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

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

How to run this example?

What is HMiner_Closed?

HMiner_Closed (2019) is an algorithm for discovering closed high-utility itemsets in a transaction database containing utility information.

There has been many work on the topic of high-utility itemset mining. A limitation of many high-utility itemset mining algorithms is that they generate too much itemsets as output. Hence, algorithms such as HMiner_Closed algorithm were 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 database, the concept of closed itemset can be understood as any itemset that is the largest set of items bought in common by a given set of customers. For more details, see the research papers. These paper provides more details about the motivation for mining closed high-utility itemsets.

It is to be noted that there exist several algorithms for discovering the closed high utility itemsets offered in SPMF. HMiner_Closed is one of the fastest.

What is the input?

HMiner_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 HMiner_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 HMiner_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 HMiner_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 HMiner_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 "#SUP:" 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 HMiner_Closed is a quite efficient algorithm for discovering closed high utility itemsets.

Where can I get more information about the HMiner_Closed algorithm?

This is the paper describing the HMiner_Closed algorithm:

Nguyen L T T, Vu V V, Lam M T H, et al. An efficient method for mining high utility closed itemsets[J]. Information Sciences, 2019, 495: 78-99.,

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