cshell {e1071} R Documentation

## 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",
```

### 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.

### 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)

# assign classes to some new data
y<-rbind(matrix(rnorm(13,sd=0.3),ncol=2),
matrix(rnorm(13,mean=1,sd=0.3),ncol=2))
#         ycl<-predict(cl, y, type="both")
```

[Package e1071 version 1.5-2 Index]