SPMF documentation > Mining Stable Periodic Frequent Patterns using the SPP-Growth algorithm

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

How to run this example?

What is SPP-Growth ?

SPP-Growth is an algorithm for discovering stable periodic frequent itemsets in a sequence of transactions (a transaction database) with or without timestamps. It was proposed by Fournier-Viger, P. Yang, P. et al. (2019). SPP-Growth can discover patterns that have a stable periodic behavior in a sequence of transactions. Periodic pattern mining has many applications such as discovering periodic behavior of customers, and finding recurring events.

What is the input of the SPP-Growth algorithm?

The input is a transaction database (a sequence of transactions) and four parameters that are set by the user:

  • a maximum periodicity threshold maxper ( a positive integer)
  • a minimum support threshold minsup ( a positive integer)
  • a maximum lability threshold maxla ( a positive integer)
  • a boolean parameter hasNoTimestamps, that must be set to true if the input dataset has no timestamps or otherwise false.

A transaction database is a set of transactions. Each transaction is a set of items (symbols) that has a timestamp. For example, consider the following transaction database. It contains 8 transactions (t1, t2, ..., t8) and 5 items (1,2, 3, 4, 5). For example, the first transaction represents the set of items 2, 3 and 5. This database is provided as the file contextSPPGrowth.txt in the SPMF distribution. It is important to note that an item is not allowed to appear twice in the same transaction and that items are assumed to be sorted according to some total order in each transaction such as the alphabetical order.

Transaction id Items Timestamp
t1 {2, 3, 5} 1
t2 {2, 3, 4, 5} 3
t3 {2, 3, 4, 5} 3
t4 {1, 2, 3, 4, 5} 5
t5 {1, 3, 5} 6
t6 {2,3,5} 7
t7 {1, 3, 4} 9
t8 {1, 3, 5} 10

 

What is the output of the algorithm?

SPP-Growth is an algorithm for discovering stable periodic frequent patterns, which are also called stable periodic frequent itemsets. An itemset is a group of items. The SPP-Growth algorithm finds itemsets that appears periodically in a sequence of transactions. To measure if an itemset is periodic, the algorithm calculates its periods. To explain this in more details, it is necessary to introduce a few definitions.

The set of transactions containing an itemset X is denoted as g(X). For example, consider the itemset {2, 3}. The set g({2,3}) is equal to {t1,t2, t3, t4, t6}. In other words, the itemset {2, 3} appears in the transactions t1 t2,t3, t4 and t6. It is also said that these are five occurrences of the itemset {2,3}.

Now, to assess the periodicity of an itemset X, its list of periods is calculated. A period is the time in terms of number of transactions between two occurences of an itemset in the database (see the paper for the formal definition). For example, the periods of the itemset {2, 3} are {1,1,1,1,2,2}. The first period of {2,3} is 1 because {2,3} appears in the first transaction after the creation of the database. The second period of {2,3} is 1 because the itemset appears in transaction t2, which is one transactions after t1. The third period of {2,3} is 1 because the itemset appears in transactions t3, which is one transactions after t3. Then, the fourth period of {2,3} is 1 because the itemset appears in t4, which is one transaction after t3. Then, the fifth period of {2,3} is 2 because the itemset appears in t6, which is one transaction after t4. Finally, the fifth period of {2,3} is 2 because there is two transactions appearing after the last occurrence of {2,3} in the database (in t6).

The SPP-Growth algorithms utilize the list of periods of an itemset X to calculate its maximum periodicity and a measure called lability that measures by how far the periods deviates from the maxper threshold set by the user . The maximum periodicity of an itemset is the largest period among the periods of the itemset. The lability of an itemset X is the cummulative sum of the difference between each period length and maxper (see the paper for a formal definition and some detailed examples).

The SPP-Growth algorithm finds all the itemsets that have maximum periodicity that is no greater than the maxper threshold, a support no less than the minsup threshold, and a maximum lability that is no greater than the maxla threshold.

For example, if SPP-Growth is run on the previous transaction database with a minper = 2, maxper = 3 , minavgper = 2, the SPP-Growth algorithm finds 7 stable periodic frequent itemsets.

itemset support (number of transactions where the itemset appear) maximum lability
{2} 4 1
{2, 5} 5 1
{2, 3, 5} 5 1
{2, 3} 5 1
{5} 6 1
{3, 5} 7 1
{3} 7 0

How should I interpret the results?

Each stable periodic frequent itemset is annotated with its support (number of transactions where it appears) as well as its maximum lability. For example, the itemset {2, 5} has a support of 5 because it appears in five transactions (t1, t3, t4 and t6. The lability of {2,5} is 1 which means that the periodic behavior of this pattern is quite stable through the database (a smaller lability value means a more stable periodic behavior).

Input file format

The input file format used by SPP-Growth is defined as follows. It is a text file. An item is represented by a positive integer. A transaction is a line in the text file. In each line (transaction), items are separated 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 line. Items are followed by the character "|" and then the timestamp of the transaction. Note that it is possible to run SPP-growth on a database that has no timestamps. In that case, the boolean parameter of SPP-Growth (the fourth parameter) should be set to true to indicate that the dataset has no timestamps.

In the previous example, the input file is defined as follows:

2 3 5|1
2 3 4 5|3
2 3 4 5|3
1 2 3 4 5|5
1 3 5|6
2 3 5|7
1 3 4|9
1 3 5|10

Note that it is also possible to use the ARFF format as an alternative to the default input format. The specification of the ARFF format can be found here. Most features of the ARFF format are supported except that (1) the character "=" is forbidden and (2) escape characters are not considered. Note that when the ARFF format is used, the performance of the data mining algorithms will be slightly less than if the native SPMF file format is used because a conversion of the input file will be automatically performed before launching the algorithm and the result will also have to be converted. This cost however should be small.

Output file format

The output file format is defined as follows. It is a text file, where each line represents a stable periodic frequent itemset. On each line, the items of the itemset are first listed. Each item is represented by an integer and it is followed by a single space. After, all the items, the keyword "#SUP:" appears, which is followed by an integer indicating the support of the itemset, expressed as a number of transactions. Then, the keyword #MAXLA: appears and is followed by a space, an integer indicating the maximum lability of the itemset.

For example, here is the output file for this example. The first line indicates that the itemset {2} is a frequent periodic itemset, having a support of 3 transactions, and a maximum lability of 1 transaction.

2 #SUP: 4 #MAXLA: 1
2 5 #SUP: 5 #MAXLA: 1
2 3 5 #SUP: 5 #MAXLA: 1
2 3 #SUP: 5 #MAXLA: 1
5 #SUP: 6 #MAXLA: 1
3 5 #SUP: 7 #MAXLA: 1
3 #SUP: 7 #MAXLA: 0

Note that if the ARFF format is used as input instead of the default input format, the output format will be the same except that items will be represented by strings instead of integers.

Optional feature: giving names to items

Some users have requested the feature of giving names to items instead of using numbers. This feature is offered in the user interface of SPMF and in the command line of SPMF. To use this feature, your file must include @CONVERTED_FROM_TEXT as first line and then several lines to define the names of items in your file. For example, consider the example database "contextSPPGrowth.txt". Here we have modified the file to give a name to each item: 

@CONVERTED_FROM_TEXT
@ITEM=1=apple
@ITEM=2=orange
@ITEM=3=tomato
@ITEM=4=milk
@ITEM=5=bread
2 3 5|1
2 3 4 5|3
2 3 4 5|3
1 2 3 4 5|5
1 3 5|6
2 3 5|7
1 3 4|9
1 3 5|10

In this file, the first line indicates, that it is a file where names are given to items. Then, the second line indicates that the item 1 is called "apple". The third line indicates that the item 2 is called "orange". Then the following lines define eight transactions in the SPMF format.

Then, if we apply an algorithm on this file using the user interface of SPMF or the command line, the output file contains several patterns, including the following ones:

orange #SUP: 4 #MAXLA: 1
orange bread #SUP: 5 #MAXLA: 1
orange tomato bread #SUP: 5 #MAXLA: 1
orange tomato #SUP: 5 #MAXLA: 1
bread #SUP: 6 #MAXLA: 1
tomato bread #SUP: 7 #MAXLA: 1
tomato #SUP: 7 #MAXLA: 0

Note that this feature could be also used from the source code of SPMF using the ResultConverter class. However, there is currently no example provided for using it from the source code.

Performance

SPP-Growth is currently the only algorithm designed to mine stable periodic frequent itemset in a sequence of transaction (a transaction database) with or without timestamps, offered in SPMF.

Where can I get more information about the SPP-Growth algorithm?

This is the article proposing the SPP-Growth algorithm:

Fournier-Viger, P., Yang, P., Lin, J. C.-W., Kiran, U. (2019). Discovering Stable Periodic-Frequent Patterns in Transactional Data. Proc. 32nd Intern. Conf. on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA AIE 2019), Springer LNAI, pp. 230-244

You can also view a PPT presentation of the SPP-Growth algorithm or the same presentation as a video

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