Dan Frankowski > Data-Mining-AssociationRules > Data::Mining:AssociationRules

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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:

0 perl Makefile.PL
0 make test
0 make install

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

0 a set map
0 a file prefix
0 support threshold
0 max frequent set size (optional)

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

0 stock market went down at time t
0 patient had symptom X
0 flower petal length was > 5mm

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.

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