NAME
Data::Mining:AssociationRules - Mine association rules and frequent sets from data.
SYNOPSIS
use Data::Mining::AssociationRules;
my %transaction_map;
my $transaction_file = "foo.txt";
read_transaction_file(\%transaction_map, $transaction_file);
generate_frequent_sets(\%transaction_map, $output_file_prefix,
$support_threshold, $max_n);
generate_rules($output_file_prefix, $support_threshold,
$confidence_threshold, $max_n);
read_frequent_sets($set_map_ref, $file_prefix)
set_debug(1);
perl arm.pl -transaction-file foo.txt -support 2 -confidence-threshold 0.01 -max-set-size 6
See also FUNCTIONS, DESCRIPTION, and EXAMPLES below.
INSTALLATION
The typical:
FUNCTIONS
read_transaction_file($transaction_map_ref, $transaction_file)
Read in a transaction map from a file which has lines of two whitespace-separated columns:
transaction-id item-id
generate_frequent_sets ($transaction_map_ref, $file_prefix, $support_threshold, $max_n)
Given
- 0 a map of transactions
- 0 a file prefix
- 0 a support threshold
- 0 a maximum frequent set size to look for (optional)
generate the frequent sets in some files, one file per size of the set. That is, all 1-sets are in a file, all 2-sets in another, etc.
The files are lines of the form:
support-count item-set
where
- 0 support-count is the number of transactions in which the item-set appears
- 0 item-set is one or more space-separated items
read_frequent_sets($set_map_ref, $file_prefix)
Given
read all the frequent sets into a single map, which has as its key the frequent set (joined by single spaces) and as its value the support.
generate_rules($file_prefix, $support_threshold, $max_n)
Given
- 0 a file prefix
- 0 a support threshold (optional)
- 0 a confidence threshold (optional)
- 0 maximum frequent set size to look for (optional)
create a file with all association rules in it. The output file is of the form:
support-count confidence left-hand-set-size right-hand-set-size frequent-set-size left-hand-set => right-hand-set
DESCRIPTION
This module contains some functions to do association rule mining from text files. This sounds obscure, but really measures beautifully simple things through counting.
FREQUENT SETS
Frequent sets answer the question, "Which events occur together more than N times?"
The detail
The 'transaction file' contains items in transactions. A set of items has 'support' s if all the items occur together in at least s transactions. (In many papers, support is a number between 0 and 1 representing the fraction of total transactions. I found the absolute number itself more interesting, so I use that instead. Sorry for the confusion.) For an itemset "A B C", the support is sometimes notated "T(A B C)" (the number of 'T'ransactions).
A set of items is called a 'frequent set' if it has support at least the given support threshold. Generating frequent set produces all frequent sets, and some information about each set (e.g., its support).
RULES
Association rules answer the (related) question, "When these events occur, how often do those events also occur?"
The detail
A rule has a left-hand set of items and a right-hand set of items. A rule "LHS => RHS" with a support s and 'confidence' c means that the underlying frequent set (LHS + RHS) occured together in at least s transactions, and for all the transactions LHS occurred in, RHS also occured in at least the fraction c (a number from 0 to 1).
Generating rules produces all rules with support at least the given support threshold, and confidence at least the given confidence threshold. The confidence is sometimes notated "conf(LHS => RHS) = T(LHS + RHS) / T(LHS)". There is also related data with each rule (e.g., the size of its LHS and RHS, the support, the confidence, etc.).
FREQUENT SETS AND ASSOCIATION RULES GENERALLY USEFUL
Although association rule mining is often described in commercial terms like "market baskets" or "transactions" (collections of events) and "items" (events), one can imagine events that make this sort of counting useful across many domains. Events could be
For this reason, I believe counting frequent sets and looking at association rules to be a fundamental tool of any data miner, someone who is looking for patterns in pre-existing data, whether commercial or not.
EXAMPLES
Given the following input file:
234 Orange
463 Strawberry
53 Apple
234 Banana
412 Peach
467 Pear
234 Pear
147 Pear
141 Orange
375 Orange
Generating frequent sets at support threshold 1 (a.k.a. 'at support 1') produces three files:
The 1-sets:
1 Strawberry
1 Banana
1 Apple
3 Orange
1 Peach
3 Pear
The 2-sets:
1 Banana Orange
1 Banana Pear
1 Orange Pear
The 3-sets:
1 Banana Orange Pear
Generating the rules at support 1 produces the following:
1 0.333 1 1 2 Orange => Pear
1 0.333 1 1 2 Pear => Orange
1 1.000 1 2 3 Banana => Orange Pear
1 0.333 1 2 3 Orange => Banana Pear
1 1.000 2 1 3 Banana Orange => Pear
1 0.333 1 2 3 Pear => Banana Orange
1 1.000 2 1 3 Banana Pear => Orange
1 1.000 2 1 3 Orange Pear => Banana
1 1.000 1 1 2 Banana => Orange
1 0.333 1 1 2 Orange => Banana
1 1.000 1 1 2 Banana => Pear
1 0.333 1 1 2 Pear => Banana
Generating frequent sets at support 2 produces one file:
3 Orange
3 Pear
Generating rules at support 2 produces nothing.
Generating rules at support 1 and confidence 0.5 produces:
1 1.000 1 2 3 Banana => Orange Pear
1 1.000 2 1 3 Banana Orange => Pear
1 1.000 2 1 3 Banana Pear => Orange
1 1.000 2 1 3 Orange Pear => Banana
1 1.000 1 1 2 Banana => Orange
1 1.000 1 1 2 Banana => Pear
Note all the lower confidence rules are gone.
ALGORITHM
Generating frequent sets
Generating frequent sets is straight-up Apriori. See for example:
http://www.almaden.ibm.com/software/quest/Publications/papers/vldb94_rj.pdf
I have not optimized. It depends on having the transactions all in memory. However, given that, it still might scale decently (millions of transactions).
Generating rules
Generating rules is a very vanilla implementation. It requires reading all the frequent sets into memory, which does not scale at all. Given that, since computers have lots of memory these days, you might still be able to get away with millions of frequent sets (which is <<millions of transactions).
BUGS
There is an existing tool (written in C) to mine frequent sets I kept running across:
http://fuzzy.cs.uni-magdeburg.de/~borgelt/software.html#assoc
I should check it out to see if it is easy or desirable to be file-level compatible with it.
One could imagine wrapping it in Perl, but the Perl-C/C++ barrier is where I have encountered all my troubles in the past, so I wouldn't personally pursue that.
VERSION
This document describes Data::Mining::AssociationRules version 0.1.
AUTHOR
Dan Frankowski
dfrankow@winternet.com
http://www.winternet.com/~dfrankow
Hey, if you download this module, drop me an email! That's the fun
part of this whole open source thing.
LICENSE
This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.
The full text of the license can be found in the LICENSE file included in the distribution and available in the CPAN listing for Data::Mining::AssociationRules (see www.cpan.org or search.cpan.org).
DISCLAIMER
To the maximum extent permitted by applicable law, the author of this module disclaims all warranties, either express or implied, including but not limited to implied warranties of merchantability and fitness for a particular purpose, with regard to the software and the accompanying documentation.