Mining High-Utility Itemsets from a Transaction Database while considering Length Constraints, using the FHM+ algorithm (SPMF documentation)

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

How to run this example?

What is FHM+?

FHM+ (Fournier-Viger et al., IEA AIE 2016) is an algorithm for discovering high-utility itemsets in a transaction database containing utility information. It extends the FHM algorithm by letting the user specify length constraints to find only patterns having a minimum and maximum size (length), and use novel optimizations to mine patterns with these constraints efficiently. Using constraints on the length of itemsets is useful because it not only reduce the number of patterns found but also can make the algorithm more than 10 times faster using the novel optimization called Length Upper-Bound Reduction.

High utility itemset mining has several applications such as discovering groups of items in transactions of a store that generate the most profit. A database containing utility information is a database where items can have quantities and a unit price. Although these algorithms are often presented in the context of market basket analysis, there exist other applications.

What is the input?

FHM+ takes as input a transaction database with utility information, a minimum utility threshold min_utility (a positive integer), a minimum pattern length (a positive number), and a maximum pattern length (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 FHM+ is the set of high utility itemsets having a utility no less than the min_utility threshold (a positive integer), and containing a number of items that is no less than the minimum pattern length and no greater the maximum pattern length, set by the user. To explain what is a 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 For example, if we run FHM+ with a minimum utility of 30, a minimum length of 2 items, and a maximum length of 3 items, we obtain 6 high-utility itemsets respecting these constraints

itemsets utility support
{2 4} 30 40 % (2 transactions)
{2 5} 31 60 % (3 transactions)
{1 3 5} 31 40 % (2 transactions)
{2 3 4} 34 40 % (2 transactions)
{2 3 5} 37 60 % (3 transactions)
{2 4 5} 36 40 % (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 contain at least 2 items, and no more than 3 items..

Input file format

The input file format of FHM+ 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 FHM+ is defined as follows. It is a text file, where each line represents a high utility itemset. 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 " #UTIL: " appears and is followed by the utility of the itemset. For example, we show below the output file for this example.

1 3 5 #UTIL: 31
2 4 #UTIL: 30
2 5 #UTIL: 31
2 3 4 #UTIL: 34
2 3 5 #UTIL: 37
2 4 5 #UTIL: 36

For example, the first line indicates that the itemset {2, 4} has a utility of 30. The following 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 FHM algorithm was shown to be up to six times faster than HUI-Miner (also included in SPMF), especially for sparse datasets (see the performance section of the website for a comparison). The FHM+ algorithm is an optimized version of FHM for efficiently discovering high utility itemsets whe length constraints are used. It can be more than 10 times faster than FHM when length constraints are applied, thanks to a novel technique called Length Upper-bound Reduction.

Implementation details

The version offered in SPMF is the original implementation of FHM+.

Note that the input format is not exactly the same as described in the article. But it is equivalent.

Where can I get more information about the FHM+ algorithm?

This is the reference of the article describing the FHM+ algorithm:

Fournier-Viger, P., Lin, C.W., Duong, Q.-H., Dam, T.-L. (2016). FHM+: Faster High-Utility Itemset Mining using Length Upper-Bound Reduction . Proc. 29th Intern. Conf. on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA AIE 2016), Springer LNAI, to appear

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