Arif Djunaidy Rully Soelaiman Daning Tyaspamadya

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MINING ASSOCIATION RULES FROM LARGE DATABASES
USING THE LATTICE-BASED APPROACH AND HYBRID
SEARCH METHOD

• Arif DjunaidyRully SoelaimanDaning Tyaspamadya

Faculty of Information Technology ITS - Surabaya
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Background - 1

• In data mining, association rules represent
  relationships that may exist among items in their
  transactional databases
• Since, the association rules that can be
  exploited may represent the customers behavior,
  identification of the frequent itemsets and the
  formation of the conditional implication rules
  among items are paramount important to perform
• Efficient algorithms capable of optimizing those
  overheads in mining meaningful association rules
  are therefore required
• However, for large databases, the extraction of a
  set of meaningful association rules may require
  substantial memory and database scanning that may
  in turn increase the overall computing time of
  the mining process

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Background - 2

• The task of discovering all frequent associations
  in very large databases is quite challenging
• The search space is exponential in the number of
  database attributes
• With millions of database objects, the problem of
  I/O minimization becomes paramount
• Most current approaches are iterative in nature,
  requiring multiple database scans
• Most approaches use very complicated data
  internal data structures, which have poor
  locality and add additional space and computation
  overheads

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Key Features of Our Approach

• All frequent itemsets are enumerated via simple
  tid-list intersections
• A lattice-theoretic approach is used to decompose
  the original search space (lattice) into smaller
  pieces (sub-lattices) that can be processed
  independently and easier
• The hybrid search strategy for enumerating the
  frequent itemsets within each sub-lattice
• Our approach is designed to involve only a few
  database scans to minimize the I/O costs

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Problem Statement - 1

• An association rule can be written as A ? B,
  where
• A is an itemset called the antecedent or
  left-hand side (LHS), and
• B is an itemset called the consequent or
  right-hand side (RHS)
• The association mining task is to discover a set
  of association rules among a large number of
  objects in a given database

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Problem Statement - 2

• The basic and fundamental task of the mining
  association rules application is to generate all
  association rules X ? Y (X, Y are itemsets) that
  can be extracted from the database. These rules
  must satisfy both the support and confidence
  constraints
• Support constraint Sup (X ? Y),
• Confidence constraint Sup (X ? Y) / Sup (X)
• Sup(X), is defined as the number of transactions
  in which it occurs as a subset
• An itemset is categorized as a frequent itemset
  if its support is more than a minimum support
  (MinSup) supplied by a user
• The confidence factor represents the conditional
  probability that a transaction contains Y (given
  that the transaction contains X)
• An association rule is said to be confident if
  its confidence factor value is more than the
  minimum confidence (MinCof) supplied by the user.

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Simple Example - 1

• Consider the sales database of food store, where
  the objects represent customers and itemsets
  represent food
• In this example, the discovered patterns are the
  set of food frequently bought together by the
  customers.
• An example pattern found could be that, 60
  percent of the customers who buy cereal also buy
  milk
• The store can then use this knowledge for shelf
  placement, controlling the stock, etc.
• There are many potential application areas for
  association rule technology, which include
  catalog design, customer segmentation, store
  layout, and so on

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Simple Example - 2
MinSup 50
MinCof 100
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The Lattice-Based Approach - 1

• We use the Lattice-Theoretic to
• Identify all frequent itemsets
• Count the support of association rules
• Pre-req Construct the tid-list from the
  transaction database

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The Lattice-Based Approach - 2

• Construct the powerset Lattice P(I)

MinSup 50
Maximal freq. itemsets
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The Lattice-Based Approach - 3

• Compute support of iternsets via tid-list
  intersections

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Hybrid Search for Freq. Itemsets - 1

• Hybrid Search used to quickly enumerate all
  frequent itemsets
• Hybrid Search combines both the top-down and
  bottom-up search strategies and is based on the
  intuition that the greater the support of a
  frequent itemset, the more likely it is to be a
  part of a longer frequent itemset
• The hybrid approach is divided in two main steps
  
• Initial phase containing the atoms rearrangement,
  and
• The hybrid process itself for generating all
  frequent itemsets. In the second step, the
  recursion process is repeated until no more
  frequent itemset can be generated

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Hybrid Search for Freq. Itemsets - 2

• The first step simply rearranges the atoms in
  descending order of their supports. The sorting
  algorithm is involved in this step
• The second step starts by intersecting a pair of
  atoms one at a time
• The intersection process is started from a pair
  of atoms each of which having the largest support
  among others to produce a larger and longer
  frequent itemset.
• The process stops when an extension becomes
  infrequent (i.e., itemset that does not satisfy
  the minimum support requirement).
• The second bottom-up phase is then entered

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Hybrid Search for Freq. Itemsets - 3
Infrequent Itemsets (MinSup 50)
Infrequent Itemsets
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Design of Application

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Test Data
Statistics of Test Data

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Experimental Results - 1

Number of k-itemsets
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Experimental Results - 2

Number of Association Rules
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Experimental Results - 3

Computing Time
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Experimental Results - 4

Support Counting Performance
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Experimental Results - 5

Comparison Results
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Conclusions

• Experimental results show that the use of this
  approach as well as the hybrid search method can
  speed-up the computing time compared to both
  apriori-based algorithms as well as the similar
  lattice-based approach that uses the bottom-up
  search strategy
• Another interesting advantage of using the
  lattice-based algorithm is concerned with time
  used for scanning the databases. In this
  context, the lattice-based algorithms requires a
  single database scan once only. Hence, the I/O
  overhead can be maximally minimized
• As far as the computing speed is concerned, it
  seems that substantial computing time are still
  required to execute large databases. Although,
  the lattice-approach is relatively powerful, it
  indicates that some other computing
  methodologies, such as the parallel algorithms
  using the distributed computing environments need
  to be considered to solve the computing speed
  problem