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 
be a set of items
(products) and subset 
is a transaction associated with item set
I. The association rule has the form: 
, where 
, 
, and
intersection of 
. The left-hand-side set of
items (
be a set of items
(products) and subset is a transaction associated with item set
I. The association rule has the form: , where , , and
intersection of X
and Y
is empty: . The left-hand-side set of
items (itemset
) X
is called antecedent, while the right-hand-side
itemset Y is called consequent of the rule.Let 
be a set of
transactions, each associated with item set I. Item subset has
support
be a set of
transactions, each associated with item set I. Item subset has
support s
in the transaction set D
if s
percent of transactions in D
contains X
.The association rule 
in the transaction set
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:
For a given set of transactions , the minimum support s and minimum confidence c discover
all item sets with confidence greater than
, the minimum support s and minimum confidence c discover
all item sets X
with support greater than s
and generate all
association rules 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 |
|---|---|
data | Pointer to the  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 |
|---|---|---|
algorithmFPType | float | The floating-point type that the algorithm uses for intermediate computations. Can be float or double . |
method | defaultDense | The computation method used by the algorithm. The only method supported so far is Apriori. |
minSupport | 0.01 | Minimal support, a number in the [0,1) interval. |
minConfidence | 0.6 | Minimal confidence, a number in the [0,1) interval. |
nUniqueItems | 0 | The total number of unique items. If set to zero, the library automatically determines the number of unique items from the input data. |
nTransactions | 0 | The total number of transactions. If set to zero, the library automatically determines the number transactions from the input data. |
discoverRules | true | A flag that enables generation of the rules from large item sets. |
itemsetsOrder | itemsetsUnsorted | The sort order of returned item sets:
|
rulesOrder | rulesUnsorted | The sort order of returned rules:
|
minItemsetSize | 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. |
maxItemsetSize | 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 |
|---|---|
largeItemsets | 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:
|
largeItemsetsSupport | Pointer to the  numeric table of support values. Each row contains two integers:
|
antecedentItemsets | Pointer to the  numeric table that contains the
left-hand-side (X) part of the association rules. Each row contains two integers:
|
conseqentItemsets | Pointer to the  numeric table that contains the
right-hand-side (Y) part of the association rules. Each row contains two integers:
|
confidence | Pointer to the  numeric table that contains confidence values
of rules, floating-point numbers between 0 and 1. Confidence value in
the i-th 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.
- 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
C++ (CPU)
Batch Processing:
Java*
Python*
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 left-hand-side and right-hand-side 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.
Product and Performance Information |
|---|
Performance varies by use, configuration and other factors.
Learn more at www.Intel.com/PerformanceIndex. Notice revision #20201201 |