pcds (version 0.1.4)

IncMatPE1D: Incidence matrix for Proportional-Edge Proximity Catch Digraphs (PE-PCDs) for 1D data - multiple interval case

Description

Returns the incidence matrix for the PE-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). Loops are allowed, so the diagonal entries are all equal to 1.

PE proximity region is constructed with an expansion parameter \(r \ge 1\) and a centrality parameter \(c \in (0,1)\).

See also (ceyhan:metrika-2012;textualpcds).

Usage

IncMatPE1D(Xp, Yp, r, c)

Value

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

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.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

c

A positive real number in \((0,1)\) parameterizing the center inside int\(=(a,b)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\).

Author

Elvan Ceyhan

References

See Also

IncMatCS1D, IncMatPEtri, and IncMatPEMT

Examples

r<-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<-IncMatPE1D(Xp,Yp,r,c)
IM

dom.greedy(IM)
IndUBdom(IM,6)
dom.exact(IM)

Arcs<-ArcsPEMI(Xp,Yp,r,c)
Arcs
summary(Arcs)
plot(Arcs)

IncMatPE1D(Xp,Yp+10,r,c)

r<-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)
IncMatPE1D(Xp,Yp,r,c)