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1. IOSR Journal of Computer Engineering (IOSRJCE)
ISSN: 2278-0661 Volume 3, Issue 5 (July-Aug. 2012), PP 26-30
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Efficient Parallel Pruning of Associative Rules with Optimized
Search
1
K.Sangeetha, 2Dr.P.S.Periasamy, 3S.Prakash
1
Assistant Professor (SG), S.N.S.College of Technology, Coimbatore
,2 Professor, K.S.R.College of Engineering, Tiruchengode
3
Assistant Professor (SG,) Sri Shakthi Institute of Engineering and Technology, Coimbatore
Abstract: The main focus of this research work is to propose an improved association rule mining algorithm to
minimize the number of candidate sets while generating association rules with efficient pruning time and search
space optimization. The relative association with reduced candidate item set reduces the overall execution time.
The scalability of this work is measured with number of item sets used in the transaction and size of the data set.
Further Fuzzy based rule mining principle is adapted in this work to obtain more informative associative rules
and frequent items with increased sensitive. The requirement for sensitive items is to have a semantic connection
between the components of the item-value pairs. The effectiveness of item-value pairs minimizes the search
space to its optimality. Optimality of the search space indicates the trade off between pruning time and size of
the data set.
I. Introduction
A rapid growth of information extraction from large transactional data sets fueled the demand of
knowledge discovery and associative relation between the items. To identify the most frequent transacted items
and generates associative rules between various items, Apriori algorithm is one such most sought solution for
association rule mining, in which scanning of transaction item was done efficiently without missing any items.
So the generation of candidate item set consumes more time to generate associative rules. To overcome the
slowness in associative rule pruning various strategies were discussed in literature to improve the speed of rule
formation. The approaches presented in the literatures adapted multifold iteration of the transaction data sets
which affected the time and search space for pruning the more sensitive item and its relative association. Some
of the sampling methods are available, but these processes will again affect the performance of the items which
leads to missed out transaction.
In this framework, many algorithms have been proposed for proficient creation of normal item sets in
the literature because the problem was first introduced. To reduce the size of the candidate item sets, the Direct
Hashing and Pruning (DHP) algorithm uses a hash table that results in efficient pruning of item sets. The
Partition algorithm decreases Input / Output (I/O) by examining the database only twice.
II. Literature Review
Ken Sun et al (2008) introduced new focus on Association Rule Mining (ARM) algorithms. This
proposal uses w-support, which does not require pre assigned weights, but this method is constraint-based in the
sense that all rules must fulfill a predefined set of conditions, such as support and confidence. However, the
main goal of this algorithm is to reduce the number of generated rules.
Jens Teubner et al (2011) explore how to accelerate the computation of frequent itemset using field-
programmable gateway. The pipeline solution was introduced to improve the performance. It uses the minimum
count as a threshold, so it is a constraint based algorithm.
Zhaonian Zou et al (2010) investigates the problem of mining uncertain graph data and especially
focuses on mining frequent sub graph patterns on an uncertain graph database. based on minimum support value
the frequent sub graph pattern is minined. Claudia Marinica et al (2010) proposed a new interactive approach to
prune and filter discovered rules to use ontologies in order to improve the integration of user knowledge in the
post processing task
Alok Sharma et al (2008), proposed a new method to reduce the search space. In that, prior to
dimensionality-reduction transformation an additional rotational transform that rotates the feature vectors in the
original feature space around their respective class centroids in such a way that the overlap between the classes
in the reduced feature space is further minimized
Elena Baralis et al (2009) proposed a method called IMine index, a general and compact structure
which provides tight integration of item set extraction in a Relational Data Base Management System. E.
Hüllermeier et al (2007) proposed an algorithm which was an adaptation of the Apriori algorithm for number of
items in the attributes. It is not easy to extend the algorithm to higher dimensional cases.
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2. Efficient Parallel Pruning of Associative Rules with Optimized Search
III. Problem Definition
Normally, the principle of association rule mining is to mine a set of shared highly correlated
attributes/features amongst a huge number of records in a given database for knowledge discovery. The fuzzy
ARM algorithms are used under large datasets for a fast and efficient performance.
A fuzzy ARM algorithm for generating fuzzy association rules is not a simple one. The first process is
conversion of crisp dataset which consists of crisp binary and numerical attributes, into a fuzzy dataset,
containing crisp binary and fuzzy binary attributes. The second process is to calculate the frequency of an item
set using the presence or absence in a transaction of the dataset, but fuzzy ARM algorithms must taken into
account in a particular transaction of the dataset, in addition to its presence or absence. This becomes tedious
process.
The problem of scalability and higher memory requirements are addressed in this research work by
deploying parallel pruning technique at different levels of items sets (one item set, two item set, etc.,). From the
recent literature we came to know that, only Apriori and its adaptations are used for generating association rules.
Thus, the Fuzzy based Optimal Search Space Pruning (FOSSP) is compared with existing fuzzy Apriori and the
execution time is recorded as in Fig.1.
IV. Objective
The objective is to minimize the number of candidate sets and enhancing the association rule mining
algorithm while creating an association rules by evaluating maximal information associated with each item that
occurs in given set of transaction. Initial work starts with the evaluation of weighted association rule mining in
terms of item-value relational metrics. Then the number of item metrics is taken into account of the association
rule mining with reduced candidate item set. This may decrease not only the number of item sets generated but
also the overall execution time of the algorithm. Any valued attribute will be treated as item-value relational
metrics and will be used to derive the minimal number of association rules which increased the rules
information content.
The research work evaluates the scalability of the FOSSP (say for car purchase dataset and bank
transaction data set) by considering transaction time, number of item sets used in the transaction and memory
utilization. In addition, further the work moves in the direction of fuzzy based item value of the rule mining
principle on associative rules of the complete item sets. To evaluate the item-value relativity metric of the
scalable association mining, optimal search on parallel pruning is planned for deployment as it can hold more
number of associative information.
V. Scalable Association Rule Mining Using Parallel Pruning
FOSSP presented in this work, first analyze the scalability issues of association rule mining in large
data sets. Parallel pruning technique is deployed in FOSSP to mine the large transactional items simultaneously
at different levels of items sets to improve the execution speed for generating frequent items and association
rules. The enhancement of Apriori algorithm is done by increasing the efficiency of candidate pruning phase by
reducing the number of candidates that are generated for further verification. The FOSSP pruning technique use
information associated to the number of items to estimate overlap items in the transactions. The basic elements
considered in the development of the FOSSP are number of transactions, average size of transaction, average
size of the maximal large item sets, number of items, and distribution of occurrences of large item sets.
The parallel pruning in FOSSP provides improvement over Apriori by generating frequent items and rules for
transaction data. It generates all candidates based on n-level frequent item sets on sorted database, and all
frequent item sets that can no longer be supported by transactions that still have to be processed. Thus the
FOSSP has no longer to maintain the covers of all past item sets sequentially. The algorithm for parallel pruning
technique to generate informative rules and strong frequent items is presented as below:
5.1 Framework of FOSSP Algorithm
Input: Number of Transactions and items, larger data sets
Output: Candidate items, number of informative rules, frequent items, execution time
Steps of Procedures
a. Initialize number of items and transactions from large data sets
b. Generate candidate item sets with information requirement
c. Reduce the candidate item with relative item values
d. With probability ratio, generate frequent item sets (i.e., satisfy minimum support)
e. Parallel prune the frequent items at different levels of the item set
f. With conditional probability on parallel pruned item levels, generate strong association rules.
g. Calculate execution time of frequent item set and informative association rules
h. Sort the item sets based on the frequency and information association
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3. Efficient Parallel Pruning of Associative Rules with Optimized Search
i. Merge the more associated rules of item pairs
j. Discard the infrequent item value pairs
k. Perform Fuzzy Parallel Pruning (PP)
l. Iterate the steps c to f till the required scalability mining results are achieved
Fuzzy PP algorithm:
For each t Є T
Search the whole Transaction and return all the items
Membership Function (mF) = {a Є A | 0 ≤ a ≤ 1}mF = 1 ; 0 ≤ a ≤ 1; mF = 0; otherwise
Perform mapping function
End
Where T - total transaction, t - transaction instance, A - complete item set, a - items of transaction instance.
For B = (y1, y2,…yn)
fuzzy set (B, n) = {n(y1)/y1,…n(yn)/ yn}
Scan the transformed database
Evaluate the support with the predefined Min Support value.
End
Where B – candidate item set, y1,y1..yn – frequent item set of transaction instances, n – number of instances.
In FOSSP the candidate item reduction object is updated in the iteration to determine the processing
items. In the Apriori association mining algorithm, the data item read, needs to be matched against all
candidates to determine the set of candidates whose counts will be incremented. It is not possible to statically
partition the reduction object so that different process update disjoint portions of the collection which made
parallel pruning in FOSSP more efficient. However as the pruning transaction item is more concerned in
parallel, the search space for frequent item generation and item-value pair based maximal information sensitive
association rules becomes complex. To overcome these facts, in the next chapter, the optimization of search
space using fuzzy rule set, is described.
VI. Optimization Of Search Space Using Fuzzy Rule Set
The traditional fuzzy ARM exploits a data-driven pre-processing approach which makes routine to the
formation of fuzzy partitions for numerical attributes. Therefore, it converts the given data set to fuzzy data set
that desires a lesser amount of human communication for even very large datasets. Numerical attributes in the
real data sets are converted to fuzzy sets which comprises of split data sets with boundary limits. The item
values in the split boundaries can have the uncertainty factor which affects the quality and accuracy of fuzzy
association rule mining. In addition the search space using fuzzy modeled association rule mining needs larger
memory to accommodate larger transactions data sets. The FOSSP presented in this work, which improves
parallel pruning technique is described in chapter 5. FOSSP utilize fuzzy rule controlled feedback scheme to
optimize the search space for more effective association rule generation. The following section describes about
various techniques to evaluate the scalability of association rule mining and the resultant optimal search space
for efficient item pruning
6.1 Partitioning Fuzzy Domain Set
In presenting the optimal search space approach for fuzzy association rule mining process, fuzzy
partition domains are made based on the user defined item-value attribute on the original dataset. To evaluate
the fuzzy data set for informative association rule mining, support and confidence metrics are redefined based
on the fuzzy binary attributes. The generation of fuzzy association rules is directly impacted by the fuzzy
measures adapted in the parallel pruning approach. The dataset is logically divided into „p‟ disjoint horizontal
partitions P1, P2… Pp. Each partition is as large as can fit in available optimal memory space. The partitions are
equal-sized, though each partition could be of any arbitrary size as well.
6.2 Optimal Search Fuzzy Feedback scheme for Informative Rule Generation
The optimal search space with fuzzy for association rule mining deployed iterative feedback on the rule
set generation. The parallel pruning of multi-level item set is split with fuzzy data set to obtain the rules from
respective partitioned domain, whereas the feedback scheme gets into each partitioned domain. Within the
partitioned domain, the initial rules generated for item value attributes that are governed by the optimal search
based feedback scheme to identify the sensitivity of fuzzy binary value in one domain to other. The optimal
fuzzy feedback scheme minimizes the number of rules being generated in each and every partitioned domain of
multiple outliers which are divided into groups.
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4. Efficient Parallel Pruning of Associative Rules with Optimized Search
VII. Experimental Results And Discussions on FOSSP
The experimental evaluation of FOSSP on identifying the results of performance metrics such as
scalability, search space optimality, informative associative rules sets, and candidate set reduction. The
scalability evaluation is made on the size of the data set used and its pruning time for generating frequent items
and association rule sets with deployment of parallel pruning of multi-level item sets simultaneously. The
optimality of search space for parallel pruning is measured by varying large items using fuzzy rule
appropriation.
For experimental purpose on the scalability issue, the samples for banking data set obtained from the
local governmental banking streams with size of transaction data with Giga Bytes (GBs) is used . The total
number of distinct items was 1000 and the average number of items in a transaction was 15.
No of Iteration Vs Execution time
140
120
Execution Time
Execution time -
100 FOSSP (Proposed)
80
60 Execution time -
40 Fuzzy Apriori
(Existing)
20
0
8 -16 16 - 32 32 - 48 48 - 60
Number of Iterations
Fig. 1. Comparision of execution time with FOSSP and Fuzzy Apriori
The confidence value of 90% and support value of 50% is given as an input. Normally, when the
number of iterations for item pruning increases then execution time gradually increases. The execution time for
parallel pruning is illustrated to evaluate the performance of the proposed technique, compared with the existing
Apriori rule generation as shown in Fig.1.
In General, when the data size for item pruning increases then execution time gradually increases. The
scalability performance of FOSSP shows 2 times faster execution time compared to that of fuzzy Apriori
models. Though the performance of scalability is considerably higher for parallel pruning, the execution time
requirement increases with the growth in the size of unique items as shown in Fig.2.
Data size Vs Time
40000
35000
30000
Time (sec)
Time for fuzzy based
25000
apriori (Existing)
20000
Time for FOSSP
15000
(Proposed)
10000
5000
0
1 2 3 4 5 6 7 8 9
Data size (MB)
Fig. 2. Scalability evaluation with FOSSP and Fuzzy Apriori
Usually, when the item set for pruning increases, the search space also gradually increase. Further
datasets from machine learning repository (Car Purchase Data set, Bank transaction data set) are extracted and
enhanced with data size to GBs with more number of unique items. The performance of FOSSP in terms of
scalability as well as the search space requirements at each of these data sets is depicted as in Fig.3. The optimal
value of memory for search space and the maximum size of the data set, minimal number of rule generation
covering most possible information of the data set, and candidate set reduction are evaluated.
The car dataset with 20 distinct items, where the average number of items per transaction is 6 to 8 are
used for the experimental evaluation of FOSSP. The total size of the dataset is 2 GBs and a confidence level(C)
of 90% is used. The support counts testified with the transaction for frequent item pruning are 70%, 85%, 93%,
and 62%. The execution time is improved for FOSSP with reduction of 2 to 4 times as compared to fuzzy
Apriori and the memory utilization reduced nearly 2 to 3 times for the data size of 2 GB Car purchase data set.
With experimental result on the car purchase data set, the performance of FOSSP is improved when compared
to Fuzzy Apriori.
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5. Efficient Parallel Pruning of Associative Rules with Optimized Search
Number of Itemsets Vs Search Space
12000
Search Space(Bytes)
10000
8000 Search Space
(FOSSP)
6000
Search Space
4000 (Fuzzy Apriori)
2000
0
24 32 36 42
Number of Itemsets
Fig. 3. Comparision of search space with FOSSP and Fuzzy Apriori
The performance results of FOSSP approach are evaluated with various values of support(S) ranging
from 25% to 40%. It is concluded from the observation of the results that the proposed FOSSP approach derives
effective item-value pair based strong association rule with optimal search space performs 25% faster than
fuzzy adapted variants of Apriori(Fig.3), based on the user defined support value. With other dataset samples,
the support value is approximated for 34%, in which optimal number of item sets is generated.
From these experiments, it is observed that the FOSSP approach performs most efficiently (more
accurate rules) and speedily at the optimal support value, which occurs in the range of 15% - 20% for car
dataset. Another purpose was to reduce the number of parallel pruning to the data transaction partitions in
FOSSP with just one partition for support values of 20% – 40% on car data sets and 10% – 40% on bank data
set, keeping in mind that the main memory is utilized in the best manner possible, without any thrashing.
Furthermore, with the fuzzy based optimal search feedback scheme, it was observed that more informative rules
for all the attributes with more sensitive frequent item have been occurred.
VIII. Conclusion
The fuzzy based optimal search pruning technique presented in this research work evaluated frequent
items with more sensitive item-value pairs. The rule obtained with FOSSP generated appropriate candidate item
set that contributes to the improvement of extracting maximal informative association rules from the large
transactional data sets. Parallel pruning of item sets at multiple levels of the complete items (one item set, two
item sets, … n item sets) decreased the execution time of the FOSSP rule mining, as the frequent items for all
the levels obtained simultaneously. Fuzzy rule is modeled to function parallel pruning with optimal search space
and reduced the trade off between scalability of data sets and the search space for larger items.
In fuzzy Apriori, search space for pruning gets increased as for larger data set which affected the
performance of association rule mining; however, FOSSP provided optimal search size for larger data sets. The
experimental results shows that FOSSP works better in terms of time reduction when contrast to fuzzy Apriori
model.
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