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# Manual Reference Pages  -  TEXT::NSP::MEASURES::2D::MI::TMI (3)

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### 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://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 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.

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