e1071 (version 1.2-0)

cmeans: 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

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,
• and
• 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.

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).

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")