inci.matCStri {pcds}

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 (Ceyhan (2005); Ceyhan et al. (2007); Ceyhan (2014)).

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

Ceyhan E (2005). An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications. Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.

Ceyhan E (2014). “Comparison of Relative Density of Two Random Geometric Digraph Families in Testing Spatial Clustering.” TEST, 23(1), 100-134.

Ceyhan E, Priebe CE, Marchette DJ (2007). “A new family of random graphs for testing spatial segregation.” Canadian Journal of Statistics, 35(1), 27-50.

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)