximity region.
c	A positive real number in (0,1) parameterizing the center inside middle intervals with the default c=.5. For the interval, int=(a,b), the parameterized center is M_c=a+c(b-a).

Value

A list with the elements

type	A description of the type of the digraph
parameters	Parameters of the digraph, here, they are expansion and centrality parameters.
tess.points	Points on which the tessellation of the study region is performed, here, tessellation is the intervalization of the real line based on Yp points.
tess.name	Name of data set used in tessellation, it is Yp for this function
vertices	Vertices of the digraph, Xp points
vert.name	Name of the data set which constitute the vertices of the digraph
S	Tails (or sources) of the arcs of CS-PCD for 1D data
E	Heads (or arrow ends) of the arcs of CS-PCD for 1D data
mtitle	Text for "main" title in the plot of the digraph
quant	Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

arcsCSend.int, arcsCSmid.int, arcsCS1D, and arcsPE1D

Examples

t<-2
c<-.4
a<-0; b<-10;

#nx is number of X points (target) and ny is number of Y points (nontarget)
nx<-20; ny<-4;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;

set.seed(1)
xr<-range(a,b)
xf<-(xr[2]-xr[1])*.1

Xp<-runif(nx,a-xf,b+xf)
Yp<-runif(ny,a,b)

Arcs<-arcsCS1D(Xp,Yp,t,c)
Arcs
summary(Arcs)
plot(Arcs)

S<-Arcs$S
E<-Arcs$E

arcsCS1D(Xp,Yp,t,c)

arcsCS1D(Xp,Yp+10,t,c)

jit<-.1
yjit<-runif(nx,-jit,jit)

Xlim<-range(a,b,Xp,Yp)
xd<-Xlim[2]-Xlim[1]

plot(cbind(a,0),
main="arcs of CS-PCD for points (jittered along y-axis)\n in middle intervals ",
xlab=" ", ylab=" ", xlim=Xlim+xd*c(-.05,.05),ylim=3*c(-jit,jit),pch=".")
abline(h=0,lty=1)
points(Xp, yjit,pch=".",cex=3)
abline(v=Yp,lty=2)
arrows(S, yjit, E, yjit, length = .05, col= 4)

t<-2
c<-.4
a<-0; b<-10;
nx<-20; ny<-4;  #try also nx<-40; ny<-10 or nx<-1000; ny<-10;
Xp<-runif(nx,a,b)
Yp<-runif(ny,a,b)

arcsCS1D(Xp,Yp,t,c)

pcds documentation built on July 9, 2023, 5:54 p.m.