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Association Analysis for
Finding Patterns in Large
Amounts of Biological Data
Vipin Kumar
William Norris Professor and
Head, Department of Computer Science
[email protected]
www.cs.umn.edu/~kumar
Association Analysis
• Given a set of records, find dependency rules which will
predict occurrence of an item based on occurrences of
other items in the record
Rules Discovered:
TID
Items
1
Bread, Coke, Milk
2
3
4
5
Beer, Bread
Beer, Coke, Diaper, Milk
Beer, Bread, Diaper, Milk
Coke, Diaper, Milk
• Applications
{Milk} --> {Coke} (s=0.6, c=0.75)
{Diaper, Milk} --> {Beer}
(s=0.4, c=0.67)
Support, s 
# transacti ons that contain X and Y
Total transacti ons
# transacti ons that contain X and Y
X
Confidence , c 
– Marketing and Sales Promotion
# transacti ons that contain
– Supermarket shelf management
– Traffic pattern analysis (e.g., rules such as "high congestion on
Intersection 58 implies high accident rates for left turning traffic")
June 15, 2006
Finding Patterns in Large Amounts of Biological Data
‹#›
Association Rule Mining Task
• Given a set of transactions T, the goal of association
rule mining is to find all rules having
– support ≥ minsup threshold
– confidence ≥ minconf threshold
• Brute-force approach: Two Steps
– Frequent Itemset Generation
• Generate all itemsets whose support  minsup
– Rule Generation
• Generate high confidence rules from each frequent itemset,
where each rule is a binary partitioning of a frequent itemset
• Frequent itemset generation is computationally
expensive
June 15, 2006
Finding Patterns in Large Amounts of Biological Data
‹#›
Efficient Pruning Strategy
(Ref: Agrawal & Srikant
1994)
null
If an itemset is infrequent,
then all of its supersets
must also be infrequent
A
B
C
D
E
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
Found to be
Infrequent
ABCD
Pruned
supersets
June 15, 2006
ABCE
ABDE
ACDE
BCDE
ABCDE
Finding Patterns in Large Amounts of Biological Data
‹#›
Illustrating Apriori Principle
Item
Bread
Coke
Milk
Beer
Diaper
Eggs
Count
4
2
4
3
4
1
Items (1-itemsets)
Itemset
{Bread,Milk}
{Bread,Beer}
{Bread,Diaper}
{Milk,Beer}
{Milk,Diaper}
{Beer,Diaper}
Minimum Support = 3
Pairs (2-itemsets)
(No need to generate
candidates involving Coke
or Eggs)
Triplets (3-itemsets)
If every subset is considered,
6C + 6C + 6C = 41
1
2
3
With support-based pruning,
6 + 6 + 1 = 13
June 15, 2006
Count
3
2
3
2
3
3
Itemset
{Bread,Milk,Diaper}
Finding Patterns in Large Amounts of Biological Data
Count
3
‹#›
Counting Candidates
•
•
Frequent Itemsets are found by counting candidates.
Simple way:
– Search for each candidate in each transaction.
Expensive!!!
Candidates Count
Transactions
ABCD
ACE
BCD
N
ABDE
BCE
BD
June 15, 2006
AB
0
1
2
Naïve approach
AC
1
2
0
requires O(NM)
A
D
1
2
AD
0
comparisons
A
0
1
2
AE
E
0
BC
1
3
BC
0
Reduce the number
BD
1
4
M
BD
0
of comparisons
ABE
0
2
(NM) by using hash
ABE
0
BCD
1
2
tables to store the
BCD
0
ABDE
0
1
candidate itemsets
0
AABBCDDEE
0
A inBLarge
C DAmounts
E
Finding Patterns
of0Biological Data
‹#›
How many roles
can these play?
How flexible and
adaptable are they
mechanically?
What are the
shared parts (bolt,
nut, washer, spring,
bearing), unique
parts (cogs,
levers)? What are
the common parts - types of parts
(nuts & washers)?
Where are
the parts
located?
Which parts
interact?
© Mark Gerstein, Yale
Association Analysis for Finding Connections of
Disease and Medical and Genomic Characteristics
• Create a data set that records the presence and
absence of
– Phenotypic characteristics
– Genetic characteristics (SNPs)
– Disease
• Apply association analysis to find groups of
phenotypic and genetic characteristics that are
highly associated with disease
– Uses characteristics of the patterns to prune the search space
• Clustering and classification can also be applied
June 15, 2006
Finding Patterns in Large Amounts of Biological Data
‹#›
The Need for Error-Tolerant Itemsets
• An error-tolerant itemset (ETI) can have a fraction
 of the items missing in each transaction.
Example: see the data in the table
– Let  = 1/4. In other words, each
transaction needs to have
3/4 (75%) of the items.
– X = {i1, i2, i3, i4} and
Y = {i5, i6, i7, i8} are both
ETIs with a support of 4.
• Algorithms to find ETIs are still in development
• You can think of these ETIs as blocks in the data
matrix
June 15, 2006
Finding Patterns in Large Amounts of Biological Data
‹#›
ETIs in For Finding Patterns in
Phenotypic and Genomic Data
• ETIs consist of
– A set of patients and
– A set of attributes
such that
– The block is relatively dense
• These blocks identify sets of
patients that are highly associated with
certain sets of attributes and vice-versa
• If most of these patients share a disease,
then these attributes (genetic and/or
phenotypic) are candidate markers for the
disease
June 15, 2006
X: Set of patients
Y: Set of attributes,
i.e., SNPs, medical
characteristics
Finding Patterns in Large Amounts of Biological Data
‹#›