java.lang.Object
- elki.itemsetmining.AbstractFrequentItemsetAlgorithm
- - elki.itemsetmining.APRIORI

All Implemented Interfaces:

elki.Algorithm
```
@Title("APRIORI: Algorithm for Mining Association Rules")
@Description("Searches for frequent itemsets")
@Reference(authors="R. Agrawal, R. Srikant",
           title="Fast Algorithms for Mining Association Rules",
           booktitle="Proc. 20th Int. Conf. on Very Large Data Bases (VLDB \'94)",
           url="http://www.vldb.org/conf/1994/P487.PDF",
           bibkey="DBLP:conf/vldb/AgrawalS94")
public class APRIORI
extends AbstractFrequentItemsetAlgorithm
```
The APRIORI algorithm for Mining Association Rules.
Reference:
R. Agrawal, R. Srikant
Fast Algorithms for Mining Association Rules
In Proc. 20th Int. Conf. on Very Large Data Bases (VLDB '94)
This implementation uses some simple optimizations for 1- and 2-itemsets, but does not implement the original hash tree (yet, please contribute).
Note: this algorithm scales well to a large number of transactions, but not so well to a large number of frequent itemsets (items). For best results, use domain-specific preprocessing to aggregate items into groups. Use statistics logging to keep track of candidate set sizes.

Since:

0.1

Author:

Arthur Zimek, Erich Schubert

Nested Class Summary

Nested Classes
Modifier and Type Class Description

static class APRIORI.Par
Parameterization class.
- Nested classes/interfaces inherited from interface elki.Algorithm
  elki.Algorithm.Utils

Field Summary

Fields
Modifier and Type Field Description

private static elki.logging.Logging LOG
The logger for this class.

private java.lang.String STAT
Statistics logging prefix.
- Fields inherited from class elki.itemsetmining.AbstractFrequentItemsetAlgorithm
  maxlength, minlength

Constructor Summary

Constructors
Constructor	Description
`APRIORI(double minfreq)`	Constructor with minimum frequency.
`APRIORI(double minfreq, int minlength, int maxlength)`	Constructor with minimum frequency.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`protected java.util.List<Itemset>`	`aprioriGenerate(java.util.List<? extends Itemset> supported, int length, int dim)`	Prunes a given set of candidates to keep only those BitSets where all subsets of bits flipping one bit are frequent already.
`private int`	`binarySearch(java.util.List<SparseItemset> candidates, SparseItemset scratch, int begin, int end)`	Binary-search for the next-larger element.
`protected java.util.List<OneItemset>`	`buildFrequentOneItemsets(elki.database.relation.Relation<? extends elki.data.SparseFeatureVector<?>> relation, int dim, int needed)`	Build the 1-itemsets.
`protected java.util.List<SparseItemset>`	`buildFrequentTwoItemsets(java.util.List<OneItemset> oneitems, elki.database.relation.Relation<elki.data.BitVector> relation, int dim, int needed, elki.database.ids.DBIDs ids, elki.database.ids.ArrayModifiableDBIDs survivors)`	Build the 2-itemsets.
`private java.lang.StringBuilder`	`debugDumpCandidates(java.lang.StringBuilder msg, java.util.List<? extends Itemset> candidates, elki.data.type.VectorFieldTypeInformation<elki.data.BitVector> meta)`	Debug method: output all itemsets.
`protected java.util.List<? extends Itemset>`	`frequentItemsets(java.util.List<? extends Itemset> candidates, elki.database.relation.Relation<elki.data.BitVector> relation, int needed, elki.database.ids.DBIDs ids, elki.database.ids.ArrayModifiableDBIDs survivors, int length)`	Returns the frequent BitSets out of the given BitSets with respect to the given database.
`protected java.util.List<SparseItemset>`	`frequentItemsetsSparse(java.util.List<SparseItemset> candidates, elki.database.relation.Relation<elki.data.BitVector> relation, int needed, elki.database.ids.DBIDs ids, elki.database.ids.ArrayModifiableDBIDs survivors, int length)`	Returns the frequent BitSets out of the given BitSets with respect to the given database.
`elki.data.type.TypeInformation[]`	`getInputTypeRestriction()`
`private boolean`	`initializeSearchItemset(elki.data.BitVector bv, int[] scratchi, int[] iters)`	Initialize the scratch itemset.
`private boolean`	`nextSearchItemset(elki.data.BitVector bv, int[] scratchi, int[] iters)`	Advance scratch itemset to the next.
`FrequentItemsetsResult`	`run(elki.database.relation.Relation<elki.data.BitVector> relation)`	Performs the APRIORI algorithm on the given database.

Methods inherited from class elki.itemsetmining.AbstractFrequentItemsetAlgorithm
autorun, getMinimumSupport

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

LOG

private static final elki.logging.Logging LOG

The logger for this class.

STAT
```
private final java.lang.String STAT
```
Statistics logging prefix.

Constructor Detail
- APRIORI
```
public APRIORI(double minfreq,
               int minlength,
               int maxlength)
```
  Constructor with minimum frequency.
  
  Parameters:
  
  minfreq - Minimum frequency
  
  minlength - Minimum length
  
  maxlength - Maximum length
- APRIORI
```
public APRIORI(double minfreq)
```
  Constructor with minimum frequency.
  
  Parameters:
  
  minfreq - Minimum frequency

Method Detail

getInputTypeRestriction

public elki.data.type.TypeInformation[] getInputTypeRestriction()

run
```
public FrequentItemsetsResult run(elki.database.relation.Relation<elki.data.BitVector> relation)
```
Performs the APRIORI algorithm on the given database.

Parameters:

relation - the Relation to process

Returns:

the AprioriResult learned by this APRIORI

buildFrequentOneItemsets

protected java.util.List<OneItemset> buildFrequentOneItemsets(elki.database.relation.Relation<? extends elki.data.SparseFeatureVector<?>> relation,
                                                              int dim,
                                                              int needed)

Build the 1-itemsets.

Parameters:: relation - Data relation; dim - Maximum dimensionality; needed - Minimum support needed
Returns:: 1-itemsets

buildFrequentTwoItemsets

protected java.util.List<SparseItemset> buildFrequentTwoItemsets(java.util.List<OneItemset> oneitems,
                                                                 elki.database.relation.Relation<elki.data.BitVector> relation,
                                                                 int dim,
                                                                 int needed,
                                                                 elki.database.ids.DBIDs ids,
                                                                 elki.database.ids.ArrayModifiableDBIDs survivors)

Build the 2-itemsets.

Parameters:: oneitems - Frequent 1-itemsets; relation - Data relation; dim - Maximum dimensionality; needed - Minimum support needed; ids - Objects to process; survivors - Output: objects that had at least two 1-frequent items.
Returns:: Frequent 2-itemsets

aprioriGenerate
```
protected java.util.List<Itemset> aprioriGenerate(java.util.List<? extends Itemset> supported,
                                                  int length,
                                                  int dim)
```
Prunes a given set of candidates to keep only those BitSets where all subsets of bits flipping one bit are frequent already.

Parameters:

supported - Support map

length - Itemset length

dim - Dimensionality

Returns:

itemsets that cannot be pruned by apriori

frequentItemsets

protected java.util.List<? extends Itemset> frequentItemsets(java.util.List<? extends Itemset> candidates,
                                                             elki.database.relation.Relation<elki.data.BitVector> relation,
                                                             int needed,
                                                             elki.database.ids.DBIDs ids,
                                                             elki.database.ids.ArrayModifiableDBIDs survivors,
                                                             int length)

Returns the frequent BitSets out of the given BitSets with respect to the given database.

Parameters:: candidates - the candidates to be evaluated; relation - the database to evaluate the candidates on; needed - Minimum support needed; ids - Objects to process; survivors - Output: objects that had at least two 1-frequent items.; length - Itemset length
Returns:: Itemsets with sufficient support

frequentItemsetsSparse

protected java.util.List<SparseItemset> frequentItemsetsSparse(java.util.List<SparseItemset> candidates,
                                                               elki.database.relation.Relation<elki.data.BitVector> relation,
                                                               int needed,
                                                               elki.database.ids.DBIDs ids,
                                                               elki.database.ids.ArrayModifiableDBIDs survivors,
                                                               int length)

Returns the frequent BitSets out of the given BitSets with respect to the given database. Optimized implementation for SparseItemset.

Parameters:: candidates - the candidates to be evaluated; relation - the database to evaluate the candidates on; needed - Minimum support needed; ids - Objects to process; survivors - Output: objects that had at least two 1-frequent items.; length - Itemset length
Returns:: Itemsets with sufficient support

initializeSearchItemset
```
private boolean initializeSearchItemset(elki.data.BitVector bv,
                                        int[] scratchi,
                                        int[] iters)
```
Initialize the scratch itemset.

Parameters:

bv - Bit vector data source

scratchi - Scratch itemset

iters - Iterator array

Returns:

true if the itemset had minimum length

nextSearchItemset
```
private boolean nextSearchItemset(elki.data.BitVector bv,
                                  int[] scratchi,
                                  int[] iters)
```
Advance scratch itemset to the next.

Parameters:

bv - Bit vector data source

scratchi - Scratch itemset

iters - Iterator array

Returns:

true if the itemset had minimum length

binarySearch
```
private int binarySearch(java.util.List<SparseItemset> candidates,
                         SparseItemset scratch,
                         int begin,
                         int end)
```
Binary-search for the next-larger element.

Parameters:

candidates - Candidates to search for

scratch - Scratch space

begin - Search interval begin

end - Search interval end

Returns:

Position of first equal-or-larger element

debugDumpCandidates

private java.lang.StringBuilder debugDumpCandidates(java.lang.StringBuilder msg,
                                                    java.util.List<? extends Itemset> candidates,
                                                    elki.data.type.VectorFieldTypeInformation<elki.data.BitVector> meta)

Debug method: output all itemsets.

Parameters:: msg - Output buffer; candidates - Itemsets to dump; meta - Metadata for item labels
Returns:: Output buffer

Modifier and Type	Field	Description
`private static elki.logging.Logging`	`LOG`	The logger for this class.
`private java.lang.String`	`STAT`	Statistics logging prefix.

Class APRIORI

Nested Class Summary

Nested classes/interfaces inherited from interface elki.Algorithm

Field Summary

Fields inherited from class elki.itemsetmining.AbstractFrequentItemsetAlgorithm

Constructor Summary

Method Summary

Methods inherited from class elki.itemsetmining.AbstractFrequentItemsetAlgorithm

Methods inherited from class java.lang.Object

Field Detail

LOG

STAT

Constructor Detail

APRIORI

APRIORI

Method Detail

getInputTypeRestriction

run

buildFrequentOneItemsets

buildFrequentTwoItemsets

aprioriGenerate

frequentItemsets

frequentItemsetsSparse

initializeSearchItemset

nextSearchItemset

binarySearch

debugDumpCandidates