Mining Closed High-Utility Itemsets from a transaction database with utility information using the EFIM-Closed Algorithm (SPMF documentation)

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

How to run this example?

What is EFIM-Closed?

EFIM-Closed (Fournier-Viger et al., 2016) is an algorithm for discovering closed high-utility itemsets in a transaction database containing utility information.

There has been many work on the design of algorithms for high-utility itemset mining. However, a limitation of many high-utility itemset mining algorithms is that they output too many itemsets. As a result, it may be inconvenient for a user to analyze the result of traditional high utility itemset mining algorithms. As a solution, algorithms have been designed to discover only the high-utility itemsets that are closed. The concept of closed itemset was previously introduced in frequent itemset mining. An itemset is closed if it has no subset having the same support (frequency) in the database. In terms of application to transaction databases, the concept of closed itemset can be understood as any itemset that is the largest set of items bought by a given set of customers. For more details, you may look at the paper about EFIM-Closed. It provides more details about the motivation for mining closed high-utility itemsets. Other popular alternative algorithms for closed high-utility itemsets mining are CHUI-Miner (2015, also offered in SPMF), and CHUD (2011,2013, currently not offered in SPMF).

What is the input?

EFIM-Closed takes as input a transaction database with utility information and a minimum utility threshold min_utility (a positive integer). Let's consider the following database consisting of 5 transactions (t1,t2...t5) and 7 items (1, 2, 3, 4, 5, 6, 7). This database is provided in the text file "DB_utility.txt" in the package ca.pfv.spmf.tests of the SPMF distribution.

Items Transaction utility Item utilities for this transaction
t1 3 5 1 2 4 6 30 1 3 5 10 6 5
t2 3 5 2 4 20 3 3 8 6
t3 3 1 4 8 1 5 2
t4 3 5 1 7 27 6 6 10 5
t5 3 5 2 7 11 2 3 4 2

Each line of the database is:

Note that the value in the second column for each line is the sum of the values in the third column.

What are real-life examples of such a database? There are several applications in real life. One application is a customer transaction database. Imagine that each transaction represents the items purchased by a customer. The first customer named "t1" bought items 3, 5, 1, 2, 4 and 6. The amount of money spent for each item is respectively 1 $, 3 $, 5 $, 10 $, 6 $ and 5 $. The total amount of money spent in this transaction is 1 + 3 + 5 + 10 + 6 + 5 = 30 $.

What is the output?

The output of EFIM-Closed is the set of closed high utility itemsets having a utility no less than a min_utility threshold (a positive integer) set by the user. To explain what is a closed high utility itemset, it is necessary to review some definitions.

An itemset is an unordered set of distinct items. The utility of an itemset in a transaction is the sum of the utility of its items in the transaction. For example, the utility of the itemset {1 4} in transaction t1 is 5 + 6 = 11 and the utility of {1 4} in transaction t3 is 5 + 2 = 7. The utility of an itemset in a database is the sum of its utility in all transactions where it appears. For example, the utility of {1 4} in the database is the utility of {1 4} in t1 plus the utility of {1 4} in t3, for a total of 11 + 7 = 18. A high utility itemset is an itemset such that its utility is no less than min_utility.

To explain what is a closed itemset it is necessary to review a few definitions.

The support of an itemset is the number of transactions that contain the itemset. For example, the itemset {1, 3, 5} has a support of 2 because it appears in three transactions from the database (t1 and t4). A closed is an itemset X such that there does not exist an itemset Y strictly included in X that has the same support. For example, itemset {1, 3, 5} is a closed itemset.

A closed high utility itemset (CHUI) is a high-utility itemset that is a closed itemset.

For example, if we run EFIM-Closed with a minimum utility of 30 we obtain 4 closed high-utility itemsets:

itemsets utility support
{1, 2, 3, 4, 5, 6} 30 1 transaction
{2, 3, 4, 5} 40 2 transactions
{2, 3, 5} 37 3 transactions
{1, 3, 5} 31 2 transactions

If the database is a transaction database from a store, we could interpret these results as all the groups of items bought together that generated a profit of 30 $ or more, and that are maximal sets of items in common for a group of customers.

Input file format

The input file format of EFIM-Closed is defined as follows. It is a text file. Each lines represents a transaction. Each line is composed of three sections, as follows.

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

3 5 1 2 4 6:30:1 3 5 10 6 5
3 5 2 4:20:3 3 8 6
3 1 4:8:1 5 2
3 5 1 7:27:6 6 10 5
3 5 2 7:11:2 3 4 2

Consider the first line. It means that the transaction {3, 5, 1, 2, 4, 6} has a total utility of 30 and that items 3, 5, 1, 2, 4 and 6 respectively have a utility of 1, 3, 5, 10, 6 and 5 in this transaction. The following lines follow the same format.

Output file format

The output file format of EFIM-Closed is defined as follows. It is a text file, where each line represents a closed high utility itemsets. On each line, the items of the itemset are first listed. Each item is represented by an integer, followed by a single space. After, all the items, the keyword "#SUPPORT:" appears and is followed by the support of the itemset. Then, the keyword #UTIL: " appears and is followed by the utility of the itemset. For example, we show below the output file for this example.

6 4 2 1 5 3 #SUP: 1 #UTIL: 30
4 3 2 5 #SUP: 2 #UTIL: 40
2 5 3 #SUP: 3 #UTIL: 37
1 3 5 #SUP: 2 #UTIL: 31

For example, the third line indicates that the itemset {2, 3, 5} has a support of 3 transactions and a utility of 37$. The other lines follows the same format.


High utility itemset mining is a more difficult problem than frequent itemset mining. Therefore, high-utility itemset mining algorithms are generally slower than frequent itemset mining algorithms. The EFIM-Closed algorithm was proposed in 2016 to discover only the high-utility itemsets that are closed itemsets. It is generally faster to mine closed high-utility itemsets than discovering all high-utility itemsets. Thus, this algorithm can in some cases outperform algorithms such as FHM and HUI-Miner, who discover all high-utility itemsets. The EFIM-Closed algorithm was shown to outperform the original algorithm for mining closed high-utility itemsets named CHUD algorithm (published in the proceedings of the ICDM 2011 conference).

Implementation details

This is an implementation of EFIM-Closed, implemented by P. Fournier-Viger. This is an alternative implementation that was not used in the paper. The main differences with the implementation in the paper is that this implementation (1) does not calculate utility-unit arrays (see the paper) and (2) adds the EUCP optimizations introduced in the FHM algorithm.

In the source code version of SPMF, there are two examples of using EFIM-Closed in the package ca.pfv.spmf.tests. The first one is MainTestEFIM_Closed_saveToFile, which saves the result to an output file. The second one is MainTestEFIM_Closed_saveToMemory, which saves the result to memory.

Where can I get more information about the EFIM_Closed algorithm?

This is the reference of the article describing the EFIM_Closed algorithm:

Fournier-Viger, P., Zida, S. Lin, C.W., Wu, C.-W., Tseng, V. S. (2016). EFIM-Closed: Fast and Memory Efficient Discovery of Closed High-Utility Itemsets. Proc. 12th Intern. Conference on Machine Learning and Data Mining (MLDM 2016). Springer, LNAI, 15 pages, to appear

Besides, for a general overview of high utility itemset mining, you may read this survey paper.