Mining the Top-K Association Rules (SPMF documentation)

This example explains how to run the TopKRules algorithm using the SPMF open-source data mining library.

How to run this example?

What is TopKRules?

TopKRules is an algorithm for discovering the top-k association rules appearing in a transaction database.

Why is it useful to discover top-k association rules? Because other association rule mining algorithms requires to set a minimum support (minsup) parameter that is hard to set (usually users set it by trial and error, which is time consuming). TopKRules solves this problem by letting users directly indicate k, the number of rules to be discovered instead of using minsup.

What is the input of TopKRules ?

TopKRules takes three parameters as input:

A transaction database is a set of transactions. Each transaction is a set of items. For example, consider the following transaction database. It contains 6 transactions (t1, t2, ..., t5, t6) and 5 items (1,2, 3, 4, 5). For example, the first transaction represents the set of items 1, 2, 4 and 5. This database is provided as the file contextIGB.txt in the SPMF distribution. It is important to note that an item is not allowed to appear twice in the same transaction and that items are assumed to be sorted by lexicographical order in a transaction.

Transaction id Items
t1 {1, 2, 4, 5}
t2 {2, 3, 5}
t3 {1, 2, 4, 5}
t4 {1, 2, 3, 5}
t5 {1, 2, 3, 4, 5}
t6 {2, 3, 4}

What is the output of TopKRules ?

TopKRules outputs the top-k association rules.

To explain what are top-k association rules, it is necessary to review some definitions. An itemset is a set of distinct items. The support of an itemset is the number of times that it appears in the database divided by the total number of transactions in the database. For example, the itemset {1 3} has a support of 33 % because it appears in 2 out of 6 transactions from the database.

An association rule X--> Y is an association between two itemsets X and Y that are disjoint. The support of an association rule is the number of transactions that contains X and Y divided by the total number of transactions. The confidence of an association rule is the number of transactions that contains X and Y divided by the number of transactions that contains X.

The top-k association rules are the k most frequent association rules in the database having a confidence higher or equal to minconf.

For example, if we run TopKRules with k = 2 and minconf = 0.8, we obtain the top-2 rules in the database having a confidence higher or equals to 80 %.

For instance, the rule 2 ==>5 means that if item 2 appears, it is likely to be associated with item 5 with a confidence of 83% in a transaction. Moreover, this rule has a support of 83 % because it appears in five transactions (t1, t2, t3, t4, t5) out of the six transactions contained in this database.

It is important to note that for some values of k, the algorithm may return slightly more than k rules. This is can happen if several rules have exactly the same support.

Input file format

The input file format is a text file containing transactions. Each lines represents a transaction. The items in the transaction are listed on the corresponding line. An item is represented by a positive integer. Each item is separated from the following item by a space. It is assumed that items are sorted according to a total order and that no item can appear twice in the same transaction. For example, for the previous example, the input file is defined as follows:

1 2 4 5
2 3 5
1 2 4 5
1 2 3 5
1 2 3 4 5
2 3 4

Consider the first line. It means that the first transaction is the itemset {1, 2, 4 and 5}. The following lines follow the same format.

Note that it is also possible to use the ARFF format as an alternative to the default input format. The specification of the ARFF format can be found here. Most features of the ARFF format are supported except that (1) the character "=" is forbidden and (2) escape characters are not considered. Note that when the ARFF format is used, the performance of the data mining algorithms will be slightly less than if the native SPMF file format is used because a conversion of the input file will be automatically performed before launching the algorithm and the result will also have to be converted. This cost however should be small.

Output file format

The output file format is defined as follows. It is a text file, where each line represents an association rule. On each line, the items of the rule antecedent are first listed. Each item is represented by a positive integer, followed by a single space. After, that the keyword "==>" appears followed by a space. Then, the items of the rule consequent are listed. Each item is represented by an integer, followed by a single space. Then, the keyword " #SUP: " appears followed by the support of the rule represented by an integer (a number of transactions). Then, the keyword " #CONF: " appears followed by the confidence of the rule represented by a double value (a value between 0 and 1, inclusively). For example, here is a few lines from the output file if we run TopKRules on contextIGB.txt with k=2 and minconf=0.8 (80 %):

2 ==> 5 #SUP: 5 #CONF: 0.8333333333333334
5 ==> 2 #SUP: 5 #CONF: 1.0

For example, the first line indicates that the association rule {2} --> {5} has a support of 5 transactions and a confidence of 83.3 %. The other lines follow the same format.

Note that if the ARFF format is used as input instead of the default input format, the output format will be the same except that items will be represented by strings instead of integers.

Optional feature: giving names to items

Some users have requested the feature of given names to items instead of using numbers. This feature is offered in the user interface of SPMF and in the command line of SPMF. To use this feature, your file must include @CONVERTED_FROM_TEXT as first line and then several lines to define the names of items in your file. For example, consider the example database "contextIGB.txt". Here we have modified the file to give names to the items: 

@CONVERTED_FROM_TEXT
@ITEM=1=apple
@ITEM=2=orange
@ITEM=3=tomato
@ITEM=4=milk
@ITEM=5=bread
1 2 4 5
2 3 5
1 2 4 5
1 2 3 5
1 2 3 4 5
2 3 4

In this file, the first line indicates, that it is a file where names are given to items. Then, the second line indicates that the item 1 is called "apple". The third line indicates that the item 2 is called "orange". Then the following lines define transactions in the SPMF format.

Then, if we apply the algorithm using this file using the user interface of SPMF or the command line, the output file contains several patterns, including the following ones:

orange ==> bread #SUP: 5 #CONF: 0.8333333333333334
bread ==> orange #SUP: 5 #CONF: 1.0

Note that this feature could be also used from the source code of SPMF using the ResultConverter class. However, there is currently no example provided for using it from the source code.

Performance

TopKRules is a very efficient algorithm for mining the top-k association rules.

It provides the benefits that it is very intuitive to use. It should be noted that the problem of top-k association rule mining is more computationally expensive than the problem of association rule mining. Using TopKRules is recommended for k values of up to 5000, depending on the datasets.

Besides, note that there is a variation of TopKRules named TNR that is available in SPMF. The improvement in TNR is that it eliminates some association rules that are deemed "redundant" (rules that are included in other rules having the same support and confidence - see the TNR example for the formal definition). Using TNR is more costly than using TopKRules but it brings the benefit of eliminating a type of redundancy in results.

Where can I get more information about this algorithm?

The TopKRules algorithm was proposed in this paper:

Fournier-Viger, P., Wu, C.-W., Tseng, V. S. (2012). Mining Top-K Association Rules. Proceedings of the 25th Canadian Conf. on Artificial Intelligence (AI 2012), Springer, LNAI 7310, pp. 61-73.

For a good overview of itemset mining and association rule mining, you may read this survey paper.

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