Mining frequent itemsets (mfi) over

International Journal of Data Mining & Knowledge Management Process (IJDKP) Vol.4, No.4, July 2014
DOI : 10.5121/ijdkp.2014.4402 17
MINING FREQUENT ITEMSETS (MFI) OVER
DATA STREAMS : VARIABLE WINDOW SIZE
(VWS) BY CONTEXT VARIATION ANALYSIS
(CVA) OF THE STREAMING TRANSACTIONS
V.Sidda Reddy1
, T.V.Rao2
and A.Govardhan3
1
Department of Computer and Engineering,
Sagar Institute of Technology, Chevella, Hyderabad, T.S, India
2
Departments of Computer and Engineering,
PVP Siddhartha Institute of Technology, Vijayawada, A.P, India
3
School of Information Technology,
Jawaharlal Nehru Technological University, Hyderabad, T.S, India
ABSTRACT
The challenges with respect to mining frequent items over data streaming engaging variable window size
and low memory space are addressed in this research paper. To check the varying point of context change
in streaming transaction we have developed a window structure which will be in two levels and supports in
fixing the window size instantly and controls the heterogeneities and assures homogeneities among
transactions added to the window. To minimize the memory utilization, computational cost and improve the
process scalability, this design will allow fixing the coverage or support at window level. Here in this
document, an incremental mining of frequent item-sets from the window and a context variation analysis
approach are being introduced. The complete technology that we are presenting in this document is named
as Mining Frequent Item-sets using Variable Window Size fixed by Context Variation Analysis (MFI-VWS-
CVA). There are clear boundaries among frequent and infrequent item-sets in specific item-sets. In this
design we have used window size change to represent the conceptual drift in an information stream. As it
were, whenever there is a problem in setting window size effectively the item-set will be infrequent. The
experiments that we have executed and documented proved that the algorithm that we have designed is
much efficient than that of existing.
KEYWORDS
Data Mining, Data Streams, Frequent Itemset, Frequent Itemset Mining, Data Stream Mining, Variable
Window, Sliding Window
1. INTRODUCTION
Association rule is an important and well researched method for finding frequent itemsets
(patterns) among set of objects in large database [1]. Frequent itemsets indicates the closeness
among the items that are available in datasets. There are very good range of applications that
includes creation of association rules for market-basket analysis, in text mining grading and
clustering of documents, text, and pages, web mining, that allows users to disclose hidden
patterns and relationships in huge datasets. The time taken to produce the data is outstripping the
speed of its mining in the present upcoming applications where the information is in the form of
an enormous and continuous stream [2]. To traditional static databases this is in quiet opposite, so
data stream mining is considerably different from traditional data mining with respect good
number of aspects. Primarily, the amount of data embedded in its lifetime in a data stream could

18
be overwhelmingly high [3]. Along with the above it is required to create spontaneous responses
by maintaining response time to queries on such information streams because of rigid pitfalls of
resource [4]. The data stream mining is the area where very high level of research is taking place
because of the above mentioned reasons and contemporary research area is the challenge of
getting timely and appropriate association rules. Migrating from conventional data mining
methods to the emerging high efficient methods those will accommodate to function on an open-
ended, high speed stream of data [5]. The challenges that are inevitable to all mining technologies
because of the unique and inherent qualities of a data stream are as follows [3]. Primarily the
conventional technology is not applicable as it is required to create model in this method database
need to be scanned multiple number of times which is not possible because of the continuous
quality of the stream data. The high priority was given to the scalability of the frequent itemsets
mining in approaches like association rules, classification and clustering. This requires high level
of data transformation from the representation to other as the algorithm is designed in such a way,
this in turn will use resources extensively resulting in high CPU overhead. Our proposal in this
paper is a model known as Mining Frequent itemsets using Variable Window Size fixed by
Context Variation Analysis (MFI-VWS-CVA). This model is the resource effective and
measurable, as it functions with limited memory requirements and limited computational
expenses. It portrays the trade-offs between computation, data representation, I/O and heuristics.
Context variation analysis based dynamic window based transaction storage is being used in the
proposed algorithm and also allows TIFIM [15] to regular itemsets from the concluded window.
2. RELATED WORK
CPS-tree a prefix-tree structure was proposed by Syed Khairuzzaman Tanbeer [6]. Dynamic tree
restructuring technique was used in the CPS tree in order to manage the stream data. The basic
pitfall of this model is, it reconstructs the tree for every new arrival of the item. This used to result
in high memory usage and a time consuming process. Weighted Sliding Window (WSW)
algorithm was initiated by Pauray S.M. Tsai [7]. In this method weight of each transaction in each
window will be calculated by the algorithm proposed. Here also same memory space and time are
the major concerns; this method failed using these two economically. An apriori algorithm is
being for candidate generation. Hue-Fu Li [8] introduced an effective bit-sequence dependent
algorithm named as MFI-TransSW (Mining Frequent Item sets with in a Transaction Sensitive
Sliding window). There as three phases in MFI algorithm. As there is any increase in the window
size, there will be a subsequent increase in the memory usage of MFI-TransSW. Similarly
whenever there is an increase in window size, the time consumption in phase 1 and phase 2 of
MFI-TransSW to process will also increase. Yo unghee Kim [9, 16] initiated an effective
algorithm with normalized weight over data stream called WSFI mine (Weighted Support
Frequent Item sets mining). From the database in one scan this WSFI-mine algorithm can mine
all frequent item sets. HUPMS (High Utility Pattern Mining in Stream data) was recommended
by Chowdhury Farhan Ahmed [10]. This is a different algorithm for sliding window based high
utility pattern mining over data stream. For interactive mining only this algorithm is suitable. In
the paper that was presented by Jing Guo [11], they have discussed about how to mine regular
patterns across multiple data streams. Here for analysis they have considered real time news paper
data. In multiple streams it is vital to identify collaborative frequent patterns and comparative
frequent patterns. Prevention of misuse of sensitive data in a stream was addressed by Anushree
Gowtham Ringe [12] in their work. They initiate a new technique for guarding the privacy of data
stream. Fan Guidan [13] proposed a model which is conceptually similar to our model. Matrix in
sliding window over data streams plays major role in this model. In order to store, this algorithms
uses two 0-1 matrices and 2-itemsets, further applies relative operation of the two matrices to
extract frequent itemsets.

19
3. MINING FREQUENT ITEMSETS OVER DATA STREAMS WITH CONTEXT
AWARE VARIABLE SIZE WINDOWS
If streaming data is input to mining strategies such as frequent itemsets mining, the traditional
approaches are not suitable, since those are mainly works by the multiple passes through entire
dataset. Henceforth the mining strategies opted for streaming data considers the tuples of the
streaming transactions as windows and these windows are used as input to the mining algorithms.
The significant issue here in this model is fixing the window size. In the case of data streams with
transitional and temporal state transactions, the transitional and temporal state identifications can
be used to fix the window size. In the other cases that are not having any transitional and temporal
state identities for streaming transactions, fixing window size is a big constraint to achieve quality
factors such as results accuracy, process scalability. In this regard here we propose a novel
context variation based dynamic window size fixing approach to mine frequent itemsets over data
streams. The proposed frequent itemsets mining strategy is centric to following qualities targeted.
• The window size should be optimal and dynamic.
• The window size should fix dynamically between minimal and maximal size given as
thresholds.
• The size of the window should be within the range of minimal and maximal size and
should fix based on the context variation observed in input transaction from the data
stream.
In regard to implementing the proposed model, the only significant constraint related to the
streaming data is that the context change of the transactions should be in an order.
The minimal memory utilization and less computational cost are two main quality metrics
expected from this proposal. The exploration of the proposed window fixing strategy is follows:
Let ds be the DataStream, and stream transactions as horizontal partitions of the transactions, let
each partition having one transaction. Let n be the total count of the attributes used to form the
transactions by ds . Let seta be the attributes set that contains attributes
1 2 1{ , ,....... , ,...... }i i na a a a a+ , which are used to form the transactions. Let
1 2 3 1 ( 1){ , , ...., , ,.... , ,......}i i i m i mt t t t t t t+ + + + be the transactions streaming in the same sequence. Let
minws be the minimum window size and maxws be the maximal window size. Let tranw be the
transaction window and ccaw be the context change analysis window. Let ( )ccas w be the size of
ccaw . The initial values to min max,ws ws and ( )ccas w will be set during the pre-processing step.
The transactions of count minws from the given data stream ds will be moved initially to tranw ,
then following transactions of count ( )ccas w will be moved to ccaw . Then context variation
analysis (CVA) process will be initialized. The exploration of the CVA process is follows:
The attributes involved to generate the transactions moved into tranw will be collected as ( )tranal w
, and attributes involved to form the transactions found in ccaw will also be collected as ( )ccaal w .
Then the similarity score of these two attribute lists ( ), ( )tran ccaal w al w will be found as follows
(Eq1), which is derived from jaccard similarity measuring approach.
( )
( ) ( )
( ) ( )trans cca
tran cca
w w
trans cca
al w al w
ss
al w al w
↔ =
I
U
… (Eq1)
If similarity score ( )tran ccaw wss ↔ is greater than the given similarity score threshold ssτ then the
transactions of ccaw will be moved to tranw (see Eq2).
tran tran ccaw w w= U … (Eq2)

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If size of the tranw is greater than or equals to maxws then the tranw will be finalized and initiates
process of mining frequent itemsets from the transactions of tranw , else the further streaming
transactions of size ( )ccas w will moved to ccaw and continues CVA process.
Once the tranw is finalized and mining of frequent itemsets is initiated, then tranw and ccaw will be
cleared and continues the process explored to prepare the window tranw will be continued for
further transactions streaming from data stream ds .
The above said process continues till transactions found from data stream ds . The mining
frequent itemsets from the finalized window will be done by using TIFIM [15], which is a tree
based incremental frequent itemsets mining approach that we devised in our earlier research paper
(see sec 3.3).
3.1 Algorithmic exploration of the Fixing Variable Window Size by Context
Variation Analysis
Inputs:
• Data stream ds
• Minimal transaction window size minws
• Maximal transaction window size maxws
• Similarity score threshold ssτ
• Size of the context change analysis window ( )ccas w
1. Begin
2. For each transaction { }t t ds∀ ∈ Begin
3. If min(| | )tranw ws< tranw t←
4. Else Begin
5. ccaw t←
6. If (| | ( ))cca ccaw s w≥
7. ( , )tran ccass CVA w w←
8. if( )ss ssτ≥ Begin
9. ( )tran tran ccaw w w← U
10. If max(| | )tranw ws≥ Begin
11. Finalize window tranw
12. Initiate ( )tranTIFIM w
13. set tranw φ← // empty tranw
14. set ccaw φ← //empty ccaw
15. End of 10
16. End of 8
17. Else Begin
18. Finalize window tranw
19. Initiate ( )tranTIFIM w
20. set tranw φ← // empty tranw
21. set tran ccaw w← //move transactions of window ccaw to new window tranw

21
22. set ccaw φ← //empty ccaw
23. End of 17
24. End of 4
25. End of 2
26. End of 1
3.2 Algorithmic exploration of the Context Variation Analysis
1. ( , )tran ccaCVA w w Begin
2. Set tranfs φ← // initiate field set tranfs of transaction window tranw empty
3. Foreach transaction { }trant t w∀ ∈ Begin
4. tran tranfs fs t← U
5. End of 3
6. Set ccafs φ← // initiate field set ccafs of transaction window ccaw empty
7. Foreach transaction { }ccat t w∀ ∈ Begin
8. cca ccafs fs t← U
9. End of 7
10. tran cca
tran cca
fs fs
ss
fs fs
=
I
U
//measuring similarity score of tranw and ccaw
11. Return ss
12. End of 1
3.3 Tree (Bush) Based Incremental Frequent Itemsets Mining (TIFIM)
3.3.1 Finding Frequent Itemsets
The primary representation of the transactions of data stream ds is as described above. An
asynchronous parallel process runs to find frequent itemsets in incremental manner.
A bush represents itemsets with two attribute pair such that these attributes belongs to tranfs and
transactions contain that pair. The coverage to measure the frequency of the itemsets can be
considered and set in the context of window tranw size. The coverage of two attribute itemsets can
be the count of number of Childs in a bush represented by each pair of attributes.
An asynchronous parallel process called frequent itemsets finder (FIF) performs as follow:
Initially picks the bushes with coverage more than given coverage thresholdcov .
Prepare new bushes from each two bushes by union the roots and intersects the Childs, and
retains it if new bush coverage is greater or equal to cov else discards.
This continues until no new bush formed.
3.3.2 The pruning process
A bush ib said to be sub-bush to bush jb if i jb br r⊆ and ( ) ( )cov covi jb b≤ . Since sub-bush ib
represented by jb , then bush ib can be pruned from the bush-set B .
3.4 Find frequent items
At an event of time, frequent itemsets can be found as follows
The roots of the bushes with coverage more than given cov can be claimed as frequent itemsets.
A bush ‘ ib ’ coverage can be find as follows

22
If a bush jb found to be such that i jb b⊆ and coverage value of jb is higher than any other bush
kb such that i kb b⊆ , then the coverage of ib said to be ( ) ( )cov covj ib b+ .
3.4.1 An algorithmic representation of the caching processes
Input: At an event of time a window iw with transaction it received
For each transaction it :
Let set of attributes
1 2 3
1 2 3
1 2 3
{( , , ,......... )
( , , ,......... )
( , , ,......... ) }
i
i i
i set
a a a a
a a a a t
a a a a A
∀
∈ ∧
⊆
For each pair of attributes{( , ) ( , ) }m n m n ia a a a t∀ ∈ , if found a bush { ( , ) }i m nb a a as root∃ then
add transaction it as node to bush ib , else prepare a bush such that
{ ( , ) t }i m n ib a a as roo t as node∃ ∧
3.4.2 An algorithmic approach of FIF
The bush set B prepared by caching process is said to be input to FIF
For each bush { }i ib b B∀ ∈ perform the following:
For each bush ( : 1,2,3....... ) )i c i cb c n b B+ +∃ = ∧ ∈
Forms a bush ( ) ( ){ }i i c i i cb b B+ +∃ ∉U U by Union the roots of the ‘ ib ’and ‘ i cb+ ’ ( ( ) ( )i i cb br r +
U ) and
intersects nodes of ib and i cb+ ( ( ) ( )i i cb bts ts +
I ).
4. EMPIRICAL ANALYSIS OF THE FIXING VARIABLE WINDOW SIZE BY
CONTEXT VARIATION ANALYSIS
4.1 Dataset characteristics
Multiple sets of data streamed to perform the experiments, and the characteristics of these
streaming data are as follows:
• To achieve the sparseness in streaming transactions, the range of fields considered as
75,100, 125 and 150, the max transaction length set in the range of 12 to 18, the min
transaction range set to 5 and the total number of transactions has taken in the range of
1000 to 10000.
• To achieve the denseness in streaming transactions, the range of fields considered as 20,
30, 40 and 50, the max transaction length set in the range of 10 to 15, the min transaction
range set to 5 and the total number of transactions has taken in the range of 1000 to
10000.
4.2 Experimental results
We compare our algorithm with frequent itemsets mining model for data streams devised in [13],
which is a matrix based frequent itemsets mining (MFIM) algorithm for data streams. The
implementation of our MFI-VWS-CVA and model MFIM done by using java 7 and set of flat
files as streaming data sources. The streaming environment is emulated using java RMI and
parallel process involved in proposed MFI-VWS-CVA is achieved by using java multi threading
concept. The three parameters of each synthetic dataset are the total number of transactions, the
average length, and divergence count of items, respectively. Each transaction of a dataset is
scanned only once in our experiments to simulate the environment of data streams. In regard to

23
measure the computational cost and scalability, the algorithms run under divergent coverage
values in the range of 10% to 90%.
Figure 1: NFI-VWS-CVA advantage over MFIM in Memory usage.
Figure 2: MFI-VWS-CVA advantage over MFIM in terms of execution time.
Figure 1 and 2 shows the comparison of the Memory usage, execution time under divergent
coverage values range given from 10% to 40% respectively. The Figure 3 explores the scalability
of MFI-VWS-CVA over MFIM under divergent streaming data sizes respectively, In Figure 1
and 2, the horizontal axis is the coverage given and the vertical axis is the memory in unit of
mega bytes and time in unit of seconds respectively. In Figure 3, the horizontal axis is the

24
streaming data size given in unit of transactions and the vertical axis is the execution time in unit
of seconds and percentage of elapsed time in unit of seconds respectively. As the coverage value
decreases the average increment in memory usage for matrix based FIM and MFI-VWS-CVA
are 2.29 and 0.7 respectively (see Figure 1) and average execution time increment for matrix
based FIM and MFI-VWS-CVA are 83.2 and 27.9 respectively (see Figure 2). The results
obtained here clearly indicating that the performance of MFI-VWS-CVA is miles ahead than the
matrix based FIM. The performance of MFI-VWS-CVA is scalable as matrix based FIM is taking
average of 14.16% elapsed time under uniform increment of streaming data size with 1500
transactions.
Figure 3: MFI-VWS-CVA advantage over MFIM about Scalability under divergent streaming
data size.
5. CONCLUSION
We explored a novel approach for mining the frequent itemsets from a data stream. We have
implemented an efficient tree based incremental frequent itemsets mining model [15] in our
earlier research paper, further here we developed an approach for mining frequent itemsets using
variable window size by context variation analysis (MFI-VWS-CVA) over data streams. Due to
the factor of fixing window size dynamically by concept variation analysis, the said model is
identified as optimal and scalable. A parallel process that determines frequent itemsets from the
concept of cached bush structures, which is our earlier proposal [15], performs frequent itemsets
mining over data streams. We extended this incremental frequent itemset mining algorithm by
introducing windowing the streaming transaction with variable window size technique in regard
to achieve efficient memory usage and execution time. The experiment results confirm that the
MFI-VWS-CVA is scalable under divergent streaming data size and coverage values. In future
this model can be extended to perform utility based frequent itemset mining over data streams.

25
ACKNOWLEDGEMENT
The authors would like to thank the anonymous reviewers for their valuable comments.
We also thank the authors of all references for helping us setup the paper.
REFERENCES
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[2] Moses Charikar, Kevin Chen and Martin Farach-Colton, “Finding frequent items in data streams”,
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[3] Mohamed Medhat Gaber, Arkady Zaslavsky and Shonali Krishnaswamy, “Mining data streams: a
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[13] Fan Guidan and Yin Shaohong, "A Frequent Itemsets Mining Algorithm Based on Matrix in Sliding
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[16] www.borgelt.net/slides/fpm.pdf.

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