Text::NSP::Measures::2D::MI::pmi - Perl module that implements Pointwise Mutual Information.


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,

  if( ($errorCode = getErrorCode()))
    print STDERR $errorCode." - ".getErrorMessage()."\n"";
    print getStatisticName."value for bigram is ".$pmi_value."\n"";


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=   ---------

Pointwise Mutual Information (pmi) is defined as the log of the devitation 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 or by passing the $exp to the
 initializeStatistic() method from their program.

 The usage for is pmi out_pmi.stt out.cnt    - for Point Wise Mutual Information
                                           $exp is 1 in this case. --pmi_exp 2 pmi out_pmi2.stt out.cnt   - for the variant with
                                                       $exp set to 2.


initializeStatistic() -Initialization of the pmi_exp parameter if required



calculateStatistic() - This method calculates the pmi value

INPUT PARAMS : $count_values .. Reference of a hash containing the count values computed by the program.

RETURN VALUES : $pmi .. PMI value for this bigram.

getStatisticName() - Returns the name of this statistic


RETURN VALUES : $name .. Name of the measure.


Ted Pedersen, University of Minnesota Duluth <>

Satanjeev Banerjee, Carnegie Mellon University <>

Amruta Purandare, University of Pittsburgh <>

Bridget Thomson-McInnes, University of Minnesota Twin Cities <>

Saiyam Kohli, University of Minnesota Duluth <>


Last updated: $Id:,v 1.23 2006/06/21 11:10:52 saiyam_kohli Exp $



  @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<> }


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 and is included in this distribution as GPL.txt.