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

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### NAME

Text::NSP::Measures::3D::MI::tmi - Perl implementation for True Mutual
Information for trigrams.

### SYNOPSIS

Basic Usage

```

use Text::NSP::Measures::3D::MI::tmi;

\$tmi_value = calculateStatistic( n111=>10,
n1pp=>40,
np1p=>45,
npp1=>42,
n11p=>20,
n1p1=>23,
np11=>21,
nppp=>100);

if( (\$errorCode = getErrorCode()))
{
print STDERR \$erroCode." - ".getErrorMessage()."\n";
}
else
{
print getStatisticName."value for bigram is ".\$tmi_value."\n";
}

```

### DESCRIPTION

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

```

tmi = [n111/nppp * log(n111/m111) + n112/nppp * log(n112/m112) +
n121/nppp * log(n121/m121) + n122/nppp * log(n122/m122) +
n211/nppp * log(n211/m211) + n212/nppp * log(n212/m212) +
n221/nppp * log(n221/m221) + n222/nppp * log(n222/m222)]

PMI =   log (n111/m111)

```

Here n111 represents the observed value for the cell (1,1,1) and m111 represents the expected value for that cell. 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:

```

n1pp * np1p * npp1
m111=   --------------------
nppp

```

#### Methods

 calculateStatistic(\$count_values) - 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 trigram. 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 1.10 2006/06/21 11:10:53 saiyam_kohli 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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