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

NAME
Text::NSP::Measures::2D::MI::tmi	- Perl module that implements True
Mutual
Information.

SYNOPSIS
Basic Usage

use Text::NSP::Measures::2D::MI::tmi;

my \$npp = 60; my \$n1p = 20; my	\$np1 = 20;  my \$n11 = 10;

\$tmi_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 ".\$tmi_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

True Mutual Information (tmi) is	defined	as the weighted	average	of the
Pointwise mutual	informations for all the observed and expected value
pairs.

tmi = [n11/npp * log(n11/m11) +	n12/npp	* log(n12/m12) +
n21/npp * log(n21/m21) +	n22/npp	* log(n22/m22)]

PMI =	log (n11/m11)

Methods
calculateStatistic() - This method calculates the tmi value
INPUT PARAMS	 : \$count_values       .. Reference of an hash
containing
the count values computed by
the
count.pl program.

RETURN VALUES : \$tmi		       .. TMI 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: tmi.pm,v 1.23	2008/03/26 17:20:28 tpederse Exp \$

BUGS
@inproceedings{moore:2004:EMNLP,
author	 = {Moore, Robert C.},
title	 = {On Log-Likelihood-Ratios and the Significance of Rare
Events },
booktitle = {Proceedings	of EMNLP 2004},
editor =	{Dekang	Lin and	Dekai Wu},
year	 = 2004,
month	 = {July},
publisher = {Association	for Computational Linguistics},
pages	 = {333--340}
url = L<http://acl.ldc.upenn.edu/acl2004/emnlp/pdf/Moore.pdf>}

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

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

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
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::tmi(3)
```