cshell: Fuzzy C-Shell Clustering

In e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien

Fuzzy C-Shell Clustering

Description

The c-shell clustering algorithm, the shell prototype-based version (ring prototypes) of the fuzzy kmeans clustering method.

Usage

cshell(x, centers, iter.max=100, verbose=FALSE, dist="euclidean",
       method="cshell", m=2, radius = NULL)

Arguments

x	The data matrix, were columns correspond to the 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	Currently, only the "cshell" method; the c-shell fuzzy clustering method
m	The degree of fuzzification. It is defined for values greater than 1
radius	The radius of resulting clusters

Details

The data given by x is clustered by the fuzzy c-shell 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 "cshell", then we have the c-shell fuzzy clustering method.

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 radius is by default set to 0.2 for every cluster.

Value

cshell returns an object of class "cshell".

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

Rajesh N. Dave. Fuzzy Shell-Clustering and Applications to Circle Detection in Digital Images. Int. J. of General Systems, Vol. 16, pp. 343-355, 1996.

Examples

## a 2-dimensional example
x <- rbind(matrix(rnorm(50, sd = 0.3), ncol = 2),
           matrix(rnorm(50, mean = 1, sd=0.3), ncol = 2))
cl <- cshell(x, 2, 20, verbose = TRUE, method = "cshell", m = 2)
print(cl)

e1071 documentation built on Sept. 17, 2024, 1:06 a.m.