Pattern Evaluation

@(Pattern Discovery in Data Mining)
本文介绍了数据挖掘中模式挖掘，评估所得模式与规则科学性的方法。

Limitation of Support-Confidence Framework

Pattern-mining will generate a large set of patterns/rules. However, not all the generated patterns/rules are interesting.

The interestingness measures: Objective vs. subjective
* Objective interestingness measures
* Support, confidence, correlation, …
* Subjective interestingness measures: One man’s trash could be another man’s treasure
* Query-based: Relevant to a user’s particular request
* Against one’s knowledge-base: unexpected, freshness, timeliness
* Visualization tools: Multi-dimensional, interactive examination

An example of limitations:

Interesting Measures: Lift and $\chi ^2$

1. Lift

   • Measure of dependent/correlated events: lift
     

     $$lift(B,C) = \frac{c(B \to C)}{s(C)} = \frac{s(B \cup C)}{s(B)\times s(C)}$$

   • Lift(B, C) may tell how B and C are correlated

   • Lift(B, C) = 1: B and C are independent
   • > 1: positively correlated
   • < 1: negatively correlated

Example:

Thus, B and C are negatively correlated since list < 1; But B and $\neg C$ are positively correlated since lift > 1.

1. $\chi ^2$

   • Measure to test correlated events
     

     $$\chi ^2 = \sum{\frac{Observed - Expected}{Expected}}$$

   • General rules:

   • $\chi ^2 = 0$, independent
   • $\chi ^2 > 0$, correlated, either positive or negative. So it needs additional test

Example:

1. Null transaction($\neg A \cap \neg B$)
   
   • Notion: Lift and $\chi ^2$ are not always good measures
     

Null Invariance Measures

• Null Invariance: Value does not change with the number of null-transactions.
• Why is null invariance crucial for the analysis of massive transaction data? Because Many transactions may contain neither milk nor coffee!

Comparison of Null-invariance Measures

Use Imbalanced Ratio to measure the imbalance of two itemsets A and B in rule implications.