SURVEY ON FREQUENT PATTERN MINING

IJESM Volume 2, Issue 3 ISSN: 2320-0294
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International Journal of Engineering, Science and Mathematics
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SURVEY ON FREQUENT PATTERN MINING
Keshav Lodhi
Abstract
In this paper we present the various elementary traversal approaches for mining frequent pattern
to find out association rules. We start with a formal definition of association rule and its basic
algorithm. We then discuss the association rule mining algorithms from several perspectives
such as breadth first approach, depth first approach and Hybrid approach. Frequent pattern
mining has been focused themes in data mining re-search for over a decade. Abundant literature
has been dedicated to this research and tremendous progress has been made, ranging from
efficient and scalable algorithms for frequent itemset mining in transaction databases to
numerous research frontiers, such as sequential pattern mining, structured pattern mining,
correlation mining , associative classiﬁcation, and frequent pattern-based clustering .
Keyword- association rules,frequent pattern mining,breadth first,defth first,hybrid approach.

S.A.T.I. (Vidisha)

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1. Introduction-
Frequent itemsets play an essential role in many data mining tasks that try to find interesting
patterns from databases, such as association rules, correlations, sequences, episodes, classifiers,
clusters and many more of which the mining of association rules is one of the most popular
problems. The original motivation for searching association rules came from the need to analyze
so called supermarket transaction data, that is, to examine customer behavior in terms of the
purchased products. Association rules describe how often items are purchased together.in fig.1
we capture the market-basket scene.
Fig.1
For example, an association rule“beer chips (80%)” states that four out of five customers
that bought beer also bought chips. Such rules can be useful for decisions concerning product
pricing, promotions, store layout and many others. Since their introduction in 1993 by Argawal ,
the frequent itemset and association rule mining problems have received a great deal of attention.
Within the past decade, hundreds of research papers have been published presenting new
algorithms or improvements on existing algorithms to solve these mining problems more
efficiently.
Association rule mining is as important research subject put forward by Agrawal in reference
[1]. Association rule mining techniques can be used to discover unknown or hidden correlation
items found in the database of transactions. The pattern of mining association rule could be
decomposed into two sub problems. First, mining of frequent itemsets/patterns and generating
association rule from frequent patterns is next . Finding frequent patterns becomes the main work
of mining association rules [2]. In this chapter, we explain the basic frequent itemset and
association rule mining problems. We describe the main techniques used to solve these problems

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and give a comprehensive survey of the most influential algorithms that were proposed during
the last decade.
2. Problem Disccription- Following the original definition by Agrawal et al. the problem of
association rule mining is defined as: Let be a set of binary attributes called items. Let be a set of
transactions called the database. Each transaction in has a unique transaction ID and contains a
subset of the items in. A rule is defined as an implication of the form where the sets of items (for
short itemsets) and are called antecedent (left-hand-side or LHS) and consequent (right-hand-
side or RHS) of the rule respectively.
For example-The rule found in the sales data of a supermarket would indicate that if a customer
buys onions and potatoes together, he or she is likely to also buy hamburger meat. Such
information can be used as the basis for decisions about marketing activities such as,
promotional pricing or product placements. In addition to the above example from market basket
analysis association rules are employed today in many application areas including Web usage
mining, intrusion detection, Continuous production and bioinformatics. As opposed to sequence
mining, association rule learning typically does not consider the order of items either within a
transaction or across transactions.Means there is no restriction on data set.In one transaction
there can be only two or three
Items and in another one can have any number items.
Transaction
Id
MILK Bread Butter Beer
1 1 1 0 0
2 0 0 1 0
3 0 0 0 1
4 1 1 1 0
5 0 1 0 0
Table 1
To illustrate the concepts, we use a small example from the supermarket domain. The set of
items is and a small database containing the items (1 codes presence and 0 absence of an item in
a transaction) is shown in the table to the right. An example rule for the supermarket could be
meaning that if butter and bread are bought, customers also buy milk.

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Note: this example is extremely small. In practical applications, a rule needs a support of several
hundred transactions before it can be considered statistically significant, and datasets often
contain thousands or millions of transactions. To select interesting rules from the set of all
possible rules, constraints on various measures of significance and interest can be used. The best-
known constraints are minimum thresholds on support and confidence.
 The support of an itemset is defined as the proportion of transactions in the data set which
contain the itemset. In the example database, the itemset has a support of since it occurs in 20%
of all transactions (1 out of 5 transactions).
 The confidence of a rule is defined. For example, the rule has a confidence of in the database,
which means that for 50% of the transactions containing milk and bread the rule is correct (50%
of the times a customer buys milk and bread, butter is bought as well). Be careful when reading
the expression: here supp(X∪Y) means "support for occurrences of transactions where X and Y
both appear", not "support for occurrences of transactions where either X or Y appears", the
latter interpretation arising because set union is equivalent to logical disjunction. The argument
of is a set of preconditions, and thus becomes more restrictive as it grows (instead of more
inclusive).
 Confidence can be interpreted as an estimate of the probability, the probability of finding the
RHS of the rule in transactions under the condition that these transactions also contain the LHS.
 The lift of a rule is defined as or the ratio of the observed support to that expected if X and Y
were independent. The rule has a lift of .
The conviction of a rule is defined as . The rule has a conviction of, and can be interpreted as the
ratio of the expected frequency that X occurs without Y (that is to say, the frequency that the rule
makes an incorrect prediction) if X and Y were independent divided by the observed frequency
of incorrect predictions. In this example, the conviction value of 1.2 shows that the rule would be
incorrect 20% more often (1.2 times as often) if the association between X and Y was purely
random chance.
2. Scope for scalability in mining frequent itemset-
There are three main areas which can be focused upon to find the association rules efficiently.
By efficient we mean to reduce time complexity, incur less I/O overhead as well as to efficiently
use the storage space. Due to large amount of data available in data warehouses, we should be
able to mine data that is scalable i.e. that can grow in size.

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As mentioned above, finding frequent itemset is a time consuming process. So the first area of
focus should be fast generation and pruning of candidate itemset. Thus by speeding up this step
we will enhance the generation of frequent itemset. There are various approaches which have
been followed such as depth first search, breadth first search, hybrid, partitioning the database as
well as sampling. A large number of increasingly efficient algorithms to mine frequent itemset
have been developed over the years [7].
Another area of focus is the data structure which has been used for storing the intermediate
candidate itemset in the first step. It should be such that the data which is stored there can be
retrieved fast. Several data structures have been used for mining frequent itemset. They can be
divided into two main categories as array-based and tree-based. In array-based representation,
transactions are stored as arrays of items in the memory. For example, H-Mine uses an array
structure called Hstruct [4]. In tree-based representation, variants of prefix trees are used. A
prefix tree can be used to organize the transactions by grouping and storing transaction data in
memory. In [6], transactions are first grouped using a compressed prefix tree and mapped to an
array-based data structure, which is then used for the mining process.
The third issue on which the research is going on is parallel mining. Parallelism can be
implemented at various stages. However synchronization can be problem while applying
parallelism. But as finding frequent itemset is most expensive, since the number of itemset grows
exponentially with the number of items, time complexity can be greatly reduced if parallelism is
applied while finding frequent itemset. In this paper we mainly concentrate on the first issue i.e.
quickly finding frequent itemset.
In this paper we elaborate on the various traversal approaches which can be used for finding the
candidate itemset. However, for mining the frequent itemset efficiently, we have to use a
combination of effective traversal scheme, an effective but simple data structure as well as
concepts of parallel mining.
3. Commonly used association rule mining algorithms
3.1Breadth First Approach
In Breadth First or bottom-up approach, the computation starts from frequent 1-itemsets (the
minimum length frequent itemset) and continues until all maximal (length) frequent itemset are
found. Because of its way of working, it is also known as hierarchical algorithm. During the
execution, every frequent itemset is explicitly considered. Such algorithms perform well when all

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maximal frequent itemset are short. However, performance drastically decreases when some of
the maximal frequent itemset are relatively long. The classical Apriori algorithm proposed by
Agrawal et al in 1993[8], its enhancement AprioriTid algorithm [9] are all examples of breadth
first approach. Apart from this there are also hash based techniques such as DHP
algorithm(Direct hashing and pruning) proposed by Park et al in 1995[10] and Tree projection
algorithm[11].The partition algorithm[12] and DIC(Dynamic Itemset counting)[13] are also
categorized as breadth first algorithms. The Apriori and AprioriTid algorithms generate the
candidate itemset to be counted in a pass by using only the itemset found large in the previous
pass {without considering the transactions in the database.} The basic concept behind this is that
any subset of a large itemset must be large. The Apriori [9] algorithm has the additional property
that the database is not used at all for counting the support of candidate itemset after the first
pass. Rather, an encoding of the candidate itemset used in the previous pass is employed for this
purpose. AprioriTid has the enhanced feature that it replaces a pass over the original dataset by a
pass over the candidate set. Another algorithm DHP [10] is a hash based algorithm and is
especially effective for generating candidate 2-itemsets, where the number of candidate 2-
itemsets in terms of magnitude is smaller than the previous algorithms, thus resolving the
performance bottleneck. The DHP algorithm (Park et al, 1995) tries to reduce the number of
candidates by collecting approximate counts in the previous level. Like Apriori it requires as
many database passes as the longest itemset. It also trims the transaction database at a much
earlier stage of the iteration, thereby reducing the computational cost for later stages
significantly. The Tree projection algorithm[11] proposed by Agrawal et al in 2001 represents
frequent patterns as nodes of a lexicographic tree and uses the hierarchical structure of the
lexicographic tree to successively project transactions and uses matrix counting on the reduced
set of transactions for finding frequent patterns. The TreeProjection algorithm outperforms the
Apriori method by more than an order of magnitude. At very low levels of support, the Apriori
algorithm runs out of memory and is unable to run to completion. This behavior illustrates the
memory advantages of using a lexicographic Tree projection algorithm over the hash tree
implementation of the Apriori algorithm. As compares the Apriori and DHP over the various
passes on a standard dataset .It is observed that DHP, because of its hashing and timely pruning
technique requires less than half the amount of time as compared to classical Apriori over 5
passes of candidate itemset generation. The partition algorithm proposed in 1995 reads the

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database at most two times to generate all significant association rules. Contrast this with the
previous algorithms, where the database is not only scanned multiple times but the number of
scans cannot even be determined in advance. All the partition algorithms such as the classic
partition algorithm proposed by Saverese et al [12] and DIC(Direct Itemset counting) proposed
by Brin [13] work well on large datasets. In partition algorithm [12], during the first scan,
algorithm generates a set of all potentially large itemsets by scanning the database once. This set
is a superset of all large item sets, i.e. it may contain false positives, but no false negatives are
reported. During the second scan, counters for each of these item sets are setup and their actual
support is measured in one scan of the database. The partition sizes are chosen such that each
partition can be accommodated in the main memory so that the partitions are read only once in
each phase. One major problem with Partition is that as the number of partitions increases, the
number of locally frequent itemsets, increases. While this can be reduced by randomizing the
partition selection, randomized partitions will have a large number of frequent itemsets in
common. Partition can thus spend a lot of time in performing these redundant intersections.DIC
[13] algorithm is also adopted by the thought of dividing the database into several partitions,
each partition is marked at the beginning in the process of scanning the database, candidate items
can be added in each marked partition, the support can be calculated when the itemsets are
calculated.DIC separates the strict restriction between counting and generating candidates.
Whenever a candidate reaches min-sup, DIC starts generating additional candidates based on it.
The main bottleneck of data set partitioning algorithm is that the execution time is long and
frequent itemsets generated are not very accurate. But this type of algorithm has a high degree of
parallelism; just scanning the database twice, greatly reduces me operation to improve the
efficiency of the algorithm. Overall, we can conclude that the breadth-first algorithm has the
shortcoming of generating a large number of candidate items and need to repeatedly scan the
database. This is definitely not suitable for databases with large number of itemsets.
3.2 Depth First Approach -
Depth first search has the advantage that it is not necessary to re-create the projected transactions
for each level-k of a search tree. The depth first projection technique provides locality of data
access, which can exploit multiple levels of cache. Some of the depth first algorithms are FP-
growth Eclat [17].

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In 2000 Han et al proposed frequent pattern tree (FP-tree) structure, which is an extended prefix
tree structure, used for mining the complete set of frequent patterns by pattern fragment growth.
It encodes the dataset using a compact data structure FP-tree and extracts frequent itemsets
directly from this structure. This algorithm is about an order of magnitude faster than the Apriori
algorithm. However, the number of conditional FP-trees is in the same order of magnitude as
number of frequent itemsets. The algorithm is not scalable to sparse and very large databases.
The OIP algorithm [15] Opportune Project mines complete set of frequent item sets, which is
efficient on both sparse and dense databases at all levels of support threshold, and scalable to
very large databases. It opportunistically chooses between two different data structures, array
based or tree-based, to represent projected transaction subsets, and heuristically decides to build
unfiltered pseudo projection or to make a filtered copy according to features of the subsets.
DepthProject [16] employs a selective projection and uses the horizontal bit string representation
for projected transaction subsets. the comparison of Tree Projection(Breadth first) and FP-
Tree(Depth first) approach of runtime on T25:I10:D10K with 1K items as dataset. It shows that
FP-growth is better than Tree Projection when support threshold is very low and database is
quite large. The Eclat algorithm [17] proposed by Zaki et al is based on a parallel approach and
partitions the database. It incorporates some features of clustering as well as parallel mining. The
algorithm uses a scheme to cluster related frequent itemsets together, and to partition them
among the processors. At the same time it also uses a different database layout which clusters
related transactions together, and selectively replicates the database so that the portion of the
database needed for the computation of association rules is local to each processor. After the
initial set-up phase, the algorithm eliminates the need for further communication or
synchronization thus eliminating the problem of synchronization faced in parallel mining. The
algorithm further scans the local database partition only three times, thus minimizing I/O
overheads.The gist is that depth first approach works well for large amount of data as compared
with bredath first approach and so it can be applied for scalable datasets.
3.3 Pattern Growth Algorithms-
Two major costs of Apriori based algorithms are the cost to generate candidate frequent itemsets
and the I/O cost. Data mining community has addressed the issues related I/O, but the issues

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related to candidate frequent itemsets generation remain. First, the cost required to generate
candidate k
itemsets especially when there are a lot of k –1 frequent itemsets. For example, if there are n
frequent 1 itemsets, Apriori based algorithms would require to generate approximately n2/2
candidate frequent itemsets. Secondly, the memory
required to hold the candidate frequent itemsets and their supports could be substantial. For
example, when n equals 10,000, there would be more than 108 length 2 candidate frequent
itemsets. Assuming it requires 4 bytes to hold the support and 4 bytes to hold the itemsets, it
would require close to 0.5 gigabytes of main memory to store the information. Furthermore, the
memory required does not include the overhead from the data structure. Thirdly, the cost
required to counting the support of candidate itemsets may not be trivial. As observed in run time
behaviour of Apriori based algorithms, the run time increases as the support decreases.
Therefore, the cost of candidate frequent itemsets generation of Apriori based algorithms could
easily overshadow the cost of I/O. Han et al. proposed a data structure called frequent pattern
tree or FPTree . FP-growth mines frequent itemsets from FP-Tree without generating candidate
frequent itemsets. FP-Tree is an extension of prefix tree structure. Only frequent items have
nodes in the tree. Each node contains the item’s label and its frequency. The paths from the root
to the leaves are arranged according to the support of the items with the frequency of each parent
is greater than or equal to the sum of its children’s frequency. The construction of FP-Tree
requires two data scans. In the first scan, the support of each item is found. In the second scan,
items within transactions are sorted in descending order according to the support of items. If two
transactions share a common prefix, the shared portion is merged and the frequencies of the
nodes are incremented accordingly. Nodes with the same label are connected with an item link.
The item link is used to facilitate frequent pattern mining. In addition, each FP-Tree has a header
that contains all frequent items and pointers to the beginning of their respective item links. FP-
growth partitions the FP-Tree based on the prefixes. FP-growth traverses the paths of FP-Tree
recursively to generate frequent itemsets. Pattern fragments are concatenated to ensure all
frequent itemsets are generated properly. In this way, FP-growth avoids the costly operations of
generating and testing of candidate itemsets. As pointed out by the authors of FP-Tree, no
algorithm works in all situations. The fact holds true for FP-Tree when the dataset is sparse.
When the data is sparse, the compression achieved by the FP-Tree is small and the FP Tree

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is bushy. As a result, FP-growth would spend a lot of effort to concatenate fragmented patterns
with no frequent itemsets being found. A new data structure called H-struct is introduced in.
Transactions are sorted with an arbitrary ordering scheme. Only frequent items are projected in
the H-struct. H-struct consists of projected transactions and each node in the projected
transactions contains item label and a hyper link pointing to the next occurrence of the item. A
header table is created for H-struct. The header contains frequencies of all items, their supports
and hyper link to the first transaction containing given item. H-mine mines the H-struct
recursively by
building a new header table for each item in the original header with subsequent headers
omitting items that have been mined previously. For each sub-header,H-mine traverses the H-
struct according to the hyper links and finds frequent itemsets for the local header. At the same
time, H-mine builds links for items that have not been mined in the local header. Those links are
used to find conditional
frequent patterns within the local header. The process is repeated until all frequent itemsets have
been mined. In case of a dense dataset, H-struct is not as efficient as FP-Tree because FP-Tree
allows compression. H-mine would dynamically switch to FP-Tree when the dataset is found to
be dense.
3.4 Incremental Update with Apriori-based Algorithms-
A general incremental update data-mining algorithm is highly desirable in frequent pattern
mining. It is because the complete dataset is normally huge and the incremental portion is
relatively small compared to the complete dataset. In many cases, it is not feasible to perform a
complete data mining process while transactions are being added continuously. Therefore,
incremental data mining algorithms have to reuse the existing information as much as possible,
so that either computational cost and/or I/O cost can be reduced. A general incremental mining
algorithm called Fast Update 2, FUP2 that allows both addition and deletion of transactions was
proposed . The major idea of FUP2 is to reduce the cost of candidate frequent itemsets
generation.
Incremental portion of the dataset is scanned; frequent patterns in the incremental data are
compared with the existing frequent itemsets in the original dataset. Previous frequent itemsets
are removed if they are no longer frequent after the incremental portion of the data is added or

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removed. The supports of previous frequent itemsets that are still frequent are updated to reflect
the changes. In those ways, previous frequent itemsets that are still frequent are not required to
be checked for their supports again. New k +1 candidate frequent itemsets are generated from
frequent k itemsets. The entire updated dataset is
scanned to verify those newly added candidate itemsets if they are indeedfrequent. The process is
repeated until the set of candidate frequent itemset
becomes empty. FUP2 offers some benefits over the original Apriori; however, it still requires
multiple scans of the dataset. Another incremental Apriori based algorithm is called Sliding
Window
Filtering, SWF for short. SWF incorporates the main idea of Partition algorithm with Apriori to
allow incremental mining. SWF divides the dataset into several partitions. During the scan of
partitions, a filtering threshold is employed in each partition to generate candidate frequent 2
itemsets. When a candidate 2 itemset is found to be frequent in the newly scanned partition, the
partition number and the frequency of the itemset are stored. Cumulative information about
candidate frequent 2 itemsets is selectively carried over toward subsequence partition scans.
Cumulative frequencies of previous generated candidate frequent 2 itemsets are maintained as
new partitions are being scanned. False candidate frequent itemsets are pruned when the
cumulative
support of the candidate frequent itemsets fall below required proportional support since they
have become frequent. Once incremental portion of the dataset is scanned, scan reduction
techniques are used to generate all subsequence candidate frequent itemsets . Another data scan
over the whole dataset is required to confirm the frequent itemsets. In the case of data removal,
the partition to be removed are scanned, the cumulative count and the start partition number of
candidate length 2 itemsets are modified accordingly. Although SWF achieves better
performance than pervious algorithms, the performance of SWF is still depending on the
selection of partition size and
removal of data can only be done at partition level.
3.5 Hybrid Approach -
There is also a hybrid approach wherein at some point breadth first approach is used and at some
point depth first approach is applied in the same process. Some of the algorithms which work on

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hybrid approach are AprioriHybrid, Pincer Search below shows an example of the two
approaches .
Algorithm Traversals
Technique
datastructure Number
of
database
scan
Apriory BFT HASH TREE K
Dhp BFT HASH TREE K
Partition BFT None 2
DIC BFT Prefix tree <=K
FP tree DFT Prefix tree 2
Eclat DFT none <=3
Pincer search Hybrid Link list <=4
Table 2: Comparison of some major algorithms shows the current scenario of research done
on frequent itemset mining [22] in context to year of publication and its number of citations. As
the data continue to increase in complexity (which includes size, type, and location of data),
parallel computing will be essential in delivering fast interactive solutions for the overall KDD
process. Applying parallel mining in collaboration with an effective data structure for storing
candidate sets can be exploited for a scalable approach in mining association rules.
Fig 1: Current status of research

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4. Conclusions
Throughout the last decade, a lot of people have implemented and compared several algorithms
that try to solve the frequent itemset mining problem as efficiently as possible. Unfortunately,
only a very small selection of researchers put the source codes of their algorithms publicly
available such that fair empirical evaluations and comparisons of their algorithms become very
difficult. Moreover, we experienced that different implementations of the same algorithms could
still result in significantly different performance results. As a consequence.
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[11] Agarwal R, Aggarwal C, Prased V V V,2001,A tree projection algorithm for generation of
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