cmeans {e1071}R Documentation

Fuzzy C-Means Clustering

Description

The fuzzy version of the known kmeans clustering algorithm as well as its online update (Unsupervised Fuzzy Competitive learning).

Usage

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

Arguments

x The data matrix where columns correspond to variables and rows to observations
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 Must be one of the following: If "euclidean", the mean square error, if "manhattan", the mean absolute error is computed. Abbreviations are also accepted.
method If "cmeans", then we have the cmeans fuzzy clustering method, if "ufcl" we have the On-line Update. Abbreviations in the method names are also accepted.
m The degree of fuzzification. It is defined for values greater than 1
rate.par The parameter of the learning rate

Details

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 fuzzy 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).

Value

cmeans returns an object of class "fclust".

centers The final cluster centers.
size The number of data points in each cluster.
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.
iter The number of iterations performed,
membership a matrix with the membership values of the data points to the clusters.
withinerror Returns the sum of square distances within the clusters.
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.

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<-cmeans(x,2,20,verbose=TRUE,method="cmeans",m=2)
print(cl)

# 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<-cmeans(x,6,20,verbose=TRUE,method="cmeans")
print(cl)

# assign classes to some new data
y<-rbind(matrix(rnorm(33,sd=0.3),ncol=3),
         matrix(rnorm(33,mean=1,sd=0.3),ncol=3),
         matrix(rnorm(3,mean=2,sd=0.3),ncol=3))
#         ycl<-predict(cl, y, type="both")

[Package e1071 version 1.5-2 Index]