inci.matCS1D {pcds}

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case

Description

Returns the incidence matrix for the CS-PCD for a given 1D numerical data set, Xp, as the vertices of the digraph and Yp determines the end points of the intervals (in the multi-interval case). If there are duplicates of Yp points, only one point is retained for each duplicate value, and a warning message is printed. Loops are allowed, so the diagonal entries are all equal to 1.

CS proximity region is constructed with an expansion parameter t>0 and a centrality parameter c \in (0,1).

See also (Ceyhan (2016)).

Usage

inci.matCS1D(Xp, Yp, t, c = 0.5)

Arguments

Xp

a set of 1D points which constitutes the vertices of the digraph.

Yp

a set of 1D points which constitutes the end points of the intervals that partition the real line.

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

Incidence matrix for the CS-PCD with vertices being 1D data set, Xp, and Yp determines the end points of the intervals (the multi-interval case)

Author(s)

Elvan Ceyhan

References

Ceyhan E (2016). “Density of a Random Interval Catch Digraph Family and its Use for Testing Uniformity.” REVSTAT, 14(4), 349-394.

See Also

inci.matCS1D, inci.matPEtri, and inci.matPE

Examples

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

set.seed(1)
Xp<-runif(nx,a,b)
Yp<-runif(ny,a,b)

IM<-inci.matCS1D(Xp,Yp,t,c)
IM
dom.num.greedy(IM)

dom.num.exact(IM)  #might take a long time depending on nx

Idom.num.up.bnd(IM,5)

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

inci.matCS1D(Xp,Yp+10,t,c)

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;

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

inci.matCS1D(Xp,Yp,t,c)