num.arcsCS1D: Number of arcs of Central Similarity Proximity Catch Digraphs...

In elvanceyhan/pcds: Proximity Catch Digraphs and Their Applications

Number of arcs of Central Similarity Proximity Catch Digraphs (CS-PCDs) and related quantities of the induced subdigraphs for points in the partition intervals - multiple interval case

Description

An object of class "NumArcs". Returns the number of arcs and various other quantities related to the partition intervals for Central Similarity Proximity Catch Digraph (CS-PCD) whose vertices are the data points in Xp in the multiple interval case.

For this function, CS proximity regions are constructed data points inside or outside the intervals based on Yp points with expansion parameter t \ge 0 and centrality parameter c \in (0,1). That is, for this function, arcs may exist for points in the middle or end intervals.

Range (or convex hull) of Yp (i.e., the interval (\min(Yp),\max(Yp))) is partitioned by the spacings based on Yp points (i.e., multiple intervals are these partition intervals based on the order statistics of Yp points whose union constitutes the range of Yp points). For the number of arcs, loops are not counted.

Usage

num.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 partition intervals.
t	A positive real number which serves as the expansion parameter in CS proximity region; must be > 0.
c	A positive real number in (0,1) parameterizing the center inside the middle (partition) intervals with the default c=.5. For an interval, int=(a,b), the parameterized center is M_c=a+c(b-a).

Value

A list with the elements

desc	A short description of the output: number of arcs and related quantities for the induced subdigraphs in the partition intervals
num.arcs	Total number of arcs in all intervals (including the end intervals), i.e., the number of arcs for the entire CS-PCD
num.in.range	Number of Xp points in the range or convex hull of Yp points
num.in.ints	The vector of number of Xp points in the partition intervals (including the end intervals) based on Yp points
weight.vec	The vector of the lengths of the middle partition intervals (i.e., end intervals excluded) based on Yp points
int.num.arcs	The vector of the number of arcs of the component of the CS-PCD in the partition intervals (including the end intervals) based on Yp points
part.int	A list of partition intervals based on Yp points
data.int.ind	A vector of indices of partition intervals in which data points reside, i.e., column number of part.int is provided for each Xp point. Partition intervals are numbered from left to right with 1 being the left end interval.
tess.points	Points on which the tessellation of the study region is performed, here, tessellation is the partition intervals based on Yp points.
vertices	Vertices of the digraph, Xp.

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

num.arcsCSint, num.arcsCSmid.int, num.arcsCSend.int, and num.arcsPE1D

Examples

tau<-1.5
c<-.4
a<-0; b<-10; int<-c(a,b);

#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)
xf<-(int[2]-int[1])*.1

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

Narcs = num.arcsCS1D(Xp,Yp,tau,c)
Narcs
summary(Narcs)
plot(Narcs)

elvanceyhan/pcds documentation built on June 29, 2023, 8:12 a.m.