Text::NSP::Measures::2D::MI::pmi - Perl module that implements Pointwise Mutual Information.
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""; }
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.
INPUT PARAMS : none
RETURN VALUES : none
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.
INPUT PARAMS : none
RETURN VALUES : $name .. Name of the measure.
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>
Last updated: $Id: pmi.pm,v 1.24 2008/03/26 17:20:28 tpederse 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<http://acl.ldc.upenn.edu/J/J90/J90-1003.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
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