#!/usr/local/bin/perl -w
=head1 NAME
combig.pl - Combine frequency counts to determine co-occurrence
=head1 SYNOPSIS
Combines (sums) the frequency counts of bigrams made up of the same pair
of words in either possible order. It will count the number of time two
words occur together in a bigram regardless of which one comes first.
=head1 DESCRIPTION
=head2 USAGE
combig.pl [OPTIONS] BIGRAM
=head3 INPUT PARAMETERS
=over 4
=item * BIGRAM
Specify a file of bigram counts created by NSP programs count.pl.
The entries in BIGRAM will be formatted as follows:
word1<>word2<>n11 n1p np1
Here, word1 is followed by word2 n11 times. word1 occurs as the 1st word in
total n1p bigrams and word2 occurs as the 2nd word in np1 bigrams.
=item * OPTIONS
--help
Displays this message.
--version
Displays the version information.
=back
=head3 OUTPUT
combig.pl produces a count of the number of times two words make up a
bigram in either order, whereas count.pl produces counts for a single
fixed ordering. In other words, combig.pl combines the counts of bigrams
that are composed of the same words but in reverse order. While the
BIGRAM shows pairs of words forming bigrams, output of combig will show
the pairs of words that are co-occurrences or that co-occur irrespective
of their order.
e.g. if bigrams
word1<>word2<>n11 n1p np1
and
word2<>word1<>m11 m1p mp1
are found in BIGRAM file, then combig.pl treats these as a single unordered bigram
word1<>word2<>n11+m11 n1p+mp1 np1+m1p
where the new bigram will show a combined contingency table in which the order of words doesn't matter.
word2 ~word2
___________________________________________________________
word1 | n11+m11 n12+m21 | n1p+mp1
| |
~word1 | n21+m12 n22+m22-n | n2p+mp2-n
___________________________________________________
np1+m1p np2+m2p-n | n
here the entry
=over 4
=item * (word1,word2)=n11+m11
shows the number of bigrams having both word1 and word2 in either order
i.e. word1<>word2 + word2<>word1
=item * (word1,~word2)=n12+m21
shows the number of bigrams having word1 but not word2 at either position
i.e. word1<>~word2 + ~word2<>word1
=item * (~word1,word2)=n21+m12
shows the number of bigrams having word2 but not word1 at either position
i.e. ~word1<>word2 + word2<>~word1
=item * (~word1,~word2)=n22+m22
shows the number of bigrams not having word1 nor word2 at either position
i.e. ~word1<>~word2 + ~word2<>~word1 - n
where n=total number of bigrams
The mathematical proof of how the cell counts in the above contingency table are
counted is explained in section Proof.
=back
When a bigram appears in only one order i.e.
word1<>word2<>n11 n1p np1
appears but
word2<>word1<>m11 m1p mp1
does not, then the combined bigram will be same as the original bigram
that appears. Or in other words,
word1<>word2<>n11 n1p np1
is displayed as it is.
=head2 PROOF OF CORRECTNESS
A bigram word1<>word2<>n11 n1p np1 represents a contingency table
word2 ~word2
--------------------------------------
word1 n11 | n12 | n1p
| |
~word1 n21 | n22 | n2p
--------------------------------------
np1 | np2 | n
while a bigram word2<>word1<>m11 m1p mp1 represents a contingency table
word1 ~word1
--------------------------------------
word2 m11 | m12 | m1p
| |
~word2 m21 | m22 | m2p
--------------------------------------
mp1 | mp2 | n
Here,
n11+n12+n21+n22 = n
Also,
m11+m12+m21+m22 = n
combig.pl combines bigram counts into a single order independant word pair
word1<>word2<>n11+m11 n12+m21 n21+m12
And the corresponding contingency table will be shown as
word2 ~word2
-----------------------------------------
word1 n11+m11 | n12+m21 | n1p+mp1
| |
~word1 n21+m12 | n22+m22-n | n2p+mp2
-----------------------------------------
np1+m1p | np2+m2p | n
The first cell (n11+m11) shows the #bigrams having word1 and word2
(irrespective of their positions) i.e. word1<>word2 or word2<>word1
which is n11+m11.
The second cell (n12+m21) shows the #bigrams having word1 but not
word2 at any position i.e. word1<>~word2 or ~word2<>word1 which is
n12+m21.
The third cell (n21+m12) shows the #bigrams having word2 but not word1
at any position i.e. ~word1<>word2 or word2<>~word1 which is n21+m12.
The fourth cell (m22+n22-n) shows the #bigrams not having word1 nor
word2 at any position which
= n - (n11+m11) - (n12+m21) - (n21+m12)
= n - (n11+n12+n21) - (m11+m12+m21)
= n - (n-n22) - (n-m22)
= n22 + m22 - n
Alternative proof -
n22 = m11 + m12 + m21 + X (a)
m22 = n11 + n12 + n21 + X (b)
where X = #bigrams not having either word1 or word2.
as both n22 and m22 have some terms in common which show the
bigrams not having either word1 or word2. But,
m11+m12+m21 = n - m22
Substituting this in eqn (a)
n22 = n - m22 + X
Or
X = n22 + m22 - n
Or add (a) and (b) to get
n22+m22 = (n11+m11) + (n12+m21) + (n21+m12) + 2X
rearranging terms,
n22+m22 = (n11+n12+n21) + (m11+m12+m21) + 2X
but
n11+n12+n21 = n - n22 and
m11+m12+m21 = n - m22
Hence,
n22+m22 = (n-n22) + (n-m22) + 2X
2(n22+m22-n) = 2X
Or
(n22+m22-n) = X
which is the fourth cell count.
=head2 Viewing Bigrams as Graphs
In bigrams, the order of words is important. Bigram word1<>word2 shows that
word2 follows word1. Bigrams can be viewed as a directed graph where a bigram
word1<>word2 will represent a directed edge e from initial vertex word1 to
terminal vertex word2(word1->word2).
In this case,
n11, which is the number of times bigram word1<>word2 occurs, becomes
the weight of the directed edge word1->word2.
n1p, which is the number of bigrams having word1 at 1st position, becomes
the out degree of vertex word1
and
np1, which is the number of bigrams having word2 at 2nd position, becomes
the in degree of vertex word2
combig.pl creates a new list of word pairs from these bigrams such that the
order of words can be ignored. Viewed another way, it converts the directed
graph of given bigrams to an undirected graph showing new word pairs.
A pair say
word1<>word2<>n11 n1p np1
shown in the output of combig can be viewed as an undirected edge joining
word1 and word2 having weight n11. If we count the degree of vertex word1 it
will be n1p and degree of vertex word2 will be np1.
=head1 AUTHORS
Amruta Purandare, pura0010@d.umn.edu
Ted Pedersen, tpederse@d.umn.edu
Last update 03/22/04 by ADP
This work has been partially supported by a National Science Foundation
Faculty Early CAREER Development award (#0092784).
=head1 BUGS
=head1 SEE ALSO
http://www.d.umn.edu/~tpederse/nsp.html
=head1 COPYRIGHT
Copyright (c) 2004, Amruta Purandare and Ted Pedersen
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.
=cut
###############################################################################
# THE CODE STARTS HERE
###############################################################################
# ================================
# COMMAND LINE OPTIONS AND USAGE
# ================================
# command line options
use Getopt::Long;
GetOptions ("help","version");
# show help option
if(defined $opt_help)
{
$opt_help=1;
&showhelp();
exit;
}
# show version information
if(defined $opt_version)
{
$opt_version=1;
&showversion();
exit;
}
# show minimal usage message if no arguments
if($#ARGV<0)
{
&showminimal();
exit;
}
#############################################################################
# ================================
# INITIALIZATION AND INPUT
# ================================
#$0 contains the program name along with
#the complete path. Extract just the program
#name and use in error messages
$0=~s/.*\/(.+)/$1/;
if(!defined $ARGV[0])
{
print STDERR "ERROR($0):
Please specify the Bigram file ...\n";
exit;
}
#accept the input file name
$infile=$ARGV[0];
if(!-e $infile)
{
print STDERR "ERROR($0):
Bigram file <$infile> doesn't exist...\n";
exit;
}
open(IN,$infile) || die "Error($0):
Error(code=$!) in opening Bigram file <$infile>.\n";
##############################################################################
$line_num=0;
while(<IN>)
{
$line_num++;
# shows total number of bigrams
if(/^\s*\d+\s*$/)
{
$total_big=$_;
}
# trimming extra spaces
chomp;
s/\s+$//g;
s/^\s+//g;
s/\s+/ /g;
# handling non-bigram lines
if(/^[\s\d]*$/ || /^\@/)
{
next;
}
# ------------------------------
# Checking for Valid bigram line
# ------------------------------
$check_bigram=$_;
$cnt=0;
#count how many times <> occurs
while($check_bigram=~/<>/)
{
$cnt++;
$check_bigram=$';
}
#should be 2 for bigrams
if($cnt!=2)
{
print STDERR "ERROR($0):
Line <$line_num> in Bigram file <$infile> is not formatted like the
bigram output of count.pl in NSP.\n";
exit;
}
# extracting word pairs forming this bigram
if(/^(.*)<>(.*)<>(\d+)\s+(\d+)\s+(\d+)\s*$/)
{
if(defined $n11{$1}{$2})
{
print STDERR "ERROR($0):
Bigram \"$1<>$2\" is repeated in Bigram file <$infile>.\n";
exit;
}
# if the reverse bigram is already seen
if(defined $n11{$2}{$1})
{
# new n11=n11{w2}{w1}+n11{w1}{w2}
$n11{$2}{$1}+=$3;
}
# make a new bigram entry
else
{
$n11{$1}{$2}=$3;
}
# marg stores total #pairs
# in which a word occurs
$marg{$1}+=$3;
$marg{$2}+=$3;
}
else
{
print STDERR "ERROR($0):
Line <$line_num> in Bigram file <$infile> is not formatted like the
bigram output of count.pl in NSP.\n";
exit;
}
}
if(defined $total_big)
{
print $total_big;
}
else
{
print STDERR "ERROR($0):
Bigram file <$infile> should show the total number of bigrams.\n";
exit;
}
foreach $w1 (keys %n11)
{
foreach $w2 (keys %{$n11{$w1}})
{
print "$w1<>$w2<>$n11{$w1}{$w2} $marg{$w1} $marg{$w2}\n";
}
}
##############################################################################
# ==========================
# SUBROUTINE SECTION
# ==========================
#-----------------------------------------------------------------------------
#show minimal usage message
sub showminimal()
{
print "Usage: combig.pl [OPTIONS] BIGRAM";
print "\nTYPE combig.pl --help for help\n";
}
#-----------------------------------------------------------------------------
#show help
sub showhelp()
{
print "Usage: combig.pl [OPTIONS] BIGRAM
Combines bigrams that are composed of same pair of words but in reverse orders.
BIGRAM
Should be an output created by count.pl program of NSP package.
OPTIONS:
--help
Displays this message.
--version
Displays the version information.
Type 'perldoc combig.pl' to view detailed documentation of combig.\n";
}
#------------------------------------------------------------------------------
#version information
sub showversion()
{
print "combig.pl - Version 0.02\n";
print "Copyright (C) 2004, Amruta Purandare & Ted Pedersen.\n";
print "Date of Last Update: 03/22/2004\n";
}
#############################################################################