Mining High-Utility Itemsets in a Transaction Database using the FHIM Algorithm (SPMF documentation)
This example explains how to run the FHIM algorithm using the SPMF open-source data mining library.
How to run this example?
- If you are using the graphical interface, (1) choose the "FHIM" 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 FHIM 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 "MainTestFHIM.java" in the package ca.pfv.SPMF.tests.
What is FHIM?
FHIM (Sahoo et al., ESWA, 2015) is an algorithm for discovering high-utility itemsets in a transaction database containing utility information.
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?
FHIM 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 FHIM is the set of 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 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 FHIM with a minimum utility of 30, we obtain 8 high-utility itemsets:
| 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) |
| {2 3 4 5} | 40 | 40 % (2 transactions) |
| {1 2 3 4 5 6} | 30 | 20 % (1 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.
Input file format
The input file format of FHIM is defined as follows. It is a text file. Each line 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 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 2 3 4 5 6 #UTIL: 30 #SUP: 1
2 4 #UTIL: 30 #SUP: 2
2 3 4 #UTIL: 34 #SUP: 2
2 4 5 #UTIL: 36 #SUP: 2
2 3 4 5 #UTIL: 40 #SUP: 2
2 5 #UTIL: 31 #SUP: 3
2 3 5 #UTIL: 37 #SUP: 3
1 3 5 #UTIL: 31 #SUP: 2
For example, the second line indicates that the itemset {2, 4} has a utility of 30. The other 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.
In 2015, the FHIM algorithm was shown to have good performance and to be faster than some previous high utility itemset mining algorithms.
Implementation details
The version offered in SPMF is the original implementation of FHIM.
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 FHIM algorithm?
This is the reference of the article describing the FHIM algorithm:
Sahoo, Jayakrushna, Das, A., Goswami, A., (2015) An efficient approach for mining association rules from high utility itemsets. Expert Syst. Appl. 42, 5754-5778.
Besides, for a general overview of high utility itemset mining, you may read this survey paper.