scaclust: 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

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".
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.
membera matrix with the membership values of the data points to the clusters.
errorReturns the value of the error function.
learninga list with elements [object Object],[object Object],and,[object Object],[object Object]
callReturns a call in which all of the arguments are specified by their names.

References

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