NAME
    Statistics::Gap - Perl extension for the "Gap Statistics"

SYNOPSIS
      use Statistics::Gap;
      &gap("GapPrefix", "InputFile", "squared", "agglo", 5, 3, "unif");

      OR

      use Statistics::Gap;
      &gap("GapPrefix", "InputFile", "squared", "agglo", 5, 3, "prop");

DESCRIPTION
        Given a dataset how does one automatically find the optimal number 
        of clusters that the dataset should be grouped into? - is one of the 
        prevailing problems. Statisticians Robert Tibshirani, Guenther Walther 
        and Trevor Hastie  propose a solution for this problem in a Techinal 
        Report named - "Estimating the number of clusters in a dataset via 
        the Gap Statistics". This perl module implements the approach proposed 
        in the above paper.

        NOTE: 
        Gap Statistics uses reference distribution in the process of estimating
        the number of clusters. The appropriate methodology for generation of this 
        reference distribution is dependent on the data to be clustered. 
        This module was implemented for data with following characteristics:
        1. highly sparse - very few features occur in any given observation.
        2. high multivariate dimensionality (i.e. large feature space)
        3. binary feature frequency - feature either occurs or does not occur 
           in an observation.

  EXPORT
     "gap" function by default.

INPUT
  Prefix
        The string that should be used to as a prefix while naming the 
        intermediate files and the .png files (graph files).

  InputFile
        The input dataset 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.

   DistanceMeasure
        The Distance Measure that should be used.
        Currrently this module supports the following distance measure:
        1. Squared Euclidean (string that should be used as an argument: "squared")
        2. Manhattan (string that should be used as an argument: "manhattan")
        3. Euclidean (string that should be used as an argument: "euclidean")

   ClusteringAlgorithm
        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.

   B value
        Specifies the number of time the reference distribution should be generated.

   ReferenceGenerationMethod
        1. Uniform - While generating the reference distribution, all the features
        in the feature set have equal probability of being selected for the observation
        under consideration.
    
        2. Proportional - Each feature is assigned a probability of being selected
        depending upon its frequency of occurrence in the observed data. Thus feature
        distribution is taken into consideration while selecting the features for the 
        reference distribution generation.

OUTPUT
        The output returned is a single integer number which indicates the optimal
        number of clusters that the input dataset should be clustered into.

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/

        2. Following Perl Modules
            1. GD   (http://search.cpan.org/~lds/GD-2.19/GD.pm)
            2. GD::Text     (http://search.cpan.org/~mverb/GDTextUtil-0.86/Text.pm)
            3. GD::Graph::lines     (http://search.cpan.org/~mverb/GDGraph-1.43/)
            4. GD::Graph::colour    (http://search.cpan.org/~mverb/GDGraph-1.43/Graph/colour.pm)

SEE ALSO
        http://citeseer.ist.psu.edu/tibshirani00estimating.html
        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.

