Text::NSP::Measures::2D::MI::ps - Perl module that implements Poisson-Stirling measure of association for bigrams.
use Text::NSP::Measures::2D::MI::ps; my $npp = 60; my $n1p = 20; my $np1 = 20; my $n11 = 10; $ps_value = calculateStatistic( n11=>$n11, n1p=>$n1p, np1=>$np1, npp=>$npp); if( ($errorCode = getErrorCode())) { print STDERR $errorCode." - ".getErrorMessage()."\n""; } else { print getStatisticName."value for bigram is ".$ps_value."\n""; }
The log-likelihood ratio measures the deviation between the observed data and what would be expected if <word1> and <word2> were independent. The higher the score, the less evidence there is in favor of concluding that the words are independent.
Assume that the frequency count data associated with a bigram <word1><word2> as shown by 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
The Poisson Stirling measure is a negative logarithmic approximation of the Poisson-likelihood measure. It uses the Stirling's formula to approximate the factorial in Poisson-likelihood measure.
Poisson-Stirling = n11 * ( log(n11) - log(m11) - 1)
which is same as
Poisson-Stirling = n11 * ( log(n11/m11) - 1)
INPUT PARAMS : $count_values .. Reference of an hash containing the count values computed by the count.pl program.
RETURN VALUES : $poissonStirling .. Poisson-Stirling 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: ps.pm,v 1.9 2008/03/26 17:20:28 tpederse Exp $
http://groups.yahoo.com/group/ngram/
http://www.d.umn.edu/~tpederse/nsp.html
@article{SmadjaMH96, author = {Quasthoff, Uwe and Wolff, Christian}, title = {The Poisson collocation measure and its application}, journal = {Workshop on Computational Approaches to Collocations}, year = {2002}, url = L<http://www.ofai.at/~brigitte.krenn/colloc02/PoissonCollocationMeasureQuasthoffWolff_final.pdf>}
Copyright (C) 2000-2006, Ted Pedersen, Satanjeev Banerjee, Amruta Purandare, Bridget Thomson-McInnes and Saiyam Kohli
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