cmeanscl: 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

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

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".
centersThe final cluster centers.
clusterVector 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.
sizeThe number of data points in each cluster.
distThe distance measure used.
mThe degree of fuzzification.
membera matrix with the membership values of the data points to the clusters.
withinssReturns the sum of square distances within the clusters.
learninga list with elements [object Object],[object Object],[object Object],and,[object Object]
callReturns a call in which all of the arguments are specified by their names.

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

Run this code

# 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)