scaclust {e1071}R Documentation

Fuzzy Clustering using Scatter Matrices

Description

The data given by x is clustered by 4 fuzzy algorithms based on the scatter matrices computation.

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 method is "ad", then we have the Adaptive distances method, if "mtv" the Minimum total volume method, if "sand" the Sum of all normalized determinants method and if "mlm" the Maximum likelihood method (Product of Determinants). Note that all these algorithms are adapted for a fuzzification parameter of a value 2.

theta is by default 1.0 for every cluster. The relative volumes of the clusters are constrained a priori by these constants. An inappropriate choice can lead to a bad clustering. The Maximum likelihood method does not need this parameter.

Usage

scaclust (x, centers, iter.max=100, verbose=FALSE, method="ad", theta = 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
method If "ad", then we have the Adaptive distances method, if "mtv" the Minimum total volume method, if "sand" the Sum of all normalized determinants method and if "mlm" the Maximum likelihood method (Product of Determinants).
theta A set of constraints for each cluster.

Value

scaclust 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.
member a matrix with the membership values of the data points to the clusters.
error Returns the value of the error function.
learning a list with elements
ncenters
The number of the centers,
initcenters
The initial cluster centers,
and
iter
The number of iterations performed.
theta
Returns the a priori defined constants.
call Returns a call in which all of the arguments are specified by their names.

Author(s)

Evgenia Dimitriadou

References

P. J. Rousseeuw, L. Kaufman, and E. Trauwaert. Fuzzy Clustering using Scatter Matrices. Computational Statistics & Data Analysis, vol.23, p.135-151, 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<-scaclust(x,2,20,verbose=TRUE,method="ad")
print(cl)
plot(cl,x)