cmeanscl {e1071}R Documentation

Fuzzy C-Means Clustering

Description

The data given by x is clustered by the fuzzy kmeans algorithm.

If centers is a matrix, its rows are taken as the initial cluster centers. If centers is an integer, centers rows of x are randomly chosen as initial values.

The algorithm stops when the maximum number of iterations (given by iter.max) is reached.

If verbose is TRUE, it displays for each iteration the number the value of the objective function.

If dist is "euclidean", the distance between the cluster center and the data points is the Euclidean distance (ordinary kmeans algorithm). If "manhattan", the distance between the cluster center and the data points is the sum of the absolute values of the distances of the coordinates.

If method is "cmeans", then we have the kmeans fuzzy clustering method. If "ufcl" we have the On-line Update (Unsupervised Fuzzy Competitive learning) method, which works by performing an update directly after each input signal.

The parameters m defines the degree of fuzzification. It is defined for real values greater than 1 and the bigger it is the more fuzzy the membership values of the clustered data points are.

The parameter rate.par of the learning rate for the "ufcl" algorithm which is by default set to rate.par=0.3 and is taking real values in (0 , 1).

Usage

cmeanscl (x, centers, iter.max=100, verbose=FALSE, dist="euclidean",
        method="cmeans", m=2, rate.par = NULL)

Arguments

x Data matrix
centers Number of clusters or initial values for cluster centers
iter.max Maximum number of iterations
verbose If TRUE, make some output during learning
dist If "euclidean", the mean square error, if "manhattan ", the mean absolute error is computed
method If "cmeans", then we have the cmeans fuzzy clustering method, if "ufcl" we have the On-line Update (Unsupervised Fuzzy Competitive learning) method
m The degree of fuzzification. It is defined for values greater than 1
rate.par The parameter of the learning rate

Value

cmeanscl returns an object of class "fclust".

centers The final cluster centers.
cluster Vector containing the indices of the clusters where the data points are assigned to. The maximum membership value of a point is considered for partitioning it to a cluster.
size The number of data points in each cluster.
dist The distance measure used.
m The degree of fuzzification.
member a matrix with the membership values of the data points to the clusters.
withinss Returns the sum of square distances within the clusters.
learning a list with elements
ncenters
The number of the centers,
initcenters
The initial cluster centers,
iter
The number of iterations performed,
and
rate.par
The learning rate for the "ufcl" algorithm.
call Returns a call in which all of the arguments are specified by their names.

Author(s)

Evgenia Dimitriadou

References

Nikhil R. Pal, James C. Bezdek, and Richard J. Hathaway. Sequential Competitive Learning and the Fuzzy c-Means Clustering Algorithms. Neural Networks, Vol. 9, No. 5, pp. 787-796, 1996.

See Also

plot.fclust

Examples

# a 2-dimensional example
x<-rbind(matrix(rnorm(100,sd=0.3),ncol=2),
         matrix(rnorm(100,mean=1,sd=0.3),ncol=2))
cl<-cmeanscl(x,2,20,verbose=TRUE,method="cmeans",m=2)
print(cl)
plot(cl,x)   

# a 3-dimensional example
x<-rbind(matrix(rnorm(150,sd=0.3),ncol=3),
         matrix(rnorm(150,mean=1,sd=0.3),ncol=3),
         matrix(rnorm(150,mean=2,sd=0.3),ncol=3))
cl<-cmeanscl(x,6,20,verbose=TRUE,method="cmeans")
plot(cl,x)