关联与解关联

Python 中的购物篮分析

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

用解关联来配对电子书

《霍比特人》封面缩略图。

《了不起的盖茨比》封面缩略图。

《傲慢与偏见》封面缩略图。

《麦田里的守望者》封面缩略图。

¹ 图片来自 goodreads.com。

Zhang 指标简介

由 Zhang（2000）提出
- 取值范围为 -1 到 +1
- +1 表示完全关联
- -1 表示完全解关联
全面且易解释
由支持度构造

¹ Zhang, T. (2000). Association Rules. Proceedings of the 4th Pacific-Asia conference, PADKK, pp.245-256. Kyoto, Japan.

定义 Zhang 指标

$$Zhang(A \rightarrow B) = $$ $$\frac{Confidence(A \rightarrow B) - Confidence(\bar{A} \rightarrow B)}{Max[Confidence(A \rightarrow B), Confidence(\bar{A} \rightarrow B)]}$$ $$Confidence = \frac{Support(A \& B)}{Support(A)}$$

用支持度构造 Zhang 指标

$$Zhang(A \rightarrow B) = $$ $$\frac{Support(A \& B) - Support(A) Support(B)}{ Max[Support(AB) (1-Support(A)), Support(A)(Support(B)-Support(AB))]}$$

计算 Zhang 指标

# Compute the support of each book
supportH = hobbit.mean()
supportP = pride.mean()

# Compute the support of both books
supportHP = np.logical_and(hobbit, pride).mean()

计算 Zhang 指标

# Compute the numerator
num = supportHP - supportH*supportP

# Compute the denominator
denom = max(supportHP*(1-supportH), supportH*(supportP-supportHP))

# Compute Zhang's metric
zhang = num / denom
print(zhang)

0.08903

开始练习！

Python 中的购物篮分析