inci.matCStri: Incidence matrix for Central Similarity Proximity Catch...

In pcds: Proximity Catch Digraphs and Their Applications

Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case

Description

Returns the incidence matrix for the CS-PCD whose vertices are the given 2D numerical data set, Xp, in the triangle tri=T(v=1,v=2,v=3).

CS proximity regions are constructed with respect to triangle tri with expansion parameter t>0 and edge regions are based on the center M=(m_1,m_2) in Cartesian coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates in the interior of the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri. Loops are allowed, so the diagonal entries are all equal to 1.

See also (\insertCiteceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

inci.matCStri(Xp, tri, t, M = c(1, 1, 1))

Arguments

Xp	A set of 2D points which constitute the vertices of CS-PCD.
tri	A 3 \times 2 matrix with each row representing a vertex of the triangle.
t	A positive real number which serves as the expansion parameter in CS proximity region.
M	A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle tri; default is M=(1,1,1) i.e., the center of mass of tri.

Value

Incidence matrix for the CS-PCD with vertices being 2D data set, Xp, in the triangle tri with edge regions based on center M

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

inci.matCS, inci.matPEtri, and inci.matAStri

Examples

A<-c(1,1); B<-c(2,0); C<-c(1.5,2);

Tr<-rbind(A,B,C);
n<-10

set.seed(1)
Xp<-runif.tri(n,Tr)$g

M<-as.numeric(runif.tri(1,Tr)$g)  #try also M<-c(1.6,1.0)

IM<-inci.matCStri(Xp,Tr,t=1.25,M)
IM
dom.num.greedy(IM) #try also dom.num.exact(IM)
Idom.num.up.bnd(IM,3)

inci.matCStri(Xp,Tr,t=1.5,M)

pcds documentation built on May 29, 2024, 9:36 a.m.