rseg: Generation of Points under Segregation of Two Classes

Description

An object of class "SpatPatterns".

Generates n_i 2D points from class \(j\) with parameters \(r_j\) for \(j=1,2\). The generated points are from two different classes which are segregated from each other. The pattern generation starts with the initial points X1.init and X2.init (with default=NULL for both). If both X1.init=NULL and X2.init=NULL, both X1.init and X2.init are generated uniformly in the unit square. If only X1.init=NULL, X1.init is the sum of a point uniformly generated in the unit square and X2.init and if only X2.init=NULL, X2.init is the sum of a point uniformly generated in the unit square and X1.init. After the initial points from each class are available, \(n_j\) points from class \(j\) are generated as Xj[i,]<-Xj[(i-1),]+ru*c(cos(tu),sin(tu)) where ru<-runif(1,0,rj) and tu<-runif(1,0,2*pi) for \(i=2,\ldots,n_j\) with Xj[1,]=Xj.init for \(j=1,2\). That is, at each step the new point in class \(j\) is generated within a circle with radius equal to \(r_j\) (uniform in the polar coordinates). Note that, the level of segregation is stronger if the initial points are further apart, and the level of segregation increases as the radius values gets smaller.

Usage

rseg(n1, n2, r1, r2, X1.init = NULL, X2.init = NULL)

Value

A list with the elements

pat.type: "2c" for the 2-class pattern of segregation of the two classes
type: The type of the point pattern
parameters: Radial (i.e., circular) within class radii of segregation, r1 and r2, controlling the level of segregation
lab: The class labels of the generated points, it is 1 class 1 or \(X_1\) points and 2 for class 2 or \(X_2\) points
init.cases: The initial points for class 1 and class 2, one initial point for each class.
gen.points: The output set of generated points (i.e., class 1 and class 2 points) segregated from each other.
ref.points: The input set of reference points, it is NULL for this function.
desc.pat: Description of the point pattern
mtitle: The "main" title for the plot of the point pattern
num.points: The vector of two numbers, which are the number of generated class 1 and class 2 points.
xlimit,ylimit: The possible ranges of the \(x\)- and \(y\)-coordinates of the generated and the initial points

Arguments

n1, n2: Positive integers representing the number of class 1 and class 2 (i.e., \(X_1\) and \(X_2\)) points to be generated under the segregation pattern.
r1, r2: Positive real numbers representing the radius of attraction within class, i.e., radius of the circle center and generated points are from the same class.
X1.init, X2.init: 2D points representing the initial points for the segregated classes, default=NULL for both. If both X1.init=NULL and X2.init=NULL, both X1.init and X2.init are generated uniformly in the unit square. If only X1.init=NULL, X1.init is the sum of a point uniformly generated in the unit square and X2.init and if only X2.init=NULL, X2.init is the sum of a point uniformly generated in the unit square and X1.init. The initial points are marked with crosses in the plot of the points.

Author

Elvan Ceyhan

Examples

Run this code

n1<-20;  #try also n1<-10; n1<-100;
n2<-20; #try also n1<-40; n2<-50

r1<-.3; r2<-.2

#data generation
Xdat<-rseg(n1,n2,r1,r2) #labeled data
Xdat

table(Xdat$lab)

summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)

#with one initial point
X1init<-c(3,2)

Xdat<-rseg(n1,n2,r1,r2,X1.init=X1init)
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)

#with two initial points
X1init<-c(3,2)
X2init<-c(4,2)

Xdat<-rseg(n1,n2,r1,r2,X1init,X2init)
Xdat
summary(Xdat)
plot(Xdat,asp=1)
plot(Xdat)