购物篮分析中的度量

R 中的购物篮分析

Christopher Bruffaerts

Statistician

用于规则提取的度量

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

目标：提取关联规则

示例：

{Bread} $\rightarrow$ {Butter}
- Bread = "前件（Antecedent）"
- Butter = "后件（Consequent）"
{Butter, Cheese} $\rightarrow$ {Wine}

度量：Support、Confidence、Lift 等

支持度（Support）

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

支持度（Support）：项集的"受欢迎度"

supp(X) = 含项集X的交易占比。
supp(X $\cup$ Y) = 同时含X与Y的交易占比。

示例：

supp({Bread}) = 3/7 = 42%
supp({Bread} $\cup$ {Butter}) = 3/7 = 42%

置信度（Confidence）

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

置信度（Confidence）：规则成立的频率

conf(X $\rightarrow$ Y) = supp(X $\cup$ Y) / supp(X)

置信度表示购买X时同时购买Y的比例。

示例：

X = {Bread}

Y = {Butter}

conf(X $\rightarrow$ Y) = $\frac{3/7}{3/7}$ = 100%

提升度（Lift）

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

提升度（Lift）：关联强度有多大

lift(X $\rightarrow$ Y) = $\dfrac{supp(X \cup Y)}{supp(X) \times supp(Y)}$

Lift > 1：Y更可能与X一起被购买
Lift < 1：若买了X，则不太可能买Y

示例：

X = {Bread}; Y = {Butter}

lift(X $\rightarrow$ Y) = $\frac{3/7}{(3/7)*(6/7)} = \frac{7}{6}$ ~ 1.16

用于频繁项集的 apriori 函数

library(arules)
# Frequent itemsets
supp.cw = apriori(trans, # the transactional dataset
                  # Parameter list
                  parameter=list(
                    # Minimum Support
                    supp=0.2,
                    # Minimum Confidence
                    conf=0.4,
                    # Minimum length
                    minlen=2,
                    # Target
                    target="frequent itemsets"),
                  # Appearence argument
                  appearance = list(
                    items = c("Cheese","Wine"))
                 )

用于规则的 apriori 函数

library(arules)
# Rules
rules.b.rhs = apriori(trans, # the transactional dataset
                  # Parameter list
                  parameter=list(
                    # Minimum Support
                    supp=0.2,
                    # Minimum Confidence
                    conf=0.4,
                    # Minimum length
                    minlen=2,
                    # Target
                    target="rules"),
                  # Appearence argument
                   appearance = list(
                     rhs = "Butter",
                    default = "lhs")
                 )

使用 apriori 的频繁项集

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

提取频繁项集

supp.all = apriori(trans, 
           parameter=list(supp=3/7,
           target="frequent itemsets"))        
inspect(head(sort(supp.all,by="support"),3))

    items          support   count
[1] {Butter}       0.8571429 6    
[2] {Wine}         0.7142857 5    
[3] {Cheese}       0.5714286 4

查看置信度与提升度

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

提取规则

# 右侧为"Butter"的规则
rules.b.rhs = apriori(trans, 
                 parameter=list(
                    minlen=2,
                    target="rules"), 
                 appearance = list(
                     rhs="Butter",
                    default = "lhs")
           )
inspect(head(sort(rules.b.rhs,by="lift")), 5)

查看置信度与提升度

TID	交易
1	{Bread, Butter, Cheese, Wine}
2	{Bread, Butter, Wine}
3	{Bread, Butter}
4	{Butter, Cheese, Wine}
5	{Butter, Cheese}
6	{Cheese, Wine}
7	{Butter, Wine}

提取规则

    lhs                    rhs      support  confidence lift  count
[1] {Bread}             => {Butter} 0.42      1.0        1.16     3    
[2] {Bread,Cheese}      => {Butter} 0.14      1.0        1.16     1    
[3] {Bread,Wine}        => {Butter} 0.28      1.0        1.16     2    
[4] {Bread,Cheese,Wine} => {Butter} 0.14      1.0        1.16     1    
[5] {Wine}              => {Butter} 0.57      0.8        0.93     4

开始练习吧！

R 中的购物篮分析