Finding the Frequent Pattern in a Database
A Study on the Apriori Algorithm
Najlaa AlHuwaishel
1
, Maram AlAlwan
2
and Ghada Badr
3
1
Department of Computer Sciences, King Saud University, Riyadh, Saudi Arabia
2
King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia
3
Department of Computer Sciences, King Saud University, Riyadh, Saudi Arabia
Keywords: Data Mining, Frequent Pattern, Apriori Algorithm.
Abstract: This paper is a study on the frequent pattern mining using the Apriori algorithm. We will present the
concept of data mining in a high level and explain how the frequent pattern is mined. We will talk about the
Apriori algorithm and the problem with this algorithm followed by exploration of some algorithms that
considered as an update on the Apriori algorithm in order to enhance the efficiency problem that we
explained. We will also compare the selected algorithms taking under consideration: 1.Number of database
scan. 2.Number of generated candidate lists. 3.Memory usage.
1 INTRODUCTION
In many knowledge fields and industries (or
business), it is important to store data and
information. There are many technologies supports
and continuously develop new efficient trusted
methods of storing data. Data can be stored in more
than a structure: Database, Data Warehouse, World
Wide Web information repository, Spreadsheets etc.
After secure, efficient and reliable Databases;
what is next? It is the time that we need to benefit
from these data - wither we are working in a
scientific or business field. The process of extracting
information or knowledge from large set of data is
called "Data Mining". One of the definitions of Data
Mining is (An essential process where intelligent
methods are applied in order to extract data patterns).
2 DATA MINING CONCEPTS
There are different kinds of data pattern that we can
mine or extract from a database, depending on the
reason of the study of a database:
1. Concept/Class Description: Characterization
and Discrimination
Data can be associated with classes or concepts. This
kind of pattern interested in the characterization of a
group of objects. For example in the owners of a
store needs to study classify the tight budget spenders
and open budget spenders and each group interests.
The output of data characterization process can be
presented in various forms: pie charts, bar charts,
curves, multidimensional data cubes, and
multidimensional tables. The resulting descriptions
can also be presented as generalized relations or in
rule form (called characteristic rules).
2. Classification and Prediction
Classification is the process of finding a model (or
function) that describes and distinguishes data classes
or concepts, for the purpose of being able to use the
model to predict the class of objects whose class
label is unknown. The derived model is based on the
analysis of a set of training data (i.e., data objects
whose class label is known).
3. Cluster Analysis
Unlike classification and prediction, which analyze
class-labeled data objects, clustering analyzes data
objects without consulting a known class label. The
objects are
Clustered or grouped based on the principle of
maximizing the interclass similarity and minimizing
the interclass similarity. That is, clusters of objects
are formed so that objects within a cluster have high
similarity in comparison to one another, but are very
dissimilar to objects in other clusters. Each cluster
that is formed can be viewed as a class of objects.
4. Evolution Analysis
From its name; Data evolution analysis describes and
388
AlHuwaishel N., AlAlwan M. and Badr G..
Finding the Frequent Pattern in a Database - A Study on the Apriori Algorithm.
DOI: 10.5220/0005147703880396
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2014), pages 388-396
ISBN: 978-989-758-048-2
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
models regularities or trends for objects whose
behavior changes over time. Although this may
include characterization, discrimination, association
and correlation analysis, classification, prediction, or
clustering of time-related data, distinct features of
such an analysis include time-series data analysis,
sequence or periodicity pattern matching, and
similarity-based data analysis.
5. Outlier Analysis
Which can be the opposite of the Frequent Pattern
mining. A database may contain data objects that do
not comply with the general behavior or model of the
data. These data objects are outliers. Most data
mining methods discard outliers as noise or
exceptions. However, in some applications such as
fraud detection, the rare events can be more
interesting than the more regularly occurring ones.
The analysis of outlier data is referred to as outlier
mining.
6. Mining Frequent Patterns
The Frequent Patterns is the most frequent items that
are occurring in a database. There are many kinds of
frequent patterns, including item-sets, subsequences,
and substructures. A frequent item-set typically
refers to a set of items that frequently appear together
in a transactional data set, such as milk and bread. A
frequently occurring subsequence, such as the pattern
that customers tend to purchase first a PC, followed
by a digital camera, and then a memory card, is a
(frequent) sequential pattern. A substructure can refer
to different structural forms, such as graphs, trees, or
lattices, which may be combined with item-sets or
subsequences. If a substructure occurs frequently, it
is called a (frequent) structured pattern. Mining
frequent patterns leads to the discovery of interesting
associations and correlations within data. A lot of
changes can be done relaying of the frequent patterns
studies that can benefit the field of interest.
Our concern here in this paper is to explore the
Data Mining most famous algorithm (Apriori
Algorithm) that is designed to find the most frequent
item set in a database and also to find the relation
between them which will lead us to better ways in
decision making.
3 MINING THE FREQUENT
PATTERNS
When we are studying the relationships or the
associations between the Frequent Patterns or the
Frequent Items there are 2 important concepts we
need to understand: Support & Confidence.
An objective measure for association rules of the
form X Y is rule support, representing the
percentage of transactions from a transaction
database that the given rule satisfies. This is taken to
be the probability P(XY ), where XY indicates
that a transaction contains both X and Y , that is, the
union of item-sets X and Y .
Another objective measure for association rules is
confidence, which assesses the degree of certainty of
the detected association. This is taken to be the
conditional probability P(Y|X ), that is, the
probability that a transaction containing X also
contains Y. More formally, support and confidence
are defined as:
support(XY ) = P(XY ).
confidence(XY ) = P(Y |X ).
Example: If we are doing an Association analysis
for an electronic store, suppose that the Manager
would like to determine which items are frequently
purchased together within the same transactions. An
example of such a rule, mined from the store
transactional database, is
buys(X , “computer”) buys(X , “software”)
[support = 1%, confidence = 50%]
Where X is a variable representing a customer. A
confidence, or certainty, of 50% means that if a
customer buys a computer, there is a 50% chance that
she/he will buy software as well. A 1% support
means that 1% of all of the transactions under
analysis showed that computer and software were
purchased together.
Dropping the predicate notation, the above rule can
be written simply as
“computer software [1%, 50%]”
This association rule involves a single attribute or
predicate (i.e., buys) that repeats. Association rules
that contain a single predicate are referred to as
Single-Dimensional Association Rules.
On the other hand; there is another kind of
association which we call the Multidimensional
Association Rule, which involve more than one
attribute in the frequent items relation. Example: For
the same pervious electronic store a data mining
system may find association rules like
age(X , “20...29”) ^ income(X , “20K...29K”)
buys(X , “CD player”)
[support = 2%, confidence = 60%]
The rule indicates that of the store customers under
study, 2% are 20 to 29 years of age with an income
of 20,000 to 29,000 and have purchased a CD player.
FindingtheFrequentPatterninaDatabase-AStudyontheAprioriAlgorithm
389
Also there is a 60% probability that a customer in
this age and income group will purchase a CD player.
As the pervious examples, any association rules
that are not satisfying the 2 concepts (minimum
support threshold and a minimum confidence
threshold), are discarded and not considered in the
analytical studies.
The association rule mining has received a great
deal of attention since its introduction. Today the
mining of such rules is still one of the most popular
and attracting pattern-discovery methods in
Knowledge Discovery and Data mining (KDD).
Therefore, the problem of mining association rules
can be converted into two sub-issues:
Identify all the frequent item sets that are set
to meet the pre-defined minimum support.
Find all association rules between the set of
all subsets of the frequent item sets, these
rules must also meet the minimum support
and minimum confidence.
In fact, the performance of association rule mining
algorithm focused on the first issue, in which the
most algorithms are focused on how to efficiently
discover frequent item sets.
4 THE APRIORI ALGORITHM
The Apriori Algorithm considered the basic
algorithm for finding a frequent item set in a
database. This algorithm was proposed by R.
Agrawal and R. Srikant in 1994 for mining frequent
item-sets for Boolean association rules.
The name of the algorithm is based on the fact
that the algorithm uses prior knowledge of frequent
item-set properties; also the threshold is already
known (the minimum support and the minimum
confidence).
Apriori is designed to operate on databases
containing transactions (for example, collections of
items bought by customers, or details of a website
frequentation).
A. How Apriori Algorithm Works
The Apriori Algorithm simply consists of two steps or
stages:
1. Find all frequent item-sets:
a) Get frequent items: Items whose occurrence in
database is greater than or equal to the
min.support threshold.
b) Generate candidates from frequent items.
c) Prune some results (the redundant records or
the ones that did not exceed the min.support).
2. Generate Strong rules from frequent item-sets:
Rules which satisfy the min.support and
min.confidence threshold.
B. Find all frequent item-sets
Apriori Algorithm employs an iterative approach
known as a level-wise search, where k-item-sets are
used to explore (k + 1)-item-sets. First, the set of
frequent 1-itemsets is found by scanning the database
to accumulate the count for each item, and collecting
those items that satisfy minimum support. The
resulting set is denoted L1. Next, L1 is used to find
L2, the set of frequent 2-itemsets, which is used to
find L3, and so on, until no more frequent k-item-sets
can be found. The finding of each Lk requires one
full scan of the database.
To improve the efficiency of the level-wise
generation of frequent item-sets, an important
property called the Apriori property is used to reduce
the search space.
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Apriori Property: All nonempty subsets of a
frequent item-set must also be frequent. The Apriori
property is based on the following observation. By
definition, if an item-set I does not satisfy the
minimum support threshold, min sup, then I is not
frequent; that is, P(I ) < min_support.
If an item A is added to the item-set I, then the
resulting item-set (i.e., I A) cannot occur more
frequently than I. Therefore, I A is not frequent
either; that is, P(I A) < min_support.
C. Generate Strong rules from frequent item-sets
In Order to complete "Find the Frequent Pattern"
process and also to reach to meaningful results that
we can benefit from and use; we need to find or
generate an association rules or a relationship
between these frequent pattern items/item-sets. We
can do that by using the following formula that
depends on the support & confidence values:
5 THE PROBLEM
Apriori algorithm is a classical algorithm that has
caused the most discussion. It can effectively carry
out the mining association rules. In the Apriori
algorithm a set of candidate item-sets Ck is generated
from Lk-1. Every item-set in Ck is tested whether it's
all k-l subsets constitute a large k-1 item-set or not. If
one of k-1 item-sets is not in Lk-1 item-sets, the
super item-set of this k-l item-set can be deleted.
That is, every time a k item-set is constituted, Apriori
must scan all Lk-1 item-sets. Because of many scan
large database many times in this way, the
identifying processes are the bottleneck of the
Apriori algorithm.
Apriori algorithm may need to generate a huge
number of candidate generations. Each time when
candidate generations are generated, the algorithm
needs to judge whether these candidates are frequent
item sets. The manipulation with redundancy result
in high frequency in querying, so tremendous
amounts of resources will be expended whether in
time or in space.
As it shows; mostly the problem with the Apriori
algorithm is the efficiency. We need to scan all the
items in the database multiple times. Also, redundant
generation of sub-item-sets during pruning the
candidate item-sets. Experiments show that time
taken for the database scan is more than the time
taken for candidate generation when the database
size is large (Tiwari et al., 2009).
We will explore in this paper two of the
enhancements and techniques that been added to the
Apriori algorithm in order to improve the efficiency.
6 THE STUDY
For more than 10 years, a lot of studies and researches
were conducted in order to find a solution to enhance
the efficiency of the Apriori algorithm. All the studies
stated that the Apriori algorithm results are trusted
and the only concern was regarding the time that it is
taking and the number of redundancy that is
generated in the candidate list of frequent item-set
list. And with the growth of the databases the problem
will become more complex. We explored lots of
researches and improvements on the Apriori
algorithms, some of them used another structure as a
tree, hash or matrixes and some updated the algorithm
by combine it with other ways like the FP-tree
concept or partition concept. However, this made it
more complex and harder to implement. In this paper
here we want to highlight some of the papers that
studied the Apriori algorithm and updated it in order
to improve the efficiency as the following:
1. The Research of Improved Apriori Algorithm for
Mining Association Rules – 2007
This paper presented an improved Apriori algorithm
to increase the efficiency of generating association
rules. This algorithm adopts a new method to reduce
the redundant generation of sub-item-sets during
pruning the candidate item-sets, which can form
directly the set of frequent item-sets and eliminate
candidates having a subset that is not frequent in the
meantime. This algorithm can raise the probability of
obtaining information in scanning database and
reduce the potential scale of item-sets.
The steps of this new algorithm are:
a) Generate a Candidate list for the frequent
items (C1)
b) Get frequent items from the Candidate lest.
(L1)
c) Generate candidates from frequent
items.(Ck+1 from Lk)
d) Check for infrequent items to be removed or
Prune from the candidate list before getting
the next L list, and so one.
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The update that made here is that there is a
candidate list and a check point for the infrequent
items to be removed before moving to the next level.
The advantages of this approach:
The size of database is reduced.
The storage space and computing time are saved.
2. A New Approach to Mine Frequent Itemsets -
The Frequent Item-sets Tree (FI-tree)- 2012
Simply; the idea here is to use a tree structure to store
the frequent item-sets along with their transaction
IDs. A distinct feature of this method is that it has
runs fast in different data characteristics. This study
showed that this new approach has high performance
in various kinds of data, outperforms the previously
developed algorithms in different settings, and is
highly scalable in mining different databases.
Steps of the proposed approach for mining
frequent item-sets from different data characteristics
are:
1. Assume that the frequent 1-itemsets and
transaction sets, require no more memory that
available and also there is space for generating
candidate 2-itemsets from frequent 1-itemset. Scan
database and find frequent 1-itemsets, at the same
time obtain transaction sets, which includes the Item-
set.
2. Generate candidate 2-itemsets from frequent 1-
itemset only.
3. The candidate 2-itemsets whose node count is
lower than min support using their FI-tree data
structure, it will be pruned off. Now frequent Item-set
tree contains only frequent 2-itemsets at the second
level.
4. Consequently, for each frequent 3, 4... n–Item-
set, scan the database to approve the consistence of
the Item-set.
Also this update is using the same concept of
checking and pruning before reaching the final
candidate in order to speed up the process and reduce
the redundancy as possible.
The advantages of this approach:
Fast approach as it is using an implicit candidate
list by using a frequent item tree structure.
3. A Novel Algorithm for Mining Frequent Item-set
From Larg Database - 2009
As the data to be mined is large, the time taken for
accessing data is considerable. In this search, a new
association rule-mining algorithm which generates the
frequent item-sets in a single pass over the database is
presented. The algorithm mainly uses two approaches
for association rule mining: The Partition approach,
where the data is mined in partitions and merges the
result, and the Apriori approach that helps to find the
frequent sets within each partition. The method
proposed in this research is pretty much depending on
the (Divide and Conquer) concept.
This partition approach used for finding frequent
item-sets in single pass over the database consists of
two phases.
Phase 1:
In this phase, the partition algorithm logically divides
the database in to a number of non-overlapping
partitions. These partitions are considered one at a
time and all frequent item-sets for that partition (Li )
are generated using the Apriori algorithm. In addition,
when taking each partition for calculating the frequent
item-sets separately the local minimum support is set
to 1. Thus, if there are n partitions, phase I of the
algorithm takes n iterations. At the end of phase I, all
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the local frequent item-sets of each partition are
merged to generate a set of all potential frequent item-
sets. In this step, the local frequent item-sets of same
lengths from all n-partitions are combined to generate
the global candidate item-sets, and also those global
candidate item-sets have their combined support
associated with it.
Phase 2:
As the above generated global candidate item-sets
have least possible frequent item-set of that partition
because, during the generation of frequent item-sets
using the Apriori algorithm of each partition, the
minimum local support was set to 1.
So this phase
just prune the item-sets from the global candidate
item-sets list whose combined support is less than the
global minimum support.
Below is the algorithm of modified partition
approach:
The following notation is used in the remainder of
this approach:
The advantages of this approach:
Database is scanned only once.
It will work most efficient in the case of large
databases with smallest minimum support
values.
4. A New Improvement of Apriori Algorithm for
Mining Association Rules – 2010
This enhanced algorithm is based on the user interest
and the importance of item-sets. In most existing
algorithms, the calculation of support only
considered the frequency of item-sets appearances,
without taking into account the importance of the
item itself. For example, shopping malls sell 10,000
towels one month, but only 300 TV sets, in the
traditional association rule-mining algorithm, the TV
is likely to be ignored. However, from the view of
the total sales amount, TV is far more than a towel,
derived from the traditional association rules
algorithm is obviously wrong. Therefore, the same
consideration of a towel and a TV is obviously
unreasonable, need to take into account the frequency
of item sets and importance of item sets when
calculate the support degree of item set, in this way,
association rules will be more scientific and reliable.
If only considering the frequency of item sets,
then calculating item set support functions can be
defined as:
f(X) = numTids(tids(X))/ numTids (tids (ø))
In order to consider the importance of item sets in
calculating support, need introduce a function which
compute support degree after quantify the importance
of item set, weight is a key quantitative indicators of
measuring the importance of item set. Because the
weight of items is a quantitative indicators that is
used to measure the importance of item, when
establish a database, can set a individual column to
store weight, also could make use of a existing
column to measure the weight.
For example, in a database that records the sales
records of shopping mall, each item will have a price,
suppose that the Px means the price of goods I ,
Pmax means the price of the most expensive goods,
then the weight of goods X can be calculated using
the following formula:
Wx = Px / Pmax
This calculation may be not very appropriate, but it
does reflect to some extent the importance of each
item. For this algorithm, the most important
consideration is that existing algorithms often ignore
these items, which have great importance but
frequency less than other items. Therefore, such an
idea can be used to assign weight to the item in the
FindingtheFrequentPatterninaDatabase-AStudyontheAprioriAlgorithm
393
item set: increase these support degree of items that
have great importance but less frequency. In order to
do this, the following formula can be used to assign
weight to the item:
Wx = (1- β) × numTids (tids (x)) / max z
(numTids (tids ((z)))
Z belongs to item set I, β is a parameter in the range
of [0, 1], which control the degree of correlation
between the frequency and weight of item. If β = 0,
then Wx = 1, that means there is no correlation
between the weight and the frequency of items, it is
always constant to 1, only considered the frequency
when calculate item set and the support of item set.
The description and process of algorithm:
Code shown in the above process, first, generate a set
of items of user interest as mining object from the
database, and then scan the database one time to
represent item set with transaction identification
number. After generating item-sets, assign weight to
element in item set, then use the introduction
function of the support of the weight to calculate the
item set degree of support to generate frequent item
set, finally, obtain association rule from these
frequent item set.
So the idea here; the pruning is done prior to the
database scan, after the pruning it is re-connected to
scan the database, thus reducing the number of scans.
The advantages of this approach:
Consider items which have great importance
and less frequency (more accurate results).
Reduces the number of database scans (the
pruning is done prior to the database scan).
Reduces the storage space.
7 FINAL COMPARISON
Algorithm
Name
Algorithm Approaches
Improved
Aproiri
algorithm
Generate candidate k-itemsets from frequent (k-
1)-itemsets.
Check if C has infrequent subset( Lk-1), If it
returns true it will remove C, Otherwise, scan
database D (Scan only the transactions that have
size >= K).
Compute the frequency of frequent k-itemsets
when k-itemsets are generated by (k-1)-itemsets.
Find frequent itemsets using an iterative level-
wise approach based on candidate generation.
FI-Tree
Algorithm
Scan database and find frequent 1-itemsets, at the
same time obtain transaction ID.
Generate candidate 2-itemsets from frequent 1-
itemset only.
The candidate 2-itemsets whose node count is
lower than min support using their FI-tree, it will
be pruned off. (Now frequent Item-set tree
contains only frequent 2-itemsets at the second
level).
Consequently, for each frequent 3, 4... n–Item-
set, scan the database to approve the consistence
of the Item-set.
Partition
algorithm
Divides the database in to n partitions.
Calculate frequent Item-Set using Aproiri (Set
min-sup to 1) in each partition.
Merges all the local frequent item-sets of the
same lengths in each partition to generate a
global frequent item-sets
Prune the global candidate item-sets whose
combined support is less than the global min-sup.
Weight
algorithm
Generate a set of items of user interest from the
database.
Scan the database one time to represent item set
with Tids.
Assign weight to each element in item set.
Use the function to calculate the support degree
of items to generate frequent item set.
Obtain association rule from these frequent item
set.
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Algorithm
Name
Database Scan
Memory
Usage
Candidate
Generation
Improved
Aproiri
algorithm
Same number
of database
scans in
aproiri but less
time in each
scan.
Reduces the
memory space
(scan only the
transactions
with
items>=K).
Same number
of candidate
generation in
aproiri.
FI-Tree
Algorithm
Less than
aproiri, it is
checking and
Pruning before
reaching the
final
candidate.
Assume that it
will not
require any
more memory
Less number
of candidate
lists generated
than aproiri
stored in tree.
Partition
algorithm
One scan
Reduces the
memory space
(Each partition
can adapting
better in
memory).
More than
aproiri
Weight
algorithm
Less than
aproiri,
where it
considers only
items with
Support
degree>= min-
supp after the
first scan)
Reduces the
memory space
Less number
of candidate
lists generated
than aproiri
8 EXAMPLES OF APRIORI
APPLICATIONS
Apriori algorithm concept is used in real life in many
fields with different level of complexity, from DNA
researches to a simple supermarket store financial
analysis tools. As an Examples:
1. Application of the Apriori algorithm for adverse
drug reaction detection - 2009 (US National Library
of Medicine/National Institutes of Health)
A research was intend to check for the detection of
adverse drug reactions (ADR) in health care data
using Apriori Algorithm. The Apriori algorithm is
used to perform association analysis on the
characteristics of patients, the drugs they are taking,
their primary diagnosis, co-morbid conditions, and
the ADRs or adverse events (AE) they experience.
This analysis produces association rules that indicate
what combinations of medications and patient
characteristics lead to ADRs. A simple data set is
used to demonstrate the feasibility and effectiveness
of the algorithm.
2. Apriori Application To Pattern Profile Creditor
Relationships With Credit Ceiling In Rural Bank -
2012 (Diponegoro University / Indonesia)
Maintaining the customer to remain loyal and
acquiring new clients are the successful capital for
financial institutions such as the BPR. One marketing
strategy is obtained from a Database, which is a
combination of hidden patterns of relationships
between items on the profile of creditors with credit
ceiling. Pattern rules creditor profile relationship
with the ceiling is presented in the model Apriori
application. Item profiles creditors and the credit
ceilings that appear simultaneously on each
transaction are important in finding new marketing
strategies such as target new creditors. The results of
the application may present Apriori pattern profile
creditor relationship with the credit ceiling with
graphs to provide a benchmark in providing the
credit limit on case that has never happened.
9 CONCLUSIONS
We have explored the Apriori Algorithm concept in
the field of minding the frequent item sets from a
database along with some enhancements and updates
on the classical Apriori algorithm that we considered
as the best simple improvements.
As a result of our study and after the comparison
that we made between the algorithms that we
explored, we found that no need to complex the
process as the Apriori algorithm is simple enough to
be trusted and rely on. However the problem was the
efficiency itself, which was taking some time to scan
the database more than once to get the candidate list
and also the redundancy problem, which is also
affecting the process. So if the Apriori algorithm will
be used in an application with a dedicated database it
is better and more efficient to use the classic Apriori
algorithm. On the other hand and with any special
conditions or under any special circumstances we
should take under consideration and choose a proper
updated Apriori to work most efficient.
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