An object of class "SpatPatterns".
Generates n_2 2D points associated with the given set of points (i.e., reference points) \(X_1\) in the
type I fashion with circular (or radial) between class attraction parameter p, which is a probability value between 0 and 1.
The generated points are intended to be from a different class, say class 2 (or \(X_2\) points) than the reference
(i.e., \(X_1\) points, say class 1 points, denoted as X1 as an argument of the function).
To generate \(n_2\) (denoted as n2 as an argument of the function) \(X_2\) points, \(n_2\) of \(X_1\) points are randomly selected (possibly with replacement) and
for a selected X1 point, say \(x_{1ref}\), a \(Uniform(0,1)\) number, \(U\), is generated.
If \(U \le p\), a new point from the class 2, say \(x_{2new}\), is generated within a
circle with radius equal to the distance to the closest \(X_1\) point (uniform in the polar coordinates),
else the new point is generated uniformly
within the smallest bounding box containing \(X_1\) points.
That is, if \(U \le p\), \(x_{2new} = x_{1ref}+r_u c(\cos(t_u),\sin(t_u))\)
where \(r_u \sim U(0,rad)\) and \(t_u \sim U(0, 2\pi)\) with \(rad=\min(d(x_{1ref},X_1\setminus \{x_{1ref}\}))\),
else \(x_{2new} \sim rect(X_1)\) where \(rect(X_1)\) is the smallest bounding box containing \(X_1\) points.
Note that, the level of association increases as p increases, and the association vanishes
when p approaches to 0.
Type I association is closely related to Type C association in
ceyhan:serra-2014;textualnnspat, see the function rassocC
and also other association types.
In the type C association pattern
the new point from the class 2, \(x_{2new}\), is generated (uniform in the polar coordinates) within a circle
centered at \(x_{1ref}\) with radius equal to \(r_0\),
in type U association pattern \(x_{2new}\) is generated similarly except it is uniform in the circle.
In type G association, \(x_{2new}\) is generated from the bivariate normal distribution centered at \(x_{1ref}\) with covariance
\(\sigma I_2\) where \(I_2\) is \(2 \times 2\) identity matrix.
rassocI(X1, n2, p)A list with the elements
equals "ref.gen" for the bivariate pattern of association of class 2 (i.e., \(X_2\)) points with the reference
points (i.e., \(X_1\)), indicates reference points are required to be entered as an argument in the function
The type of the point pattern
Radial (i.e., circular) between class attraction parameter controlling the level of association
The output set of generated points (i.e., class 2 points) associated with reference (i.e. \(X_1\) points)
The input set of reference points \(X_1\), i.e., points with which generated class 2 points are associated.
Description of the point pattern
The class labels of the generated points, it is NULL for this function, since only class 2
points are generated in this pattern
The "main" title for the plot of the point pattern
The vector of two numbers, which are the number of generated class 2 points and
the number of reference (i.e., \(X_1\)) points.
The possible ranges of the \(x\)- and \(y\)-coordinates of the generated and the reference points
A set of 2D points representing the reference points, also referred as class 1 points. The generated points are associated in a type I sense (in a circular/radial fashion) with these points.
A positive integer representing the number of class 2 (i.e., \(X_2\)) points to be generated.
A real number between 0 and 1 representing the attraction probability of class 2 points associated with a randomly selected class 1 point (see the description below).
Elvan Ceyhan
rassocC, rassocG, rassocU, and rassoc
n1<-20; n2<-1000; #try also n1<-10; n2<-1000;
p<- .75 #try also .25, .5, .9, runif(1)
#with default bounding box (i.e., unit square)
X1<-cbind(runif(n1),runif(n1)) #try also X1<-1+cbind(runif(n1),runif(n1))
Xdat<-rassocI(X1,n2,p)
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)
Run the code above in your browser using DataLab