Association Rules¶
Association rules mining is the method for uncovering the most important relationships between variables. Its main application is a store basket analysis, which aims at discovery of a relationship between groups of products with some level of confidence.
Details¶
The library provides Apriori algorithm for association rule mining [Agrawal94].
Let \(I = \{i_1, i_2, \ldots, i_m\}\) be a set of items (products) and subset \(T \subset I\) is a transaction associated with item set I. The association rule has the form: \(X \Rightarrow Y\), where \(X \subset I\), \(Y \subset I\), and intersection of \(X\) and \(Y\) is empty: \(X \cap Y = \emptyset\). The lefthandside set of items (itemset) \(X\) is called antecedent, while the righthandside itemset Y is called consequent of the rule.
Let \(D = \{T_1, T_2, \ldots, T_n\}\) be a set of transactions, each associated with item set I. Item subset \(X \subset I\) has support \(s\) in the transaction set \(D\) if \(s\) percent of transactions in \(D\) contains \(X\).
The association rule \(X \Rightarrow Y\) in the transaction set \(D\) holds with confidence \(c\) if \(c\) percent of transactions in \(D\) that contain \(X\) also contains \(Y\). Confidence of the rule can be represented as conditional probability:
\(confidence(X \Rightarrow Y) = support (X \cup Y)/support(X)\)
For a given set of transactions \(D = \{T_1, T_2, \ldots, T_n\}\), the minimum support s and minimum confidence c discover all item sets \(X\) with support greater than \(s\) and generate all association rules \(X \Rightarrow Y\) with confidence greater than \(c\).
Therefore, the association rule discovery is decomposed into two stages: mining (training) and discovery (prediction). The mining stage involves generation of large item sets, that is, the sets that have support greater than the given parameters. At the discovery stage, the algorithm generates association rules using the large item sets identified at the mining stage.
Batch Processing¶
Algorithm Input¶
The association rules algorithm accepts the input described below.
Pass the Input ID
as a parameter to the methods that provide input
for your algorithm.
Input ID 
Input 


Pointer to the \(n \times 2\) numeric table t with the mining data. Each row consists of two integers:
The input can be an object of any class derived from NumericTable except PackedTriangularMatrix and PackedSymmetricMatrix. 
Algorithm Parameters¶
The association rules algorithm has the following parameters:
Parameter 
Default Value 
Description 



The floatingpoint type that the algorithm uses for intermediate computations. Can be 


The computation method used by the algorithm. The only method supported so far is Apriori. 

\(0.01\) 
Minimal support, a number in the [0,1) interval. 

\(0.6\) 
Minimal confidence, a number in the [0,1) interval. 

\(0\) 
The total number of unique items. If set to zero, the library automatically determines the number of unique items from the input data. 

\(0\) 
The total number of transactions. If set to zero, the library automatically determines the number transactions from the input data. 


A flag that enables generation of the rules from large item sets. 


The sort order of returned item sets:



The sort order of returned rules:


\(0\) 
A parameter that defines the minimal size of item sets to be included into the array of results. The value of zero imposes no limitations on the minimal size of item sets. 

\(0\) 
A parameter that defines the maximal size of item sets to be included into the array of results. The value of zero imposes no limitations on the maximal size of item sets. 
Algorithm Output¶
The association rules algorithm calculates the result described
below. Pass the Result ID
as a parameter to the methods that access
the results of your algorithm.
Result ID 
Result 


Pointer to the numeric table with large item sets. The number of rows in the table equals the number of items in the large item sets. Each row contains two integers:


Pointer to the \(nLargeItemsets \times 2\) numeric table of support values. Each row contains two integers:


Pointer to the \(nAntecedentItems \times 2\) numeric table that contains the lefthandside (X) part of the association rules. Each row contains two integers:


Pointer to the \(nConsequentItems \times 2\) numeric table that contains the righthandside (Y) part of the association rules. Each row contains two integers:


Pointer to the \(nRules \times 1\) numeric table that contains confidence values of rules, floatingpoint numbers between 0 and 1. Confidence value in the ith position corresponds to the rule with the index i. 
By default, the result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except PackedSymmetricMatrix, PackedTriangularMatrix, and СSRNumericTable.
Note
The library requires transactions and items for each transaction to be passed in the ascending order.
Numbering of rules starts at 0.
The library calculates the sizes of numeric tables intended for results in a call to the algorithm. Avoid allocating the memory in numeric tables intended for results because, in general, it is impossible to accurately estimate the required memory size. If the memory interfaced by the numeric tables is allocated and its amount is insufficient to store the results, the algorithm returns an error.
Examples¶
Batch Processing:
Batch Processing:
Performance Considerations¶
To get the best overall performance of the association rules algorithm, whenever possible use the following numeric tables and data types:
A SOA numeric table of type int to store features.
A homogenous numeric table of type int to store large item sets, support values, and lefthandside and righthandside parts of association rules.
A numeric table with the confidence values of the same data type as specified in the algorithmFPType template parameter of the class.
Optimization Notice 

Intel’s compilers may or may not optimize to the same degree for nonIntel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessordependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice. Notice revision #20110804 