NAME
Text::NSP::Measures::2D::MI::pmi  Perl module that implements Pointwise Mutual Information.
SYNOPSIS
Basic Usage
use Text::NSP::Measures::2D::MI::pmi;
my $npp = 60; my $n1p = 20; my $np1 = 20; my $n11 = 10;
$pmi_value = calculateStatistic( n11=>$n11,
n1p=>$n1p,
np1=>$np1,
npp=>$npp);
if( ($errorCode = getErrorCode()))
{
print STDERR $errorCode."  ".getErrorMessage()."\n"";
}
else
{
print getStatisticName."value for bigram is ".$pmi_value."\n"";
}
DESCRIPTION
Assume that the frequency count data associated with a bigram <word1><word2> is stored in a 2x2 contingency table:
word2 ~word2
word1 n11 n12  n1p
~word1 n21 n22  n2p

np1 np2 npp
where n11 is the number of times <word1><word2> occur together, and n12 is the number of times <word1> occurs with some word other than word2, and n1p is the number of times in total that word1 occurs as the first word in a bigram.
The expected values for the internal cells are calculated by taking the product of their associated marginals and dividing by the sample size, for example:
np1 * n1p
m11= 
npp
Pointwise Mutual Information (pmi) is defined as the log of the deviation between the observed frequency of a bigram (n11) and the probability of that bigram if it were independent (m11).
PMI = log (n11/m11)
The Pointwise Mutual Information tends to overestimate bigrams with low
observed frequency counts. To prevent this sometimes a variation of pmi
is used which increases the influence of the observed frequency.
PMI = log((n11^$exp)/m11)
The $exp is 1 by default, so by default the measure will compute the
Pointwise Mutual Information for the given bigram. To use a variation of
the measure, users can pass the $exp parameter using the pmi_exp
command line option in statistic.pl or by passing the $exp to the
initializeStatistic() method from their program.
The usage for statistic.pl is
statistic.pl pmi out_pmi.stt out.cnt  for Point Wise Mutual Information
$exp is 1 in this case.
statistic.pl pmi_exp 2 pmi out_pmi2.stt out.cnt  for the variant with
$exp set to 2.
Methods
 initializeStatistic() Initialization of the pmi_exp parameter if required

INPUT PARAMS : none
RETURN VALUES : none
 calculateStatistic()  This method calculates the pmi value

INPUT PARAMS : $count_values .. Reference of a hash containing the count values computed by the count.pl program.
RETURN VALUES : $pmi .. PMI value for this bigram.
 getStatisticName()  Returns the name of this statistic

INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
AUTHOR
Ted Pedersen, University of Minnesota Duluth <tpederse@d.umn.edu>
Satanjeev Banerjee, Carnegie Mellon University <satanjeev@cmu.edu>
Amruta Purandare, University of Pittsburgh <amruta@cs.pitt.edu>
Bridget ThomsonMcInnes, University of Minnesota Twin Cities <bthompson@d.umn.edu>
Saiyam Kohli, University of Minnesota Duluth <kohli003@d.umn.edu>
HISTORY
Last updated: $Id: pmi.pm,v 1.24 2008/03/26 17:20:28 tpederse Exp $
BUGS
SEE ALSO
@inproceedings{ church89word,
author = {Kenneth W. Church and Patrick Hanks},
title = {Word association norms, mutual information, and Lexicography},
booktitle = {Proceedings of the 27th. Annual Meeting of the Association for Computational Linguistics},
publisher = {Association for Computational Linguistics},
address = {Vancouver, B.C.},
pages = {7683},
year = {1989},
url = L<http://acl.ldc.upenn.edu/J/J90/J901003.pdf> }
http://groups.yahoo.com/group/ngram/
http://www.d.umn.edu/~tpederse/nsp.html
COPYRIGHT
Copyright (C) 20002006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget ThomsonMcInnes and Saiyam Kohli
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 021111307, USA.
Note: a copy of the GNU General Public License is available on the web at http://www.gnu.org/licenses/gpl.txt and is included in this distribution as GPL.txt.