rhor.clust: Generation of Points with Clusters along the Horizontal Axis

Description

An object of class "Clusters".

Generates n 2D points with k ( $k \geq 2$ ) clusters along the horizontal axis where about $n / k$ points belongs to each cluster.

If distribution="uniform", the points are uniformly generated in their square supports where one square is the unit square (i.e., with vertices $(0, 0), (1, 0), (1, 1), (0, 1)$ ), and the others are $d$ units shifted horizontally from each other so that their lower end vertices are $(j - 1) + (j - 1) d$ for $j = 1, 2, \dots, k$ .

If distribution="bvnormal", the points are generated from the bivariate normal distribution with means equal to the centers of the above squares (i.e., for each cluster with mean=(j+(j-1)d-1/2,1/2) for $j = 1, 2, \dots, k$ and the covariance matrix $s d I_{2}$ , where $I_{2}$ is the $2 \times 2$ identity matrix.

Notice that the clusters are more separated, i.e., generated data indicates more clear clusters as $d$ increases in either direction with $d = 0$ indicating one cluster in the data. For a fixed $d$ , when distribution="bvnormal", the clustering gets stronger if the variance of each component, $s d^{2}$ , gets smaller, and clustering gets weaker as the variance of each component gets larger where default is $s d = 1 / 6$ .

Usage

rhor.clust(n, k, d, sd = 1/6, distribution = c("uniform", "bvnormal"))

Value

A list with the elements

type: The type of the clustering pattern
parameters: The number of clusters, k, and the horizontal shift, d, representing the level of clustering (for both distribution types) and standard deviation, sd, for the bivariate normal distribution only.
gen.points: The output set of generated points from the k clusters.
desc.pat: Description of the clustering pattern
mtitle: The "main" title for the plot of the point pattern
num.points: The number of generated points.
xlimit,ylimit: The possible ranges of the $x$ - and $y$ -coordinates of the generated points

Arguments

n: A positive integer representing the number of points to be generated from all the clusters
k: A positive integer representing the number of clusters to be generated
d: Horizontal shift indicating the level of clustering in the data. Larger absolute values in either direction (i.e., positive or negative) would yield stronger clustering.
sd: The standard deviation of the components of the bivariate normal distribution with default $s d = 1 / 6$ , used only when distribution="bvnormal".
distribution: The argument determining the distribution of each cluster. Takes on values "uniform" and "bvnormal" whose centers are $d$ units apart along the horizontal direction.

Author

Elvan Ceyhan

Examples

Run this code

n<-100;  #try also n<-50; or n<-1000;
d<-.5 #try also -.5,.75, 1
k<-3 #try also 5

#data generation
Xdat<-rhor.clust(n,k,d)
Xdat

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

#data generation (bvnormal)
n<-100;  #try also n<-50; n<-1000;
d<-.1 #try also -.1, .75, 1
k<-3 #try also 5
Xdat<-rhor.clust(n,k,d,distr="bvnormal") #try also Xdat<-rhor.clust(n,k,d,sd=.15,distr="bvnormal")
Xdat

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

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