1. William Norris Professor and Head, Department of Computer Science
Association Analysis for Finding Patterns in Large Amounts of Biological Data
Vipin Kumar
William Norris Professor and Head, Department of Computer Science

2. 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
Applications
Marketing and Sales Promotion
Supermarket shelf management
Traffic pattern analysis (e.g., rules such as "high congestion on Intersection 58 implies high accident rates for left turning traffic")
Rules Discovered:
{Milk} --> {Coke} (s=0.6, c=0.75)
{Diaper, Milk} --> {Beer} (s=0.4, c=0.67)

3. 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

4. Efficient Pruning Strategy (Ref: Agrawal & Srikant 1994)
Found to be Infrequent
Pruned supersets
If an itemset is infrequent, then all of its supersets must also be infrequent

5. Illustrating Apriori Principle
Items (1-itemsets)
Pairs (2-itemsets)
(No need to generate candidates involving Coke or Eggs)
Minimum Support = 3
Triplets (3-itemsets)
If every subset is considered,
6C1 + 6C2 + 6C3 = 41
With support-based pruning,
= 13

6. Counting Candidates A B C D A C E B C D A B D E B C E B D Candidates
Frequent Itemsets are found by counting candidates.
Simple way:
Search for each candidate in each transaction.
Expensive!!!
Candidates
Count
Transactions 1
A D
A E
A B C D E
A B D E
B C D
A B E
B D
B C
A C
A B 2 1
A D
A E
A B C D E
A B D E
B C D
A B E
B D
B C
A C
A B
A B
A C
A D
A E
B C
B D
A B E
B C D
A B D E
A B C D E
Reduce the number of comparisons (NM) by using hash tables to store the candidate itemsets 2
A D
A E
A B C D E
A B D E
B C D
A B E
B D
B C
A C
A B 1 4 3
Naïve approach requires O(NM) comparisons
A B C D
A C E
B C D
A B D E
B C E
B D M N

10. Where are the parts located?
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

19. Create a data set that records the presence and absence of
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

20. 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

21. 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
X: Set of patients
Y: Set of attributes, i.e., SNPs, medical characteristics