rrot.clust | R Documentation |
An object of class "Clusters"
.
Generates n
2D points with k
(k ≥ 2) clusters with centers d unit away from origin and angles
between the rays joining successive centers and origin is 2 π/k where about n/k points belongs to each cluster.
If distribution="uniform"
, the points are uniformly generated in their square
supports with unit edge lengths and centers at (d \cos(j 2 π/k),d \cos(j 2π/k)) for j=1,2,…,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=
(d \cos(j 2 π/k),d \cos(j 2π/k))
for j=1,2,…,k and the covariance matrix sd I_2, where sd=d√{2 (1-cos(2 π/k))}/3
and 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, sd^2, gets smaller, and clustering gets weaker
as the variance of each component gets larger where default is sd=d√{2 (1-cos(2 π/k))}/3.
rrot.clust( n, k, d, sd = d * sqrt(2 * (1 - cos(2 * pi/k)))/3, distribution = c("uniform", "bvnormal") )
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 |
Radial 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
sd=d√{2 (1-cos(2 π/k))}/3, used only when |
distribution |
The argument determining the distribution of each cluster. Takes on values |
A list
with the elements
type |
The type of the clustering pattern |
parameters |
The number of clusters, |
gen.points |
The output set of generated points from the |
desc.pat |
Description of the clustering pattern |
mtitle |
The |
num.points |
The number of generated points. |
xlimit,ylimit |
The possible ranges of the x- and y-coordinates of the generated points |
Elvan Ceyhan
rdiag.clust
and rhor.clust
n<-100; #try also n<-50; n<-1000; d<- 1.5 #try also -1, 1, 1.5, 2 k<-3 #try also 5 #data generation Xdat<-rrot.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<- 1.5 #try also -1, 1, 1.5, 2 k<-3 #try also 5 Xdat<-rrot.clust(n,k,d,distr="bvnormal") #also try Xdat<-rrot.clust(n,k,d,sd=.5,distr="bvnormal") Xdat summary(Xdat) plot(Xdat,asp=1) plot(Xdat)
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