1. Slides for KDD07
Mining statistically important equivalence classes and delta-discriminative emerging patterns
Jinyan Li
School of Computer Engineering
Nanyang Technological University, Singapore
A joint work with Guimei Liu, Limsoon Wong
13 August 2007

2. The research problem Input data: x_11 x_12 x_13 x_14 … x_1n
………………………………….
x_m1 x_m2 x_m3 x_m4 … x_mn
n features (order of 1000)
m samples
class P N
gene1 gene2 gene3 gene4 … gene_n

3. Objectives
To discover
Which itemsets are statistically important to separate these different classes?
Which itemsets are redundant?
The concise representation.
Test statistics: odds ratio, relative risk, student’s-t, chi-square, etc.
Output: a ranking list of equivalence classes under some statistical test.
<generators, closed pattern>

4. … New problem Not an enumeration of frequent itemsets
Not an enumeration of solely closed patterns
Not an enumeration of solely generators
Not a simple sum of the closed patterns and generators
The output is:
Closed pattern
Its generators
Closed pattern
Its generators
Closed pattern
Its generators …

5. Contribution
Depth-first search of closed patterns and their associated generators in parallel
A unified approach regardless of the variety of the test statistics
Easy to handle multiple classes of data
Not one-vs-one style
Not all-vs-all style (exhaustive pairwise, like in SVM)

6. A data set

7. Frequent itemsets (patterns)
Support threshold = 2
A total of 16
Freq. patterns

8. Equivalence classes
The empty set ({}:5); its tid-set={T1 … T5}
{b:4, e:4, be:4}; its tid-set={T2…T5}
{c:4}; its tid-set={T1, T2, T3, T5}
{a:3, ac:3}; its tid-set={T1, T3, T5}
{bc:3, ce:3, bce:3}
{ab, ae, abc, abe, ace, abce}
An EC is a set of itemsets which always occur in the same set of
transactions.

9. Closed Patterns and Generators
A closed pattern is the
maximal pattern of an
equivalence class;
the minimal ones are called generators.
Support threshold = 2

10. An example

11. Observation 1

12. Observation 2

14. Revised FP-tree for pruning non-generators

15. To identify closed patterns in parallel
(1) Tail structure is added
(2) Store all full-support items

16. An option to find Delta-discriminative equivalence classes
Non-redundant
Actually, they are emerging patterns
But equivalence of the minimal EPs is identified
Unknown before

17. Performance comparison

20. Conclusion
Useful for
Classification problems, in particular multiple-class classification problems
Risk factors assessment for financial market analysis
Bioinformatics: evaluation of motifs/signature patterns