Mining Frequent Closed Itemsets using the AprioriClose Algorithm (SPMF documentation)

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

How to run this example?

What is AprioriClose?

AprioriClose (aka Close) is an algorithm for discovering frequent closed itemsets in a transaction database. It was proposed by Pasquier et al. (1999).

What is the input of the AprioriClose algorithm?

The input is a transaction database (aka binary context) and a threshold named minsup (a value between 0 and 100 %).

A transaction database is a set of transactions. Each transaction is a set of items. For example, consider the following transaction database. It contains 5 transactions (t1, t2, ..., t5) and 5 items (1,2, 3, 4, 5). For example, the first transaction represents the set of items 1, 3 and 4. This database is provided as the file contextPasquier99.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, 3, 4}
t2 {2, 3, 5}
t3 {1, 2, 3, 5}
t4 {2, 5}
t5 {1, 2, 3, 5}

What is the output of the AprioriClose algorithm?

AprioriClose outputs frequent closed itemsets. To explain what is a frequent closed itemset, it is necessary to review a few definitions.

An itemset is an unordered set of distinct items. The support of an itemset is the number of transactions that contain the itemset. For example, consider the itemset {1, 3}. It has a support of 3 because it appears in three transactions (t1, t3 and t5) from the transaction database .

A frequent itemset is an itemset that appears in at least minsup transactions from the transaction database, where minsup is a threshold set by the user. A frequent closed itemset is a frequent itemset that is not included in a proper superset having exactly the same support. The set of frequent closed itemsets is thus a subset of the set of frequent itemsets. Why is it interesting to discover frequent closed itemset ? The reason is that the set of frequent closed itemsets is usually much smaller than the set of frequent itemsets and it can be shown that no information is lost (all the frequent itemsets can be regenerated from the set of frequent closed itemsets - see Pasquier(1999) for more details).

If we apply AprioriClose on the previous transaction database with a minsup of 40 % (2 transactions), we get the following five frequent closed itemsets:

frequent closed itemsets support
{3} 4
{1, 3} 3
{2, 5} 4
{2, 3, 5} 3
{1, 2, 3, 5} 2
If you would apply the regular Apriori algorithm instead of AprioriClose, you would get 15 itemsets instead of 5, which shows that the set of frequent closed itemset can be much smaller than the set of frequent itemsets.

How should I interpret the results?

In the results, each frequent closed itemset is annotated with its support. For example, the itemset {2, 3, 5} has a support of 3 because it appears in transactions t2, t3 and t5. The itemset {2, 3, 5} is a frequent itemset because its support is higher or equal to the minsup parameter. Furthermore, it is a closed itemsets because it has no proper superset having exactly the same support.

Input file format

The input file format used by AprioriClose is defined as follows. It is a text file. An item is represented by a positive integer. A transaction is a line in the text file. In each line (transaction), items are separated by a single space. It is assumed that all items within a same transaction (line) are sorted according to a total order (e.g. ascending order) and that no item can appear twice within the same line.

For example, for the previous example, the input file is defined as follows:

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

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 a frequent closed itemset. On each line, the items of the itemset are first listed. Each item is represented by an integer and it is followed by a single space. After, all the items, the keyword "#SUP:" appears, which is followed by an integer indicating the support of the itemset, expressed as a number of transactions. For example, we show below the output file for this example. The second line indicates the frequent itemset consisting of the item 1 and 3, and it indicates that this itemset has a support of 4 transactions.

3 #SUP: 4
1 3 #SUP: 3
2 5 #SUP: 4
2 3 5 #SUP: 3
1 2 3 5 #SUP: 2

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 "contextPasquier99.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 3 4
2 3 5
1 2 3 5
2 5
1 2 3 5

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 tomato bread #SUP: 3
orange bread #SUP: 4
apple orange tomato bread #SUP: 2

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

The AprioriClose algorithm is important for historical reasons because it is the first algorithm for mining frequent closed itemsets. However, there exists several other algorithms for mining frequent closed itemsets. In SPMF, it is recommended to use DCI_Closed or Charm instead of AprioriClose, because they are more efficient.

Implementation details

In SPMF, there are two versions of AprioriClose. The first version is named "AprioriClose" and is based on the "Apriori" algorithm. The second version is named "Apriori_TIDClose" and is based on the AprioriTID algorithm instead of Apriori (it uses tidsets to calculate support to reduce the number of database scans). Both version are available in the graphical user interface of SPMF. In the source code, the files "MainTestAprioriClose1.java" and"MainTestAprioriTIDClose.java" respectively correspond to these two versions.

Where can I get more information about the AprioriClose algorithm?

The following article describes the AprioriClose algorithm:

Nicolas Pasquier, Yves Bastide, Rafik Taouil, Lotfi Lakhal: Discovering Frequent Closed Itemsets for Association Rules. ICDT 1999: 398-416

Also, for a good overview of frequent itemset mining algorithms, you may read this survey paper.

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