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Text::NSP::Measures::2UserIContributed PerlText::NSP::Measures::2D::MI::pmi(3)NAMEText::NSP::Measures::2D::MI::pmi - Perl module that implements Pointwise Mutual Information.SYNOPSISBasicUsageuse 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""; }DESCRIPTIONAssume 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.MethodsinitializeStatistic()-Initialization of the pmi_exp parameter if required INPUT PARAMS : none RETURN VALUES : nonecalculateStatistic()- 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.AUTHORTed 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>HISTORYLast updated: $Id: pmi.pm,v 1.24 2008/03/26 17:20:28 tpederse Exp $BUGSSEE ALSO@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>COPYRIGHTCopyright (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. perl v5.32.0 2008-03-2Text::NSP::Measures::2D::MI::pmi(3)

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