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```Text::NSP::Measures::2UserIContributed PerlText::NSP::Measures::2D::MI::pmi(3)

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 Thomson-McInnes,	    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 = {76--83},
year = {1989},
url = L<http://acl.ldc.upenn.edu/J/J90/J90-1003.pdf> }

<http://groups.yahoo.com/group/ngram/>

<http://www.d.umn.edu/~tpederse/nsp.html>

COPYRIGHT
Copyright (C) 2000-2006,	Ted Pedersen, Satanjeev	Banerjee, Amruta
Purandare, Bridget Thomson-McInnes 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  02111-1307, 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.

perl v5.32.0			  2008-03-2Text::NSP::Measures::2D::MI::pmi(3)
```

NAME | SYNOPSIS | DESCRIPTION | AUTHOR | HISTORY | BUGS | SEE ALSO | COPYRIGHT

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