mining multiple-level association rules in large databases authors : jiawei han simon fraser...
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● Mining Multiple-level Association Rules in Large Databases
Authors :Jiawei Han
Simon Fraser University, British Columbia.
Yongjian FuUniversity of Missouri-Rolla,
Missouri.
Presented by Michael Johnson
IEEE Transactions on Knowledge and Data Engineering, 1999
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Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions2
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions3
What is MLDM?What's the difference between the following
rules: Rule A →70% of customers who bought
diapers also bought beer Rule B →45% of customers who bought
cloth diapers also bought dark beer Rule C →35% of customers who bought
Pampers also bought Samuel Adams beer.
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Rule A applies at a generic higher level of abstraction (product)
Rule B applies at a more specific level of abstraction (category)
Rule C applies at the lowest level of abstraction (brand).
This process is called drilling down.5
What is MLDM?
What Do We Gain?
Concrete rules allow for More targeted marketing
New marketing strategies
More concrete relationships
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Hierarchy Types
Generalization/Specialization (is a relationships)
Is a With Multiple Inheritance Whole-Part hierarchies (is-part-of; has-part)
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Is A Relationship
2-Wheels
MotorcycleSUV
Vehicle
4-Wheels
Sedan Bicycle
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Generalization to Specialization
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
3. Conclusions/Future Work
4. Exam Questions
11
MLAR: Main Goal
As usual we are trying to develop a method to extract non-trivial, interesting, and strong rules from our transactional database.
A method which:
Avoids trivial rules (Milk→Bread) Common sense
Avoids coincidental rules (Toy→Milk) Low support
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What Do We Need?
1. Data Representation At Different Levels Of Abstraction
● Explicitly stored in databases
● Provided by experts or users
● Generated via clustering (OLAP)
2. Efficient Methods for ML Rule Mining (focus of this paper)
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Possible Methods
Apply single-level Apriori Algorithm to each of the multiple levels under the same miniconf and minsup.
Potential Problems? Higher Levels of abstraction will naturally have higher
support, support decreases as we drill down What is the optimal minsup for all levels? Too high a minsup → too few itemsets for lower levels Too low a minsup → too many uninteresting rules
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Possible Solutions
Adapt minsup for each level Adapt minconf for each level Do both This paper studies a progressive deepening
method developed by extension of the Apriori Algorithm, focused on minsup
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Assumption
If an item is non-frequent at one level, its descendants no longer figure in further analysis.
Explore only descendants of frequent items as we drill down
Are there problems that arise from making these assumptions?
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May eliminate possible interesting rules for itemsets at one level whose ancestors are not frequent at higher levels.
If so, can be addressed by 2 workarounds
2 minsup values at higher levels – one for filtering infrequent items, the other for passing down frequent items to lower levels; latter called level passage threshold (lph)
The lph may be adjusted by user to allow descendants of sub frequent items
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Problems
Differences From Previous Research
Other studies use same minsup across different levels of the hierarchy
This study…. Uses different minsup values at different levels of
the hierarchy Analyzes different optimization techniques Studies the use of interestingness measures
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Requirements
Transactional database must contain:1. Item dataset containing item description:
{<Ai>,<description>}
2. A transaction dataset T containing set of transactions..{Tid*,{Ap…Aq}}
*Tid is a transaction identifier (key)
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Algorithm Flow
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At Level 1: Generate frequent itemsets
Get table filtered for frequent itemsets T[2]
At subsequent levels: Generate candidate subsets using Apriori
Calculate support for generated candidates
Union 'passing' subsets with existing rule set
Repeat until no additional rules are generated, or desired level is reached
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions21
Definitions
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A pattern or an itemset A is one item Ai or a set of conjunctive items Ai Λ …. Λ Aj
The support of a pattern is the number of transactions that contain A vs. the total number of transactions σ(A|S)
The confidence of a rule A → B in S is given by:φ(A→B) = σ(AUB)/σ(A) (i.e. conditional probability)
Specify 2 thresholds: minsup(σ’) and miniconf (φ’); different values at different levels
Definitions
A pattern A is frequent in set S at if: the support of A is no less than the corresponding minimum
support threshold σ’
A rule A → B is strong for a set S, if:a. each ancestor of every item in A and B is frequent at its
corresponding level
b. A Λ B is frequent at the current level and
c. φ(A→B)≥ φ’ (miniconf criteria)
This ensures that the patterns examined at the lower levels arise from itemsets that have a high support at higher levels
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Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
3. Conclusions/Future Work
4. Exam Questions
24
food
milk
2% chocolate
bread
white wheat
Dairyland Foremost Old Mills Wonder
Generalized ID System:
2% Foremost Milk Coded as GID:112
(1st item in Level 1, 1st item in level 2, 2nd item in level 3)
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Level 1:
Level 2:
Level 3: ... .........
● Example: Taxonomy
Trans-id Bar_code_set
351428 {17325, 92108, ….}
653234 {23423, 56432,…}
Bar_code GID Category Brand Content Size Price
17325 112 milk Foremost 2% 1 Gal $3.31
….. ….. …… ….. ….. …..
Table 1:A sales-transaction Table
Table 2:A sales_item Description Relation
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Example: Dataset
TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222 , 323}
T3 {112 , 122 , 221 , 411}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221 , 413}
T6 {211 , 323 , 524}
T7 {323 , 411 , 524 , 713}27
Example: Preprocessing
Join sales_transaction table to sales_item table to produce encoded transaction table T[1]:
T[1]
Find Level-1 frequent itemsets
Minsup = 4Level-1 Frequent-1 Itemsets
L[1,1]
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Example: Step 1
TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222 , 323}
T3 {112 , 122 , 221 , 411}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221 , 413}
T6 {211 , 323 , 524}
T7 {323 , 411 , 524 , 713}
Itemset Support
{1**} 5
{2**} 5
Level-1 Frequent 2-Itemsets
L[1,2]Itemset Support
{1**,2**} 4
T[1]
Create T[2] by filtering T[1] w/ L[1,1]
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Example: Step 2
TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222 , 323}
T3 {112 , 122 , 221 , 411}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221 , 413}
T6 {211 , 323 , 524}
T7 {323 , 411 , 524 , 713}
Itemset Support
{1**} 5
{2**} 5
Filtered T[2]TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222}
T3 {112 , 122 , 221}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221}
T6 {211}
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Example: Step 3
Filtered T[2]TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222}
T3 {112 , 122 , 221}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221}
T6 {211}Itemset Support
{11*, 12*, 22*} 3
{11*, 21*, 22*} 3
L[2,1]
Itemset Support
{11*, 12*} 4
{11*, 21*} 3
{11*,22*} 4
{12*, 22*} 3
{21*, 22*} 3
L[2,2]
Itemset Support
{11*} 5
{12*} 4
{21*} 4
{22*} 4
L[2,2]
L[2,3]
Find Level-2 Frequent Itemsets
Minsup = 3
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Example: Step 4
Filtered T[2]TID Items
T1 {111 , 121 , 211 , 221}
T2 {111 , 211 , 222}
T3 {112 , 122 , 221}
T4 {111 , 121}
T5 {111 , 122 , 211 , 221}
T6 {211}
Itemset Support
{111, 211*} 3
L[3,1]Itemset Support
{111} 4
{211} 4
{221} 3
L[3,2]
Find Level-3 Frequent Itemsets
Minsup = 3
Stop: Lowest Level Reached
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions
32
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Are All Of The Strong Rules Interesting?
MLDM creates unique challenges for rule pruning
The paper defines two filters for interesting rules:
1. Removal of redundant rules
2. Removal of unnecessary rules
Redundant Rules
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Consider a strong rule at Level 1: Milk→Bread
food
milk
2% chocolate
bread
white wheat
Dairyland Foremost Old Mills Wonder ... .........
This rule is likely to have descendent rules which may or may not contain additional information, even if they met our minconf and minsup criteria at that level:
2% Milk→Wheat Bread, 2% Milk→White Bread, Chocolate Milk→Wheat Bread
We need a way to distinguish between rules that add information and those that are redundant
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A rule is redundant if the confidence for a rule falls in a certain range and the items in the rule are descendents of a different rule.
Redundant Rules
Unnecessary Rules
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Consider the following rules:
R: Milk→Bread (minsup = 80%)
R': Milk, Butter → Bread (minsup = 80%)
How much additional information do we gain from the R'?
MLDM can produced very complex rules that meet our minsup and minconf criteria, but do contain much unique/useful information.
We need a way to distinguish between rules that add information and those that are Unnecessary
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A rule R is unnecessary if there is a simpler rule R' and φ(R) is within a given range of φ(R')
Unnecessary Rule
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions39
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Authors proposed 3 iterations of the original algorithm1)ML_T1LA
●Use only one encoded table T[1]
2)ML_TML1
●Generate T[1], T[2], … T[n+1]
3)ML_T2LA
●Uses T[2], but calculates down level support with a single scan
Algorithm Optimizations
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Instead of generating T[2] from T[1], ML_T1LA algorithm generates support for all levels of hierarchy in a single scan from T[1]
Pros:Avoids generation of new transaction table
Limits number of scans to the size of the largest transaction
Cons:Scanning T[1] requires scanning all items, even infrequent ones
Performance may suffer for DB w/ many infrequent itemsets
Large memory required (32MB RAM = page swapping!!!)
ML_T1LA
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Instead of using only T[2] for rule mining, ML_TML1 algorithm generates a table for each level, using L[i,1] to filter T[i] and create T[i+1]
Pros:Saves significant processing time if only a small portion of the data is frequent at each level
●Allows for creation of T[i] and L[i,1] in parallel
Cons:May not be efficient if only a small number of items is filtered at each level
ML_TML1
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Like the base algorithm, ML_T2LA creates T[2] table from the frequent itemsets in T[1]. However, it allows for parallel creation of L[i,k].
Pros:
Saves time by limiting the number of scans
Cons:
May not be efficient if only a small number of items is filtered at each level
ML_T2LA
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While the figures show that T2LA is best for most of the time, the authors preferred ML_T1LA
Experimental Results
Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions46
Conclusions
This paper demonstrated: Extending association rules from single-level to multiple-
level.
A top-down progressive deepening technique for mining multiple-level association rules.
Filtering of uninteresting association rules
Performance optimization techniques (not covered)
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Future Work
Develop efficient algorithms for mining multiple-level sequential patterns
Cross-level associations Improve interestingness of rules
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Outline1. What is MLAR?
● Concepts
● Motivation
2. A Method For Mining M-L Association Rules● Problems/Solutions
● Definitions
● Algorithm Example
● Interestingness
● Optimizations
3. Conclusions/Future Work
4. Exam Questions49
Exam Question 1
Q. What is a major drawback to multiple-level data mining using the same minsup at all levels of a concept hierarchy?
A. Large support exists at higher levels of the hierarchy; smaller support at lower levels. In order to insure that sufficiently strong association rules are generated at the lower levels, we must reduce the support at higher levels which, in turn, could result in generation of many uninteresting rules at higher levels. Thus we are faced with the problem of determining which is the optimal minsup at all levels
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Exam Question 2
Q. Give an example of a multiple level association rule
A.
High level: 80% of people who buy cereal also buy milk
Low Level: 25% of people who buy Cheerios cereal buy Hood 2% Milk
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Exam Question 3
Q. There were 3 examples of hierarchy types in multiple level rule mining. Pick one and draw an example
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2-Wheels
MotorcycleSUV
Vehicle
4-Wheels
Sedan Bike Recreational
SnowmobileBicycle
Vehicle
Commuting
Car
Hard Drive
PlatterCPU
Computer
Motherboard
RAM RW Head
Is-A Is-AMultiple
Inheritance
Whole-Part
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