Mining Closed High-Utility Itemsets from a Transaction Database using the MEHUIM-Closed Algorithm (SPMF documentation)
This example explains how to run the MEHUIM-Closed algorithm using the SPMF open-source data mining library.
How to run this example?
- If you are using the graphical interface, (1) choose the "MEHUIM-Closed" 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 MEHUIM-Closed 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 "MainTestMEHUIMClosed_saveToFile.java" in the package ca.pfv.SPMF.tests.
What is MEHUIM-Closed?
MEHUIM-Closed (Yang, Hongyang, 2024) is an algorithm for discovering closed high-utility itemsets in a transaction database containing utility information. It is an extension of the MEHUIM algorithm that adds strategies to discover only the closed high-utility itemsets, thereby producing a more concise and informative result than traditional high-utility itemset mining.
A limitation of many high-utility itemset mining algorithms is that they output too many itemsets, which can be inconvenient to analyze. As a solution, MEHUIM-Closed discovers only the high-utility itemsets that are closed. An itemset is closed if it has no superset appearing in exactly the same set of transactions. MEHUIM-Closed incorporates backward extension checking and a closed pattern jumping strategy to efficiently identify and output only closed high-utility itemsets, while maintaining the memory-efficient search structure of MEHUIM.
What is the input?
MEHUIM-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:
- 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 MEHUIM-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.
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.
The support of an itemset is the number of transactions that contain the itemset. A closed itemset is an itemset X such that there does not exist a superset Y strictly containing X that appears in exactly the same set of transactions. A closed high utility itemset (CHUI) is a high-utility itemset that is also a closed itemset.
For example, if we run MEHUIM-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 shared by a given group of customers.
Input file format
The input file format of MEHUIM-Closed 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 of MEHUIM-Closed is defined as follows. It is a text file, where each line represents a closed 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.
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 follow 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.
MEHUIM-Closed addresses the problem of outputting too many itemsets by mining only the closed high-utility itemsets, which form a more compact and lossless representation of all high-utility itemsets. By combining the memory-efficient search structure of MEHUIM with backward extension checking and a closed pattern jumping strategy, MEHUIM-Closed can efficiently discover this concise result set. It is generally faster and produces fewer results than mining all high-utility itemsets, particularly on dense datasets.
Implementation details
The implementation offered in SPMF is the original implementation of MEHUIM-Closed by Hongyang Yang and Philippe Fournier-Viger.
In the source code version of SPMF, there are two examples of using MEHUIM-Closed in the package ca.pfv.spmf.tests. The first one is MainTestMEHUIMClosed_saveToFile.java, which saves the result to an output file. The second one is MainTestMEHUIMClosed_saveToMemory.java, which saves the result to memory.
Where can I get more information about the MEHUIM-Closed algorithm?
The MEHUIM-Closed algorithm is described in the following Master's thesis:
Yang, Hongyang (2024). Research on Efficient High-Utility Mining Algorithms Based on Transaction Lists (基于事务列表的高效用挖掘算法研究). Master's thesis (电子信息硕士), School of Computer Science and Software Engineering (计算机与软件学院), Shenzhen University (深圳大学), June 2024.
Besides, for a general overview of high utility itemset mining, you may read this survey paper.