Mining Correlated High-Utility Itemsets in a Database with Utility Information using the FCHM_allconfidence Algorithm (SPMF documentation)

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

How to run this example?

What is FCHM_allconfidence?

FCHM_allconfidence (Fournier-Viger et al., 2018) is an algorithm for discovering correlated high-utility itemsets in a transaction database containing utility information.

A limitation of traditional high utility itemset mining algorithms is that they may find many itemsets having a high utility but containing items that are weakly correlated (as shown in the FCHM papers). The FCHM_allconfidence algorithm addresses this issue by combining the idea of correlated pattern with high-utility pattern, to find high-utility itemsets where items are highly correlated. FCHM_allconfidence uses the allconfidence measure to evaluate whether an itemset is a correlated itemset.

What is the input?

FCHM_allconfidence takes as input a transaction database with utility information, a minimum utility threshold min_utility (a positive integer), and a minallconfidence threshold (a double number in the [0,1] interval). 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 FCHM_allconfidence is the set of correlated high utility itemsets having a utility no less than a min_utility threshold (a positive integer) set by the user, and a allconfidence no less than a minallconfidence threshold also set by the user.

To explain what is a correlated 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.

A correlated itemset is an itemset such that its allconfidence is no less than a minallconfidence threshold set by the user. The allconfidence of an itemsets is the number of transactions containing an itemset divided by the number of transactions containing the most frequent item that appear in that itemset. The allconfidence is a value in the [0,1] interval. A high value means a highly correlated itemset. Note that single items have by default a allconfidence of 1. A correlated high-utility itemset is a high-utility itemset that is also a correlated itemset.

For example, if we run FHM with a minimum utility of 30 and minallconfidence = 0.5, we obtain 8 correlated high-utility itemsets:

itemsets allconfidence utility
{2, 4} 0.66 30
{2, 4, 5} 0.5 36
{2, 5} 0.75 31
{2, 3, 5} 0.6 37

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 containing items that are correlated (are likely to be bought together).

Input file format

The input file format of FCHM_allconfidence 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 FCHM_allconfidence is defined as follows. It is a text file, where each line represents a correlated 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. Then, there is a single space, followed by the keyword "#allconfidence: ", followed by the allconfidence of the itemset. For example, we show below the output file for this example.

4 2 #UTIL: 30 #ALLCONF: 0.6666666666666666
4 2 5 #UTIL: 36 #ALLCONF: 0.5
2 5 #UTIL: 31 #ALLCONF: 0.75
2 5 3 #UTIL: 37 #ALLCONF: 0.6

For example, the first line indicates that the itemset {2, 4} has a utility of 30 and a allconfidence of 0.66. 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 FCHM_allconfidence algorithm is the first algorithm for mining correlated high-utility itemsets using the allconfidence measure. It extends FHM, one of the fastest algorithm for high-utility itemsets mining.

Note that there is another variation of this algorithm called FCHM_bond, which is also offered in SPMF. This latter uses the bond measure instead of the allconfidence to measure correlation.

Implementation details

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

Where can I get more information about the FCHM_allconfidence algorithm?

The following article describes the first version of the FCHM algorithm which used the bond measure to assess correlation:

Fournier-Viger, P., Lin, C. W., Dinh, T., Le, H. B. (2016). Mining Correlated High-Utility Itemsets Using the bond Measure. Proc. 11 th International Conference on Hybrid Artificial Intelligence Systems (HAIS 2016), Springer LNAI, 14 pages, to appear.

This is an extended version of the above paper, which modifies FCHM to use the all-confidence measure. This is the FCHM_allconfidence algorithm .

Fournier-Viger, P., Zhang, Y., Lin, J. C.-W., Dinh, T., Le, B. (2018) Mining Correlated High-Utility Itemsets Using Various Correlation Measures. Logic Journal of the IGPL, Oxford Academic, to appear.

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

You can also view a video presentation of the FCHM algorithm