NEW FAST ALGORITHM FOR INCREMENTAL MINING OF
ASSOCIATION RULES
Yasser El Sonbati, Rasha Kashef
Arab Academy for science & Technology, College of Comuputing and Information Technology
P.0.Box. 1029. Abu Kir , AlexandriaEgypt
Key
words: Data mining, Association rules, Incremental mining.
Abstract: Mining association rules is a well-studied problem, and several algorithms were presented for finding large
itemsets. In this paper we present a new algorithm for incremental discovery of large itemsets in an
increasing set of transactions. The proposed algorithm is based on partitioning the database and keeping a
summary of local large itemsets for each partition based on the concept of negative border technique. A
global summary for the whole database is also created to facilitate the fast updating of overall large
itemsets. When adding a new set of transactions to the database, the algorithm uses these summaries instead
of scanning the whole database, thus reducing the number of database scans. The results of applying the
new algorithm showed that the new technique is quite efficient, and in many respects superior to other
incremental algorithms like Fast Update Algorithm (FUP) and Update Large Itemsets (ULI).
1 INTRODUCTION
Data mining is the process of discovering potentially
valuable patterns, associations, trends, sequences
and dependencies in data [
Agrawal et al.,
1993
][Agrawal et al., 1994][Agrawal and Yu 1998].
Mining association rules is one of the vital data
mining problems. An association rule is a relation
between items in a set of transactions. This rule must
have a statistical significance (support) with respect
to the whole database and its structure must have a
semantic prospective (confidence), as will be stated
in more details later in section 2. Apriori algorithm
[Agrawal et al., 1994] is the first successful
algorithm for mining association rules. It introduces
a method to generate candidate itemsets C
k
in pass k
using only large itemsets L
k-1
in the previous pass.
Direct Hashing and Pruning (DHP) algorithm [Park
et al., 1997] is the next algorithm for efficient
mining of association rules. It employs a hash
technique to reduce the size of the candidate
itemsets and the database The Continuous
Association Rule Mining Algorithm (CARMA)
[Hidber 1998] allows the user to change the support
threshold and continuously displays the resulting
association rules with support and confidence
bounds.
After some Update activities, new transactions are
added to the database. When new transactions are
added to the database, insignificant rules will be
discarded. Similarly new valid ones that satisfy the
statistical and the semantic constraints will be
included. The Adaptive algorithm [Sarda and
Srinivas 1998] is not only incremental but also
adaptive in nature. By inferring the nature of the
incremental database, it can avoid unnecessary
database scans. The Fast Update algorithm (FUP) is
an incremental algorithm which makes use of past
mining results to speed up the mining process
[Cheung et al., 1996]. Update Large Itemsets
algorithm (ULI) [Thomas et al., 1997] uses negative
borders to decide when to scan the whole database.
Recently Fast Online Dynamic Association Rule
Mining (FODARM) algorithm [Woon et al., 2002] is
introduced for incremental mining in electronic
commerce. It uses a novel tree structure known as a
Support-Ordered Trie Itemset (SOTrieIT) structure
to hold pre-processed transactional data. Another
algorithm for Online Generation of Profile
Association Rules is introduced in [Aggarwal et al.,
275
El Sonbati Y. and Kashef R. (2004).
NEW FAST ALGORITHM FOR INCREMENTAL MINING OF ASSOCIATION RULES.
In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 275-281
DOI: 10.5220/0002624102750281
Copyright
c
 SciTePress

2002]. A New approach to Online Generation of
Association Rules [Aggarwal and Yu 2001]
introduces the concept of storing the preprocessed
data in such a way that online processing may be
done by applying a graph theoretic search algorithm
whose complexity is proportional to the size of the
output .
The algorithm presented in this paper NBP: Negative
Border with Partitioning is based on partitioning the
database, keeping a summary for each partition. This
summary includes the locally large itemsets, their
negative border and any other previously counted
itemset in the partition. Another global summary
including the large and negative border itemsets is
also created for the whole database. When adding a
new set of transactions to the database, the NBP
applies the Update Large Itemsets (ULI)-like
algorithm [Thomas et al., 1997] that uses these
summaries instead of scanning the whole database,
thus reducing the number of database scans to less
than one scan.
The rest of the paper is organized as follows. The
next section gives a description of the association
rules mining (ARM) problem while section 3
presents the negative border with partitioning
algorithm. Section 4 describes performance analysis
of the proposed algorithm in comparison with some
related algorithms. Finally conclusions are discussed
in Section 5.
2 PROBLEM DESCRIPTION
The problem of association rules mining is described
in the following two subsections.
2.1 Mining of association rules
The problem of mining association rules is described
as follow: let the universal itemset, I = {i
1
, i
2
,.., i
m
}
be a set of literals called items , D be a database of
transactions, where each transaction T contains a set
of items such that T
⊆ I. An itemset is a set of items
and k-itemset is an itemset that contains exactly k
items. For a given itemset X
⊆ I and a given
transaction T, T contains X if and only if X
⊆ T.
The support count σ
x
of an itemset X is defined as
the number of transactions in D containing X. An
item set is large, with respect to a support threshold
of s%, if σ
x
≥ |D| × s, where |D| is the number of
transactions in the database D. An association Rule
is an implication of the form “X
⇒ Y” where X, Y ⊆ I
and X
∩ Y = ∅ . The association rule X ⇒ Y holds in
the database with confidence c% if no less than c%
of the transactions in D that contain X also contain Y.
The rule X
⇒ Y has support s% in D if σ
x ∪ y
= |D|
×s%. For a given pair of confidence and support
thresholds, the problem of mining association rules
is to find out all the association rules that have
confidence and support greater than the
corresponding thresholds. This problem can be
reduced to the problem of finding all large itemsets
for the same support threshold [
Agrawal et al., 1993].
2.2 Update of association rules
After some Update activities, new transactions are
added to the original database D. When new
transactions are added to the database, an old large
itemset could potentially become small in the
updated database. Similarly, an old small itemset
could potentially become large in the new database.
Let ∆
+
be the set of newly added transactions
(increment database), D
’
be the updated database
where D
’
= ( D ∪ ∆
+
), σ
x
’
be the new support count
of an itemset X in the updated database D
’
, L
D’
be
the set of large itemset in D
’
, C
k
is the set of
candidate k-itemsets in D and δ
x
be the support
count of an itemset X in the increment database ∆
+
.
3 THE PROPOSED ALGORITHM
In this section, we develop an efficient algorithm for
updating the association rules when new transactions
are added to the database. The proposed algorithm
uses negative borders [Thomas et al., 1997]. The
intuition behind the concept of negative border is
that, for a given set of large itemsets L, the negative
border NBd(L) contains the closest itemsets that
could be large too.
The list of symbols that used in our algorithm is
shown in Table 1.
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Table 1: Symbols of the proposed algorithm NBP.
Symbol Definition
q Partition size
|p
i
| Cardinality of partition p
i
L
pi
Large itemset of partition p
i
NBd(L
pi
) Negative border itemset of
partition p
i
NBd(L
D
) Negative border itemset of
original database D
NBd(L
D’
) Negative border itemset of
updated database D
’
n Total Number of partitions
3.1 Algorithm Description
The new algorithm can be described in two main
steps.
Preprocessing step
In this step we divide the original transactional
database into number of partitions with size q. For
simplicity we assume q as a multiple of | ∆
+
| (for
generality q can be of any size). Total number of
partitions is assumed to be n. In the preprocessing
step we evaluate for each partition p
i
; i =1, 2... n the
large itemset L
pi
with its corresponding negative
border itemset NBd(L
pi
). Each itemset in L
pi
or
NBd(L
pi
) is stored with its corresponding support
count in the partition p
i
. Also we compute the large
itemset L
D
and negative border itemset NBd(L
D
) for
the whole database D.
The size of large and negative border itemsets for all
partitions may be big enough not to be fitted into the
computer memory due to memory limitations, so we
suggest adding another support threshold ls “local
support threshold” as a fraction of the global support
threshold s which limits the size of negative border
itemsets for all partitions. Itemsets with support
count less than ls×s×|pi| are discarded from the
negative border itemset of the partition p
i.
The large
itemsets for all partitions is kept unchanged as they
contain significant information of most frequent
itemsets.
The Pseudo code of preprocessing step is described
in both Figures 1and 2.
Function preprocessing (D, n,q)
Divide the original database into n partitions, each
partition with size q.
for i = 1 to n do
pi
L = large-itemset for partition p
i
NBd(L
pi
)=Negtiveborder_gen (L
pi
)
L
D
= large-itemset for the whole database
NBd(L
D
) = Negtiveborder_gen (L
D
)
Figure 1: A high-level description of preprocessing step
Function Negtiveborder_gen (L)
Split L into L
1
, L
2
,.., L
r
where r is the size of the
largest itemset in L
For all k=1, 2, ….,r do
Compute C
k+1
using apriori-gen(L
k
)
//Apriori[Agrawal et al., 1994]
L∪NBd(L) = U
i=2,….,r+1
C
k
∪ I
1
, where I
1
is the set
of 1-itemset.
Figure 2: The of Negativeborder_gen function.
Updating Step
In this step we have the incremental database ∆
+
, set
of n partitions with their corresponding large and
negative border itemsets. With the assumption that
partition size q is multiple of the incremental
database size, ∆
+
is added either to the last partition
or to a new partition. The next step is to update the
large itemsets L
pn
and negative border itemsets
NBd(L
pn
) of the partition p
n
using NBP(p
n
, ∆
+
, p
n
)
function. If ∆
+
is added to a new partition evaluate
L
pn
and NBd(L
pn
) using Apriori as a level wise
algorithm (Apriori [Agrawal et al., 1994] generates
only candidate itemsets, we get the negative border
itemsets by applying the function
Negtiveborder_gen(L) to the resulting large itemset
from Apriori algorithm .
After updating the partitions, the next step is to
update L
D
and NBd(L
D
) of the whole database to
obtain the updated large itemset L
D’
and updated
negative border itemset NBd(L
D’
). First we compute
the large itemset L
∆+
and negative border itemset
NBd(L
∆+
) of ∆
+
, simultaneously we count the
support for all itemsets t ∈L
D
∪NBd(L
D
) in ∆
+
. If an
itemset t
∈
L
D
or NBd(L
D
) has minimum support in
D
’
, then t is added to L
D’
otherwise it is added to
NBd(L
D’
). For each itemset x∈ L
∆+
∪ NBd(L
∆+
) , x ∉
L
D
and x∉ NBd(L
D
) add x into NBd(L
D’
).The change
in L
D
could potentially change NBd(L
D
) also.
NEW FAST ALGORITHM FOR INCREMENTAL MINING OF ASSOCIATION RULES
277

Therefore some itemsets may be missed in both L
D’
and NBd(L
D’
). We define two sets Large_to_Large
(set of itemsets that moved from L
D
to L
D’
) and
Negative_to_Large (set of itemsets that moved from
NBd(L
D
) to L
D’
). Join Negative_to_Large with
Large_to_Large to get new set Self_Join_Set, using
the function join (L
k-1
) which join a set of large
itemsets with length (k-1) with itself to get C
k
a set
of candidate itemsets with length k. the join (L
k-1
)
function is described in Figure 3.
function join (L
k-1
)
C
k
= Φ
For each X , Y ⊂ L
k-1
do
if X.item
1
= Y.item
1
,..,X.item
k-2
= Y.item
k-2
,
X.item
k-1
< Y.item
k-1
then
Z = X.item
1
, X.item
2
,.., X.item
k-1,
Y.item
k-1
Insert Z into C
k
//pruning step
For all itemsets c
∈
C
k
do
For all (k-1) subsets s of c do
if (s
∉ L
k-1
) then
delete c from C
k
Return C
k
Figure 3: High Level Description of the join function
For each itemset t ∈ Self_Join_Set, check all
partitions p
i
, i = 1, 2, …, n. If t is found at the large
itemset L
pi
or negative border itemset NBd(L
pi
), then
update the support count of t. If t is not found in
either L
pi
or NBd(L
pi
) then scan partition p
i
to get the
support count of t. Scanning a partition is done once
for all itemsets need to be scanned in this partition.
This means, we only need maximum of one scan for
the whole database (all partitions) at worst case. In
general, the proposed algorithm needs a fraction of a
scan to update the large and negative border itemsets
for the updated database. We use the hash tree
structure (Apriori [Agrawal et al., 1994]) to get the
support count of a set of itemsets within this
partition. If the support count of t ≥ the support
threshold of D
’
, then add t to L
D’
; otherwise add t to
NBd(L
D’
).
The description of the NBP (D, ∆
+
, Partitions)
function is described Figure 4.
Function NBP ( D, ∆
+
, Partitions)
L
D’
= Ф , NBd(L
D’
)= Ф, Large_to_Large = Ф and
Negative_to_Large = Ф // initialization
Compute L
∆+
, NBd(L
∆+
)
If | p
n
| < q then
Add ∆
+
to p
n
and update the partition p
n
else n++, Add ∆
+
to the new partition ,Compute
L
pn
, NBd(L
pn
)
For each itemset x ∈ L
D
if (σ
x
+δ
x
≥ s * (|D| +| ∆
+
|) then
//s :minimum support threshold
add x to both L
D’
and Large_to_Large sets
else add x to NBd(L
D’
)
For each itemset x
∈
NBd(L
D
)
if (σ
x
+δ
x
≥ s * (|D| +| ∆
+
|) then
add x to both L
D’
and Negative_to_Large sets
else add x to NBd(L
D’
)
For each itemset x ∈ L
∆+
∪ NBd(L
∆+
) , x∉ L
D
and
x
∉
NBd(L
D
) do
add x to NBd(L
D’
)
if L
D
≠ L
D’
then
ULNBd(L
D’
,NBd(L
D’
), Large_to_Large,
Negative_to_Large, Partitions)
Figure 4: Negative Border with Partitioning algorithm
using function NBP ( )
The pseudo code of the function ULNBd () is given
in Figure5.
ULNBd (L
D’
,NBd(L
D’
),Large_to_Large,
Negative_to_Large, Partitions)
// generate all possible candidates “Self_Join_Set”
//for the set of large items in the updated database D
’
Self_Join_Set
1
= Ф
// initialize Self_Join_Set of length1 to be empty
For k = 1, 2, ….,ℓ do
//ℓ:size of the largest itemset in Negative_to_Large
LL
k
= set of itemsets with length k from
Large_to_Large
NL
k
= set of itemsets with length k from
Negative_to_Large
Self_Join_Set
k+1
= join(LL
k
∪ NL
k
∪
Self_Join_Set
k
)
For i=1, 2, …, n do // n: number of partitions
p
i
_itemsets= Ф // p
i
_itemsets: set of items to
be scanned within a partition p
i
For each itemset t∈ Self_Join_Set do
σ
t
’
=0 // initialize support count of itemset t
For i=1, 2, …, n do
// search all partitions for the support count of
all elements found in Self_Join_Set
if t ∈ L
pi
then
σ
t
’
= σ
t
’
+ support count of t in L
pi
else if t ∈ NBd(L
pi
) then
σ
t
’
= σ
t
’
+ support count of t in NBd(L
pi
)
else add t to p
i
_itemsets
For i=1, 2, …, n do
if p
i
_itemsets ≠ Ф then
Scan p
i
to get support count of each itemset
x ∈ p
i
_itemsets
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//scanning using hash tree structure // (Apriori [Agrawal et al.,
1994])
For each itemset t
∈ Self_Join_Set do
//Update support count of t after scanning all
//partitions
if σ
t
’
≥ minsup*(|D| +| ∆
+
|) then
add t to L
D’
else add t to NBd(L
D’
)
Figure 5: Update Large and Negative Border of D
’
using
ULNBd () function
The number of scans over the whole database
needed for NBP algorithm is varying from 0 to 1.
The zero scan is obtained when the information
needed after adding the increment database is found
in either the global summary of the whole database
or the local summary in each partition. The one scan
is occurred at the worst case when the algorithm
needs to scan all partitions (whole database) to get
the count of some itemsets. In general, the algorithm
needs a fraction of a scan to reach the final results
4 PERFORMANCE ANALYSIS
In this section, the proposed algorithm is tested
using several test data to show its efficiency in
handling the problem of incremental mining of
association rules.
4.1 Generation of synthetic data
In this experiment, we used synthetic data as the
input database to the algorithms. The data are
generated using the same technique as introduced in
[Agrawal et al., 1994], modified in [Park et al.,
1997] and used in many algorithms like [Thomas et
al., 1997] and [Cheung et al., 1996]. Table 2 gives a
list of the parameters used in the data generation
method.
Table 2: Parameters for data generation
|| D
Number of transactions in original
database
||
'
D
Number of transactions in the
updated database
||
+
∆
Number of added transactions
|T| Mean size of transactions
| I | Mean size of potentially large
itemsets
| £ | Number of potentially large itemsets
N
Number of items
We use the notation Tx.Iy.Di+d , and modified from
the one used in [Agrawal et al., 1994] , to denote an
experiment using databases with the following sizes
|D| = i thousands, ∆
+
=k thousands, |T|= x, and |I|=y .
In the Experiments we set N=1000 and |£|=2000.The
increment database is generated as follow: we
generate 100 thousand transactions, of which (100-
d) thousands is used for the initial computation and d
thousands is used as the increment, where d is the
fractional size (in percentage) of the increment.
4.2 Experimental Results
In each experiment, we run the proposed algorithm
NBP on the previous test data. We compare the
execution time of the incremental algorithm NBP
with respect to running Apriori on the whole data
set. The proposed algorithm is tested using the
settings T10.I4.D100+d. The support threshold is
varying between 0.5% and 3.0%. For simplicity we
assumed that the partition size q is a multiple of the
size of the increment database | ∆
+
| .We run the
algorithm for q = 1, 2, 5, 10 multiples of | ∆
+
| and d
= 1% as a fraction from the whole database size.
Figure 6 shows the speed up of the incremental
algorithm over Apriori with support threshold is
varying between 0.5% and 3.0%. It can be shown
that when applying the NBP algorithm on the test
data it achieves an average speed up ranging from 6
to 67 in comparison with Apriori
algorithm.
0
10
20
30
40
50
60
70
80
3 2 .5 2 1.5 1 0 .75 0 .5
Support Threshold (%)
1 ∆+
2 ∆+
5 ∆+
10 ∆+
Figure 6: Performance Ratio of NBP at ∆
+
= 1%
Figures 7 and 8, show the experimental results when
applying the new algorithm NBP on the same test
data but with d is 2% and 5% respectively. The
support threshold is varying between 0.5%and 3.0%
in both experiments. It can be concluded from
Figure 7 that the proposed algorithm has an average
speed up ranging from 4 to 37 in comparison with
Apriori algorithm. From Figure 8 the NBP algorithm
achieves an average speed up ranging from 2 to 14.
NEW FAST ALGORITHM FOR INCREMENTAL MINING OF ASSOCIATION RULES
279

0
10
20
30
40
50
3 2.5 2 1.5 1 0.75 0.5
Support Threshold(%)
Speed Up
1 ∆+
2 ∆+
5 ∆+
10 ∆+
Figure 7: Performance Ratio of NBP at ∆
+
=
2%
0
2
4
6
8
10
12
14
16
18
3 2.5 2 1.5 1 0.75 0.5
Support Threshold (%)
Speed Up
1 ∆+
2 ∆+
5 ∆+
10 ∆+
Figure 8: Performance Ratio of NBP at ∆
+
= 5%
From Figures 6, 7 and 8, it is noticed that the
proposed algorithm shows better performance for
high support than low support. At high support
thresholds, the possibility to get new large itemsets
from the original negative border is low so the
searching time within the partitions’ large itemsets
and negative border itemsets is small. At low
support thresholds, there is a high probability of
getting more new large itemsets immigrating from
the set of negative border to the set of large itemsets.
This increases the possibility to scan most partitions
causing the increase of execution time. Also, the
speed up of the proposed algorithm is higher for
smaller increment sizes since the new algorithm
needs to process less data. It can be shown that the
NBP algorithm achieves better performance when
the partition size is five times of the increment
database ∆
+
and the size of increment database is 1%
of the whole database.
4.3 Comparisons with FUP
FUP may require O (k) scans over the whole
database where k is the size of maximal large
itemsets, while the new NBP algorithm needs a
fraction of a scan to update the results. In this
experiment, we run the proposed algorithm NBP on
the previous test data. We compare the execution
time of the incremental algorithm NBP with respect
to running FUP on the same data set. For support
threshold varying between 1.0% and 3.0%, and | ∆
+
|
= 1 % Figure 9 shows that the proposed NBP
algorithm has an average speed up ranging from 6 to
67 while FUP algorithm achieves a speed up from 2
to 7 against Apriori algorithm.
0
10
20
30
40
50
60
70
3 2.5 2 1.5 1
Support Threshold (%)
Speed Up
NBP
FUP
Figure 9: Speed up of NBP against FUP
4.4 Comparisons with ULI
It is costly to run ULI at high support thresholds
where the number of large itemsets is less and at low
support threshold the probability of the negative
border expanding is higher so ULI may have to scan
the whole database. We run the proposed algorithm
NBP on the previous test data and compare the
execution time of the incremental algorithm NBP
with respect to running ULI on the same data set.It is
concluded from Figure 10 that for support threshold
varying between 0.5%and 3.0%, and | ∆
+
| = 1 % The
NBP algorithm has an average speed up ranging
from 6 to 67 while ULI algorithm achieves a speed
up from 5 to 20 against Apriori algorithm.
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0
10
20
30
40
50
60
70
3
2.5
2
1
.
5
1
0
.7
5
0.5
Support Threshold (%)
Speed Up
NBP
ULI
Figure 10: Speed up of NBP against ULI
5 CONCLUSIONS
In this paper a new algorithm NBP: Negative
Border with Partitioning is presented for
incremental mining of association rules. The
proposed algorithm is based on partitioning the
database, keeping a summary for each partition.
Another global summary including the large and
negative border itemsets is also created for the
whole database. When adding a new set of
transactions to the database, the NBP applies a ULI-
like algorithm that uses these summaries instead of
scanning the whole database, thus reducing the
number of database scans to less than one scan.
From algorithm discussion and experimental results,
the following points can be concluded:
1. The new algorithm NBP, can efficiently
handle the problem of incremental mining
of association rules. NBP shows better
performance than the algorithms of FUP
and ULI.
2. The number of scans over the whole
database needed for NBP algorithm is
varying from 0 to 1.
3. NBP achieves high speed up from 6 to 67
for support threshold varying from 0.5 to
3.0 against the Apriori algorithm.
REFERENCES
Agrawal, R. ,Imielinski, T. and Swami, A., 1993. Mining
Association Rules between Sets of Items in Large
Databases. Proc. ACM SIGMOD. Int Conf, 1993.
Agrawal, R. and Srikant, R..Fast Algorithms for Mining
Association Rules .Proc.(VLDB).Int Conf, 1994.
Cheung, D.W. Lee, S.D. and Kao, B. A General
Incremental Technique for Maintaining Discovered
Association Rules. Proc. Database systems for
Advanced Applications, Int Conf, 1998.
Park, J.S. Chen, M.S. and Yu, P.S.. Using a Hash Based
Method with Transaction Trimming for Mining
Association Rules. IEEE Trans on Knowledge and
Data Engineering, 1997.
Agrawal, C.C. and Yu, P.S. Mining Large Itemsets for
Association Rules, Bulletin of the IEEE Computer
Society Technical Committee on Data Engineering
1998.
Sarasere, A. Omiecinsky, E. and Navathe, S. An Efficient
Algorithm for Mining Association Rules in Large
Databases. Very Large Databases (VLDB). Int Conf.
1995.
Hidber,C.Online Association Rule Mining.Proc.ACM
SIGMOD Int Conf. Management of Data, 1998.
Han, J. ,Pei, J. and Yin, Y. Mining frequent patterns
without candidate generation. Proc. ACM SIGMOD.
Int Conf. on management of Data,2000.
Woon , Ng, Y. W. and Das, A. , Fast Online Association
Rule Mining , IEEE transactions on Knowledge and
Data Engineering ,2002.
Sarda, N.L. and Srinivas, N. V.An Adaptive Algorithm
for Incremental Mining of Association Rules. Proc
.Database and Experts systems. Int Conf , 1998.
Thomas, S., Bodagala, S. Alsabti, K. and Ranka, S.. An
Efficient Algorithm for the Incremental Updation of
Association Rules in Large Databases. Proc.
Knowledge Discovery and Data Mining (KDD 97). Int
conf, 1997.
Aggarwal, C.C., Sun, Z. and Yu, P.S., Fast Algorithms for
Online Generation of Profile Association Rules, IEEE
transactions on knowledge and Data Engineering,
September 2002.
Cheung, D.W. Han, J. Ng, V.T. and Wong, C.Y.
Maintenance of Discovered Association Rules in
Large Databases: An Incremental Updating
Technique. Proc. Data Engineering. Int Conf, 1996.
Aggarwal, C. and Yu, P. A new Approach for Online
Generation of Association Rules, IEEE transactions
on Knowledge and Data Engineering, 2001
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