决策树问题：为什么 tree() 不选择节点的所有变量

Question

我正在工作场所从事一个项目，但我的决策树分析遇到了一些问题。这不是家庭作业。 样本数据集

PRODUCT_SUB_LINE_DESCR    MAJOR_CATEGORY_DESCR       CUST_REGION_DESCR
SUNDRY                         SMALL EQUIP           NORTH EAST REGION
SUNDRY                         SMALL EQUIP           SOUTH EAST REGION
SUNDRY                         SMALL EQUIP           SOUTH EAST REGION
SUNDRY                         SMALL EQUIP           NORTH EAST REGION
SUNDRY                         PREVENTIVE            SOUTH CENTRAL REGION
SUNDRY                         PREVENTIVE            SOUTH EAST REGION
SUNDRY                         PREVENTIVE            SOUTH EAST REGION
SUNDRY                         SMALL EQUIP           NORTH CENTRAL REGION
SUNDRY                         SMALL EQUIP           MOUNTAIN WEST REGION
SUNDRY                         SMALL EQUIP           MOUNTAIN WEST REGION
SUNDRY                         COMPOSITE             NORTH CENTRAL REGION
SUNDRY                         COMPOSITE             NORTH CENTRAL REGION
SUNDRY                         COMPOSITE             OHIO VALLEY REGION
SUNDRY                         COMPOSITE             NORTH EAST REGION

Sales   QtySold      MFGCOST    MarginDollars   new_ProductName
209.97  3             134.55    72.72            no
-76.15  -1            -44.85    -30.4            no
275.6   2             162.5     109.84           no
138.7   1             81.25     55.82            no
226     2             136       87.28            no
115     1             68        45.64            no
210.7   2             136       71.98            no
29      1             18.85     9.77             no
29      1             18.85     9.77             no
46.32   2             37.7      7.86             no
159.86  1             132.4     24.81            no
441.3   2             264.8     171.2            no
209.62  1             132.4     74.57            no
209.62  1             132.4     74.57            no

1) 我的树只有两个节点，原因如下

>summary(tree_model)
Classification tree:
tree(formula = new_ProductName ~ ., data = training_data)
Variables actually used in tree construction:
[1] "PRODUCT_SUB_LINE_DESCR"
Number of terminal nodes:  2 
Residual mean deviance:  0 = 0 / 41140 
Misclassification error rate: 0 = 0 / 41146 

2) 我确实创建了一个新的数据框，其中只有级别低于 22 级别的因子。有一个因素有 25 个级别，但是 tree() 没有给出错误，所以我认为该算法接受 25 个级别

>str(new_Dataset)
'data.frame':   51433 obs. of  7 variables:
 $ PRODUCT_SUB_LINE_DESCR: Factor w/ 3 levels "Handpieces","PRIVATE 
                             LABEL",..: 3 3 3 3 3 3 3 3 3 3 ...
 $ MAJOR_CATEGORY_DESCR  : Factor w/ 25 levels "AIR ABRASION",..: 23 23 23 
                             23 21 21 21 23 23 23 ...
 $ CUST_REGION_DESCR     : Factor w/ 7 levels "MOUNTAIN WEST REGION",..: 3 
                             6 6 3 5 6 6 2 1 1 ...
 $ Sales                 : num  210 -76.2 275.6 138.7 226 ...
 $ QtySold               : int  3 -1 2 1 2 1 2 1 1 2 ...
 $ MFGCOST               : num  134.6 -44.9 162.5 81.2 136 ...
 $ MarginDollars         : num  72.7 -30.4 109.8 55.8 87.3 ...

3) 以下是我设置分析的方式

 # I choose product name as my main attribute(maybe that is why it appears at 
 the root node?)
 new_ProductName = ifelse( PRODUCT_SUB_LINE_DESCR == "PRIVATE 
                              LABEL","yes","no")
 data = data.frame(new_Dataset, new_ProductName)
 set.seed(100)
 train = sample(1:nrow(data), 0.8*nrow(data)) # training row indices
 training_data = data[train,] # training data
 testing_data = data[-train,] # testing data

 #fit the tree model using training data
 tree_model = tree(new_ProductName ~.,data = training_data)
 summary(tree_model)
 plot(tree_model)
 text(tree_model, pretty = 0)
 out = predict(tree_model) # predict the training data
 # actuals
 input.newproduct = as.character(training_data$new_ProductName)
 # predicted
 pred.newproduct = colnames(out)[max.col(out,ties.method = c("first"))] 
 mean (input.newproduct != pred.newproduct) # misclassification % 

# Cross Validation to see how much we need to prune the tree
set.seed(400)
cv_Tree = cv.tree(tree_model, FUN = prune.misclass) # run cross validation
attach(cv_Tree)
plot(cv_Tree) # plot the CV
plot(size, dev, type = "b")
# set size corresponding to lowest value in the plot above.
treePruneMod = prune.misclass(tree_model, best = 9) plot(treePruneMod)
text(treePruneMod, pretty = 0)
out = predict(treePruneMod) # fit the pruned tree
# Predicted
pred.newproduct = colnames(out)[max.col(out,ties.method = c("random"))] 
# calculate Mis-classification error
mean(training_data$new_ProductName != pred.newproduct)
# Predict testData with Pruned tree
out = predict(treePruneMod, testing_data, type = "class") 

4) 我以前从未这样做过。我看了几个 youtube 视频并开始这样做。我欢迎很好的建议、解释和批评，请帮助我完成这个过程。这对我来说是一个挑战。

> table(data$PRODUCT_SUB_LINE_DESCR, data$new_ProductName)

                  no      yes
  Handpieces      164     0
  PRIVATE LABEL   0       14802
  SUNDRY          36467    0

Answer 1

简而言之，Trees 的工作原理是找到一个变量，该变量在每个节点处提供最佳*拆分（即区分两个类），如果分支是纯的，则终止分支。

对于您的问题，该算法评估“PRODUCT_SUB_LINE_DESCR”是最好的拆分变量，并在任一侧产生纯分支，因此不需要进一步拆分。

这是由于您定义类的方式以及您的直觉有些正确：

# I choose product name as my main attribute (maybe that is why it appears at 
# the root node?)
new_ProductName = ifelse( PRODUCT_SUB_LINE_DESCR == "PRIVATE 
                          LABEL","yes","no")

通过上面的代码/规则，您同时定义了您的类和最佳拆分。此时基于树的分类相当于简单的基于规则的分类。不是一个好主意。

您应该首先考虑您想要实现的目标。如果要在给定其他属性的情况下预测产品名称。然后从数据框中创建类（即“new_ProductName”）后删除“PRODUCT_SUB_LINE_DESCR”列，然后运行树分类。

*注意：最佳分割是基于信息增益或基尼指数。