Mining Minimal High-Utility Itemsets from a transaction database with utility information using the MinFHM Algorithm (SPMF documentation)
This example explains how to run the MinFHM algorithm using the SPMF open-source data mining library.
How to run this example?
- If you are using the graphical interface, (1) choose the "MinFHM" algorithm, (2) select the input file "DB_utility.txt", (3) set the output file name (e.g. "output.txt") (4) set the minimum utility to 30 and (5) click "Run algorithm".
- If you want to execute this example from the command line,
then execute this command:
java -jar spmf.jar run MinFHM DB_utility.txt output.txt 30 in a folder containing spmf.jar and the example input file DB_utility.txt. - If you are using the source code version of SPMF, launch the file "MainTestMinFHM.java" in the package ca.pfv.SPMF.tests.
What is MinFHM?
MinFHM (Fournier-Viger et al., 2016) is an algorithm for discovering minimal high-utility itemsets in a transaction database containing utility information.
There has been quite a huge amount of work on the topic of high-utility itemset mining in recent years. High-utility itemset mining consists of finding sets of items that yield a high profit in a database of customer transaactions where the purchase quantities of items in transactions is indicated and each item has a unit profit. Several algorithms have been proposed for high-utility itemset mining. However, they may find a huge number of patterns. These patterns are often very long and often represent rare cases, as in real-life, few customers exactly buy the same large set of items. For marketing purpose, a retailer may be more interested in finding the smallest sets of items that generate a high profit, since it is easier to co-promote a small set of items targeted at many customers rather than a large set of items targeted at few customers. The MinFHM algorithm was designed to address this issues by discovering only the high-utility itemsets that are minimal.
A high-utility itemset is said to be minimal if it has no subset that is also a high-utility itemset. In terms of application to transaction database, the concept of minimal high-utility itemsets can be understood as the smallest sets of items that yield a high profit.. The concept of minimal high-utility itemset can also be understood as the opposite of the concept of maximal high-utility itemset proposed in other work.
This is the original implementation of MinFHM.
What is the input?
MinFHM 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:
- a set of items (the first column of the table),
- the sum of the utilities (e.g. profit) of these items in this transaction (the second column of the table),
- the utility of each item for this transaction (e.g. profit generated by this item for this transaction)(the third column of the table).
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 MinFHM is the set of minimal 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 minimal high-utility itemsets, 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.
A minimal high utility itemsets (MinHUI) is a high-utility itemset that is has no subset that is a high-utility itemset
For example, if we run MinFHM with a minimum utility of 30, we obtain 3 minimal high-utility itemsets:
| itemsets | utility |
| {2, 4} | 30 |
| {1 3 5} | 31 |
| {2 5} | 31 |
If the database is a transaction database from a store, we could interpret these results as all the smallest groups of items bought together that generated a profit of 30 $ or more (that are minimal).
Input file format
The input file format of MinFHM is defined as follows. It is a text file. Each lines represents a transaction. Each line is composed of three sections, as follows.
- First, the items contained in the transaction are listed. An item is represented by a positive integer. Each item is separated from the next item 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 transaction.
- Second, the symbol ":" appears and is followed by the transaction utility (an integer).
- Third, the symbol ":" appears and is followed by the utility of each item in this transaction (an integer), separated by single spaces.
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 MinFHM is defined as follows. It is a text file, where each line represents a minimal 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.
4 2 #UTIL: 30
2 5 #UTIL: 31
1 5 3 #UTIL: 31
For example, the third line indicates that the itemset {2, 4} has a utility of 30$. The following lines follows the same format.
Performance
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 MinFHM algorithm was proposed in 2016 to discover only the high-utility itemsets that are minimal. It was found that MinFHM can be orders of magitude faster than algorithms such as FHM for mining all high-utility itemsets.
Implementation details
This is the original implementation of the MinFHM algorithm
Where can I get more information about the MinFHM algorithm?
This is the reference of the article describing the MinFHM algorithm:
Fournier-Viger, P., Lin, C.W., Wu, C.-W., Tseng, V. S., Faghihi, U. (2016). Mining Minimal High-Utility Itemsets. Proc. 27th International Conference on Database and Expert Systems Applications (DEXA 2016). Springer, LNCS, 13 pages, to appear
You can also view a video presentation of the MinFHM algorithm
Besides, for a good overview of itemset mining algorithms, you may read this survey paper.