# NAME

Statistics::CalinskiHarabasz - Perl extension to the cluster stopping rule proposed by Calinski and Harabasz (C&H)

# SYNOPSIS

```
use Statistics::CalinskiHarabasz;
&ch(InputFile, "agglo", 10);
Input file is expected in the "dense" format -
Sample Input file:
6 5
1 1 0 0 1
1 0 0 0 0
1 1 0 0 1
1 1 0 0 1
1 0 0 0 1
1 1 0 0 1
```

# DESCRIPTION

C&H use the Variance Ratio Criterion which is analogous to F-Statistics to estimate the number of clusters a given data naturally falls into. They minimize Within Cluster/Group Sum of Squares (WGSS) and maximize Between Cluster/Group Sum of Squares (BGSS)

## EXPORT

"ch" function by default.

# INPUT

## InputFile

The input dataset is expected in "dense" matrix format. The input dense matrix is expected in a plain text file where the first line in the file gives the dimensions of the dataset and then the dataset in a matrix format should follow. The contexts / observations should be along the rows and the features should be along the column.

```
eg:
6 5
1 1 0 0 1
1 0 0 0 0
1 1 0 0 1
1 1 0 0 1
1 0 0 0 1
1 1 0 0 1
```

The first line (6 5) gives the number of rows (observations) and the number of columns (features) present in the following matrix. Following each line records the frequency of occurrence of the feature at the column in the given observation. Thus features1 (1st column) occurs once in the observation1 and infact once in all the other observations too while the feature3 does not occur in observation1.

## ClusteringMethod

The Clustering Measures that can be used are: 1. rb - Repeated Bisections [Default] 2. rbr - Repeated Bisections for by k-way refinement 3. direct - Direct k-way clustering 4. agglo - Agglomerative clustering 5. graph - Graph partitioning-based clustering 6. bagglo - Partitional biased Agglomerative clustering

## K value

This is an approximate upper bound for the number of clusters that may be present in the dataset. Thus for a dataset that you expect to be seperated into 3 clusters this value should be set some integer value greater than 3.

# OUTPUT

A single integer number which is the estimate of number of clusters present in the input dataset.

# PRE-REQUISITES

1. This module uses suite of C programs called CLUTO for clustering purposes. Thus CLUTO needs to be installed for this module to be functional. CLUTO can be downloaded from http://www-users.cs.umn.edu/~karypis/cluto/

# SEE ALSO

1. T. Calinski and J. Harabasz. A dendrite method for cluster analysis. Communications in statistics, 3(1):1--27, 1974. 2. http://www-users.cs.umn.edu/~karypis/cluto/

# AUTHOR

Anagha Kulkarni, University of Minnesota Duluth kulka020 <at> d.umn.edu

Guergana Savova, Mayo Clinic savova.guergana <at> mayo.edu

# COPYRIGHT AND LICENSE

Copyright (C) 2005-2006, Guergana Savova and Anagha Kulkarni

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.