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

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### 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

```

@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},
pages = {76--83},
year = {1989},
url = L<http://acl.ldc.upenn.edu/J/J90/J90-1003.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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