An improved apriori algorithm for association rules

International Journal on Natural Language Computing (IJNLC) Vol. 3, No.1, February 2014
DOI : 10.5121/ijnlc.2014.3103 21
AN IMPROVED APRIORI ALGORITHM FOR
ASSOCIATION RULES
Mohammed Al-Maolegi1
, Bassam Arkok2
Computer Science, Jordan University of Science and Technology, Irbid, Jordan
ABSTRACT
There are several mining algorithms of association rules. One of the most popular algorithms is Apriori
that is used to extract frequent itemsets from large database and getting the association rule for
discovering the knowledge. Based on this algorithm, this paper indicates the limitation of the original
Apriori algorithm of wasting time for scanning the whole database searching on the frequent itemsets, and
presents an improvement on Apriori by reducing that wasted time depending on scanning only some
transactions. The paper shows by experimental results with several groups of transactions, and with
several values of minimum support that applied on the original Apriori and our implemented improved
Apriori that our improved Apriori reduces the time consumed by 67.38% in comparison with the original
Apriori, and makes the Apriori algorithm more efficient and less time consuming.
KEYWORDS
Apriori, Improved Apriori, Frequent itemset, Support, Candidate itemset, Time consuming.
1. INTRODUCTION
With the progress of the technology of information and the need for extracting useful information
of business people from dataset [7], data mining and its techniques is appeared to achieve the
above goal. Data mining is the essential process of discovering hidden and interesting patterns
from massive amount of data where data is stored in data warehouse, OLAP (on line analytical
process), databases and other repositories of information [11]. This data may reach to more than
terabytes. Data mining is also called (KDD) knowledge discovery in databases [3], and it includes
an integration of techniques from many disciplines such as statistics, neural networks, database
technology, machine learning and information retrieval, etc [6]. Interesting patterns are extracted
at reasonable time by KDD’s techniques [2]. KDD process has several steps, which are performed
to extract patterns to user, such as data cleaning, data selection, data transformation, data pre-
processing, data mining and pattern evaluation [4].
The architecture of data mining system has the following main components [6]: data warehouse,
database or other repositories of information, a server that fetches the relevant data from
repositories based on the user’s request, knowledge base is used as guide of search according to
defined constraint, data mining engine include set of essential modules, such as characterization,
classification, clustering, association, regression and analysis of evolution. Pattern evaluation
module that interacts with the modules of data mining to strive towards interested patterns.
Finally, graphical user interfaces from through it the user can communicate with the data mining
system and allow the user to interact.

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2. ASSOCIATION RULE MINING
Association Mining is one of the most important data mining’s functionalities and it is the most
popular technique has been studied by researchers. Extracting association rules is the core of data
mining [8]. It is mining for association rules in database of sales transactions between items
which is important field of the research in dataset [6]. The benefits of these rules are detecting
unknown relationships, producing results which can perform basis for decision making and
prediction [8]. The discovery of association rules is divided into two phases [10, 5]: detection the
frequent itemsets and generation of association rules. In the first phase, every set of items is called
itemset, if they occurred together greater than the minimum support threshold [9], this itemset is
called frequent itemset. Finding frequent itemsets is easy but costly so this phase is more
important than second phase. In the second phase, it can generate many rules from one itemset as
in form, if itemset {I1, I2, I3}, its rules are {I1 I2, I3}, {I2 I1, I3}, {I3 I1, I2}, {I1, I2 I3}, {I1,
I3 I1}, {I2, I3 I1}, number of those rules is n2
-1 where n = number of items. To validate the rule
(e.g. X Y), where X and Y are items, based on confidence threshold which determine the ratio
of the transactions which contain X and Y to the transactions A% which contain X, this means
that A% of the transactions which contain X also contain Y. minimum support and confidence is
defined by the user which represents constraint of the rules. So the support and confidence
thresholds should be applied for all the rules to prune the rules which it values less than
thresholds values. The problem that is addressed into association mining is finding the correlation
among different items from large set of transactions efficiency [8].
The research of association rules is motivated by more applications such as telecommunication,
banking, health care and manufacturing, etc.
3. RELATED WORK
Mining of frequent itemsets is an important phase in association mining which discovers frequent
itemsets in transactions database. It is the core in many tasks of data mining that try to find
interesting patterns from datasets, such as association rules, episodes, classifier, clustering and
correlation, etc [2]. Many algorithms are proposed to find frequent itemsets, but all of them can
be catalogued into two classes: candidate generation or pattern growth.
Apriori [5] is a representative the candidate generation approach. It generates length (k+1)
candidate itemsets based on length (k) frequent itemsets. The frequency of itemsets is defined by
counting their occurrence in transactions. FP-growth, is proposed by Han in 2000, represents
pattern growth approach, it used specific data structure (FP-tree), FP-growth discover the frequent
itemsets by finding all frequent in 1-itemsets into condition pattern base , the condition pattern
base is constructed efficiently based on the link of node structure that association with FP-tree.
FP-growth does not generate candidate itemsets explicitly.
4. APRIORI ALGORITHM
Apriori algorithm is easy to execute and very simple, is used to mine all frequent itemsets in
database. The algorithm [2] makes many searches in database to find frequent itemsets where k-
itemsets are used to generate k+1-itemsets. Each k-itemset must be greater than or equal to
minimum support threshold to be frequency. Otherwise, it is called candidate itemsets. In the first,
the algorithm scan database to find frequency of 1-itemsets that contains only one item by
counting each item in database. The frequency of 1-itemsets is used to find the itemsets in 2-
itemsets which in turn is used to find 3-itemsets and so on until there are not any more k-itemsets.

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If an itemset is not frequent, any large subset from it is also non-frequent [1]; this condition prune
from search space in database.
5. LIMITATIONS OF APRIORI ALGORITHM
Apriori algorithm suffers from some weakness in spite of being clear and simple. The main
limitation is costly wasting of time to hold a vast number of candidate sets with much frequent
itemsets, low minimum support or large itemsets. For example, if there are 104
from frequent 1-
itemsets, it need to generate more than 107
candidates into 2-length which in turn they will be
tested and accumulate [2]. Furthermore, to detect frequent pattern in size 100 (e.g.) v1, v2…
v100, it have to generate 2100
candidate itemsets [1] that yield on costly and wasting of time of
candidate generation. So, it will check for many sets from candidate itemsets, also it will scan
database many times repeatedly for finding candidate itemsets. Apriori will be very low and
inefficiency when memory capacity is limited with large number of transactions.
In this paper, we propose approach to reduce the time spent for searching in database transactions
for frequent itemsets.
6. THE IMPROVED ALGORITHM OF APRIORI
This section will address the improved Apriori ideas, the improved Apriori, an example of the
improved Apriori, the analysis and evaluation of the improved Apriori and the experiments.
6.1. The improved Apriori ideas
In the process of Apriori, the following definitions are needed:
Definition 1: Suppose T={T1, T2, … , Tm},(m≥1) is a set of transactions, Ti= {I1, I2, … , In},(n≥1)
is the set of items, and k-itemset = {i1, i2, … , ik},(k≥1) is also the set of k items, and k-itemset ⊆
I.
Definition 2: Suppose σ (itemset), is the support count of itemset or the frequency of occurrence
of an itemset in transactions.
Definition 3: Suppose Ck is the candidate itemset of size k, and Lk is the frequent itemset of size
k.
Scan all transactions to generate L1 table
L1(items, their support, their transaction IDs)
Construct Ck by self-join
Use L1 to identify the target transactions for Ck
Scan the target transactions to generate Ck
Figure 1: Steps for Ck generation

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In our proposed approach, we enhance the Apriori algorithm to reduce the time consuming for
candidates itemset generation. We firstly scan all transactions to generate L1 which contains the
items, their support count and Transaction ID where the items are found. And then we use L1 later
as a helper to generate L2, L3 ... Lk. When we want to generate C2, we make a self-join L1 * L1 to
construct 2-itemset C (x, y), where x and y are the items of C2. Before scanning all transaction
records to count the support count of each candidate, use L1 to get the transaction IDs of the
minimum support count between x and y, and thus scan for C2 only in these specific transactions.
The same thing for C3, construct 3-itemset C (x, y, z), where x, y and z are the items of C3 and use
L1 to get the transaction IDs of the minimum support count between x, y and z, then scan for C3
only in these specific transactions and repeat these steps until no new frequent itemsets are
identified. The whole process is shown in the Figure 1.
6.2. The improved Apriori
The improvement of algorithm can be described as follows:
//Generate items, items support, their transaction ID
(1) L1 = find_frequent_1_itemsets (T);
(2) For (k = 2; Lk-1 ≠Φ; k++) {
//Generate the Ck from the LK-1
(3) Ck = candidates generated from Lk-1;
//get the item Iw with minimum support in Ck using L1,(1≤w≤k).
(4) x = Get _item_min_sup(Ck, L1);
// get the target transaction IDs that contain item x.
(5) Tgt = get_Transaction_ID(x);
(6) For each transaction t in Tgt Do
(7) Increment the count of all items in Ck that are found in Tgt;
(8) Lk= items in Ck ≥ min_support;
(9) End;
(10) }
6.3. An example of the improved Apriori
Suppose we have transaction set D has 9 transactions, and the minimum support = 3. The
transaction set is shown in Table.1.
Table 1: The transactions
T_ID Items
T1 I1, I2, I5
T2 I2, I4
T3 I2, I4
T4 I1, I2, I4
T5 I1, I3
T6 I2, I3
T7 I1, I3
T8 I1, I2, I3, I5
T9 I1, I2, I3

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Table 2: The candidate 1-itemset
Items support
I1 6
I2 7
I3 5
I4 3
I5 2 deleted
firstly, scan all transactions to get frequent 1-itemset l1 which contains the items and their support
count and the transactions ids that contain these items, and then eliminate the candidates that are
infrequent or their support are less than the min_sup. The frequent 1-itemset is shown in table 3.
Table 3: Frequent 1_itemset
Items support T_IDs
I1 6 T1, T4, T5, T7, T8, T9
I2 7 T1, T2, T3, T4, T6, T8, T9
I3 5 T5, T6, T7, T8, T9
I4 3 T2, T3, T4
I5 2 T1, T8 deleted
The next step is to generate candidate 2-itemset from L1. To get support count for every itemset,
split each itemset in 2-itemset into two elements then use l1 table to determine the transactions
where you can find the itemset in, rather than searching for them in all transactions. for example,
let’s take the first item in table.4 (I1, I2), in the original Apriori we scan all 9 transactions to find
the item (I1, I2); but in our proposed improved algorithm we will split the item (I1, I2) into I1 and I2
and get the minimum support between them using L1, here i1 has the smallest minimum support.
After that we search for itemset (I1, I2) only in the transactions T1, T4, T5, T7, T8 and T9.
Table 4: Frequent 2_itemset
Items support Min Found in
I1, I2 4 I1 T1, T4, T5, T7, T8, T9
I1, I3 4 I3 T5, T6, T7, T8, T9
I1, I4 1 I4 T2, T3, T4 deleted
I2, I3 3 I3 T5, T6, T7, T8, T9
I2, I4 3 I4 T2, T3, T4
I3, I4 0 I4 T2, T3, T4 deleted
The same thing to generate 3-itemset depending on L1 table, as it is shown in table 5.
Table 5: Frequent 3-itemset
Items support Min Found in
I1, I2 , I3 2 I3 T5, T6, T7, T8, T9 deleted
I1, I2 , I4 1 I4 T2, T3, T4 deleted

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For a given frequent itemset LK, find all non-empty subsets that satisfy the minimum confidence,
and then generate all candidate association rules.
In the previous example, if we count the number of scanned transactions to get (1, 2, 3)-itemset
using the original Apriori and our improved Apriori, we will observe the obvious difference
between number of scanned transactions with our improved Apriori and the original Apriori.
From the table 6, number of transactions in1-itemset is the same in both of sides, and whenever
the k of k-itemset increase, the gap between our improved Apriori and the original Apriori
increase from view of time consumed, and hence this will reduce the time consumed to generate
candidate support count.
Table 6: Number of transactions scanned Experiments
Original Apriori Our improved Apriori
1-itemset 45 45
2-itemset 54 25
3-itemset 36 14
sum 135 84
We developed an implementation for original Apriori and our improved Apriori, and we collect 5
different groups of transactions as the follow:
• T1: 555 transactions.
The first experiment compares the time consumed of original Apriori, and our improved
algorithm by applying the five groups of transactions in the implementation. The result is shown
in Figure 2.
Figure 2: Time consuming comparison for different groups of transactions
The second experiment compares the time consumed of original Apriori, and our proposed
algorithm by applying the one group of transactions through various values for minimum support
in the implementation. The result is shown in Figure 3.

27
Figure 3: Time consuming comparison for different values of minimum support
6.4. The analysis and evaluation of the improved Apriori
As we observe in figure 2, that the time consuming in improved Apriori in each group of
transactions is less than it in the original Apriori, and the difference increases more and more as
the number of transactions increases.
Table 7 shows that the improved Apriori reduce the time consuming by 61.88% from the original
Apriori in the first group of transactions T1, and by 77.80% in T5. As the number of transactions
increase the rate is increased also. The average of reducing time rate in the improved Apriori is
67.38%.
Table 7: THE time reducing rate of improved Apriori on the original Apriori according to the number of
transactions
T Original Apriori (S) Improved Apriori (S) Time reducing rate (%)
T1 1.776 0.677 61.88%
T2 8.221 4.002 51.32%
T3 6.871 2.304 66.47%
T4 11.940 2.458 79.41%
T5 82.558 18.331 77.80%
As we observe in figure 3, that the time consuming in improved Apriori in each value of
minimum support is less than it in the original Apriori, and the difference increases more and
more as the value of minimum support decreases.
Table 8 shows that the improved Apriori reduce the time consuming by 84.09% from the original
Apriori where the minimum support is 0.02, and by 56.02% in 0.10. As the value of minimum
support increase the rate is decreased also. The average of reducing time rate in the improved
Apriori is 68.39%.

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Table 8: The time reducing rate of improved Apriori on the original Apriori according to the value of
minimum support
Min_Sup Original Apriori (S) Improved Apriori (S) Time reducing rate (%)
0.02 6.638 1.056 84.09%
0.04 1.855 0.422 77.25%
0.06 1.158 0.330 71.50%
0.08 0.424 0.199 53.07%
0.10 0.382 0.168 56.02%
7. CONCLUSION
In this paper, an improved Apriori is proposed through reducing the time consumed in
transactions scanning for candidate itemsets by reducing the number of transactions to be
scanned. Whenever the k of k-itemset increases, the gap between our improved Apriori and the
original Apriori increases from view of time consumed, and whenever the value of minimum
support increases, the gap between our improved Apriori and the original Apriori decreases from
view of time consumed. The time consumed to generate candidate support count in our improved
Apriori is less than the time consumed in the original Apriori; our improved Apriori reduces the
time consuming by 67.38%. As this is proved and validated by the experiments and obvious in
figure 2, figure 3, table 7 and table 8.
ACKNOWLEDGEMENTS
We would like to thank all academic staff in our university for supporting us in each research
projects specially this one.
REFERENCES
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Authors
Mohammed Al-Maolegi Obtained his Master degree in computer science from Jordan
University of Science and Technology University (Jordan) in 2014. He received his B.Sc. in
computer information system from Mutah University (Jordan) in 2010. His research interests
include: softw are engineering, software metrics, data mining and wireless sensor networks.
Bassam Arkok Obtained his Master degree in computer science from Jordan University of Science and
Technology University (Jordan) in 2014. He received his B.Sc. in computer science from Alhodidah
University (Yemen). His research interests include: software engineering, software metrics, data mining
and wireless sensor networks.

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