1. Summarizing Itemset Patterns: A Profile-Based Approach
Xifeng Yan, Hong Cheng, Jiawei Han, Dong Xin
ACM KDD 05’
Advisor：Jia-Ling Koh
Speaker：Yu-Jiun Liu
2006/01/06

2. Introduction Ⅰ Closed frequent pattern no super-pattern with the same
support.
Maximal
no frequent super-pattern.
Top-K V.S. K representatives

3. Introduction Ⅱ The format of these representatives.
How to find these representatives?
The measure of their quality.

4. Definition
Bernoulli Distribution Vector
Pattern Profile

5. Equations
The relative frequency of item οi in D’.
Estimated Support

6. Pattern Profile Example
Both of the above datasets can be summarized by <abcd>, but the quality is better for D1.
p(a) = ( )/( ) = 0.91
Mabc = <[0.91,0.96,1], abcd, 0.87>
M = <[0.91,0.96,1,1], abcd, 1>

7. Pattern Summarization
First, construct a special profile for each pattern that only contains that pattern itself.
Use the Kullback-Leibler divergence to merge similar patterns.
KL-divergence

8. Hierarchical Agglomerative Clustering

9. K-means Clustering

10. Optimization Heuristics
Closed Itemset vs. Frequent Itemsets
Given patterns α and β, if and their supports are equal, then
Approximate Profiles
Using the following two equations to instead of original profile updating.
for Algorithm 1
for Algorithm 2

11. Quality Evaluation Definition (Restoration Error)
T is a testing pattern set.
T’ is the collection of the itemsets generated by the master patterns in profiles and

12. Quality Evaluation
J tests “frequent patterns”, some of which may be estimated as “infrequent”.
Jc tests “estimated frequent patterns”, some of which are actually “infrequent”.
Therefore J and Jc are complementary to each other.

13. Quality Evaluation Lemma
For any frequent itemset π, there must exist a profile Mk such that , where ψk is the master itemset of Mk.

14. Optimal Number of Profiles
How to determine K?
M = (p, ψ , ρ)
Ex: require for any i such that
p~q α~β  Dα~Dβ~Dα∪Dβ
Checking the derivative of the quality over K
, If J increase suddenly from K* to K* - 1,
K* is likely to be a good choice.

15. Optimal Number of Profiles

16. Experiment Three real datasets and a series of synthetic datasets.
Language: Visual C++
CPU: Intel 3.2GHz
Memory: 1GB
OS: Windows XP

17. Mushroom
※688 closed patterns

18. BMS-Webview1 ＆ Replace ※threshold = 0.1% ※4195 closed patterns
※many small frequent itemsets
※threshold = 3%
※4315 closed patterns
※many small frequent itemsets

19. Synthetic Datasets Provided by IBM
7 datasets, each has transactions. Choose top-500.
K = 50 and 100