The function pkbc
performs the Poisson kernel-based clustering
algorithm on the sphere based on the Poisson kernel-based densities.
Usage
pkbc(
dat,
nClust = NULL,
maxIter = 300,
stoppingRule = "loglik",
initMethod = "sampleData",
numInit = 10
)
# S4 method for ANY
pkbc(
dat,
nClust = NULL,
maxIter = 300,
stoppingRule = "loglik",
initMethod = "sampleData",
numInit = 10
)
# S4 method for pkbc
show(object)
Arguments
- dat
Data matrix or data.frame of data points on the sphere to be clustered. The observations in dat are normalized to ensure that they lie on the d-simensional sphere. Note that d > 1.
- nClust
Number of clusters. It can be a single value or a numeric vector.
- maxIter
The maximum number of iterations before a run is terminated.
- stoppingRule
String describing the stopping rule to be used within each run. Currently must be either:
'max'
(until the change in the log-likelihood is less than a given threshold (1e-7)),'membership'
(until the membership is unchanged), or'loglik'
(based on a maximum number of iterations).- initMethod
String describing the initialization method to be used. Currently must be
'sampleData'
.- numInit
Number of initializations.
- object
Object of class
pkbc
Value
An S4 object of class pkbc
containing the results of the
clustering procedure based on Poisson kernel-based distributions. The object
contains the following slots:
res_k
: List of results of the Poisson kernel-based clustering
algorithm for each value of number of clusters specified in nClust
.
Each object in the list contains:
postProbs
Posterior probabilities of each observation for the indicated clusters.LogLik
Maximum value of log-likelihood functionwcss
Values of within-cluster sum of squares computed with Euclidean distance and cosine similarity, respectively.params
List of estimated parameters of the mixture modelmu
estimated centroidsrho
estimated concentration parameters rhoalpha
estimated mixing proportions
finalMemb
Vector of final membershipsrunInfo
List of information of the EM algorithm iterationslokLikVec
vector of log-likelihood valuesnumIterPerRun
number of E-M iterations per run
input
: List of input information.
Details
The function estimates the parameter of a mixture of Poisson
kernel-based densities. The obtained estimates are used for assigning final
memberships, identifying the nClust
clusters.
References
Golzy, M., Markatou, M. (2020) Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling, Journal of Computational and Graphical Statistics, 29:4, 758-770, DOI: 10.1080/10618600.2020.1740713.
Examples
#We generate three samples of 100 observations from 3-dimensional
#Poisson kernel-based densities with rho=0.8 and different mean directions
size<-100
groups<-c(rep(1, size), rep(2, size),rep(3,size))
rho<-0.8
set.seed(081423)
data1<-rpkb(size, c(1,0,0),rho,method="rejvmf")
data2<-rpkb(size, c(0,1,0),rho,method="rejvmf")
data3<-rpkb(size, c(0,0,1),rho,method="rejvmf")
dat<-rbind(data1$x,data2$x, data3$x)
#Perform the clustering algorithm with number of clusters k=3.
pkbd<- pkbc(dat, 3)