Supervised 2

Decision Tree

2.1 Decision Tree

• 순수도를 더 이상 높일 수 없거나, 말단 노드에 포함된 개체의 수가 사전에 정한 최소값에 도달하였을 때, 노드의 깊이가 사전에 정해놓은 한계에 이를때 재귀적 분할 반복이 일어난다.

지니척도

• 복원 추출했을때의 동일 범주가 개체가 선택될 확률
• 지니계수가 크면, 순수도가 낮음 : 균등할수록 0.5 에 수렴
• 순수도가 높은 변수로 가지치기
• 순수도 = 1- 불순도

엔트로피

• 무질서의 정도
• 엔트로피가 클수록 순수도가 낮음
• 엔트로피가 가장 작은 예측 변수와 이떄의 최적의 분리 규칙에 따라 자식 마디를 형성함

2.1.1 Binary Prediction

setwd("C:/Users/Administrator/Desktop/R Analysis")

read.csv('autoparts.csv') -> autopart

#---------------------------------------------------
#   Selecting Features 
#----------------------------------------------------

autopart %>% 
  filter(prod_no == "90784-76001") %>% 
  filter(c_thickness < 1000) %>% 
  filter(highpressure_time < 1000) %>%  
  mutate(target = ifelse(c_thickness<20| c_thickness>32,1 ,0) %>% 
           as.factor()) %>% 
  select(-prod_no, -c_thickness) -> df


#---------------------------------------------------
#   train/test 
#----------------------------------------------------

set.seed(2022)

sort(sample(nrow(df), nrow(df)*0.7)) -> flag

train <- df[flag,]
test <- df[-flag,]

#---------------------------------------------------
#   tree()
#----------------------------------------------------


tree(target~., data=train) -> treeRaw

plot(treeRaw)
text(treeRaw)

가지치기 기준 9~10개

• 너무 많이 가지기를 하면 모델이 복잡해지기 때문에 9개로 지정

cv.tree(treeRaw, FUN = prune.misclass) -> cv_tree

plot(cv_tree)

prune.tree(treeRaw, best=9)->prune_tree_nine

plot(prune_tree_nine)
text(prune_tree_nine)

prune.tree(treeRaw, best=3)->prune_tree_three

plot(prune_tree_three)
text(prune_tree_three)

#---------------------------------------------------
#   가지 9개 
#----------------------------------------------------
predict(prune_tree_nine, test, type = 'class') -> pred_test_nine
confusionMatrix(pred_test_nine, test$target)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1
##          0 5415  253
##          1  260  600
##                                           
##                Accuracy : 0.9214          
##                  95% CI : (0.9146, 0.9278)
##     No Information Rate : 0.8693          
##     P-Value [Acc > NIR] : <2e-16          
##                                           
##                   Kappa : 0.6553          
##                                           
##  Mcnemar's Test P-Value : 0.7911          
##                                           
##             Sensitivity : 0.9542          
##             Specificity : 0.7034          
##          Pos Pred Value : 0.9554          
##          Neg Pred Value : 0.6977          
##              Prevalence : 0.8693          
##          Detection Rate : 0.8295          
##    Detection Prevalence : 0.8683          
##       Balanced Accuracy : 0.8288          
##                                           
##        'Positive' Class : 0               
## 

#---------------------------------------------------
#   가지 3개 
#----------------------------------------------------
predict(prune_tree_three, test, type = 'class') -> pred_test_three
confusionMatrix(pred_test_three, test$target)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1
##          0 5585  706
##          1   90  147
##                                           
##                Accuracy : 0.8781          
##                  95% CI : (0.8699, 0.8859)
##     No Information Rate : 0.8693          
##     P-Value [Acc > NIR] : 0.0183          
##                                           
##                   Kappa : 0.2257          
##                                           
##  Mcnemar's Test P-Value : <2e-16          
##                                           
##             Sensitivity : 0.9841          
##             Specificity : 0.1723          
##          Pos Pred Value : 0.8878          
##          Neg Pred Value : 0.6203          
##              Prevalence : 0.8693          
##          Detection Rate : 0.8555          
##    Detection Prevalence : 0.9637          
##       Balanced Accuracy : 0.5782          
##                                           
##        'Positive' Class : 0               
## 

• 9개가 더 높은 정확도를 보여준다.

library(Epi)
#---------------------------------------------------
#   가지 9개 
#----------------------------------------------------

ROC(test=pred_test_nine, stat=test$target, plot="ROC", AUC=T)

#---------------------------------------------------
#   가지 3개 
#----------------------------------------------------

ROC(test=pred_test_three, stat=test$target, plot="ROC", AUC=T)

예측하기

new.data=data.frame(fix_time=87,a_speed=0.609,b_speed=1.715,separation=242.7,s_separation=657.5,rate_terms=95,mpa=78,load_time=18.1,highpressure_time=82)


predict(prune_tree_nine, newdata = new.data, type="class")

## [1] 0
## Levels: 0 1

predict(prune_tree_three, newdata = new.data, type="class")

## [1] 0
## Levels: 0 1

2.1.1 multile level Prediction

Target 을 1,2,3 으로 나눈다.

autopart %>% 
  filter(prod_no == "90784-76001") %>% 
  filter(c_thickness < 1000) %>% 
  filter(highpressure_time < 1000) %>%  
  mutate(target = ifelse(c_thickness <20,1,
                         ifelse(c_thickness < 32, 2,3)) %>% 
             as.factor()) %>% 
  select(-prod_no, -c_thickness) -> df1



sort(sample(nrow(df1), nrow(df1)*0.7)) -> fla

train <-df1[fla,]
test <- df1[-fla,]



tree(target~., data=train) -> raw_tree

plot(raw_tree)
text(raw_tree)

# 오분류 기준 가지치기 기준 선정 

cv.tree(raw_tree, FUN=prune.misclass) ->cv_tree

plot(cv_tree)

prune.misclass(raw_tree, best=9) ->pruned_tree

plot(pruned_tree)
text(pruned_tree)

predict(pruned_tree, test, type='class') -> pred_tree_9

confusionMatrix(pred_tree_9, test$target)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    1    2    3
##          1  363  185    0
##          2  265 5351    6
##          3    4  141  213
## 
## Overall Statistics
##                                           
##                Accuracy : 0.9079          
##                  95% CI : (0.9007, 0.9148)
##     No Information Rate : 0.8696          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.6181          
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
## 
## Statistics by Class:
## 
##                      Class: 1 Class: 2 Class: 3
## Sensitivity           0.57437   0.9426  0.97260
## Specificity           0.96862   0.6816  0.97702
## Pos Pred Value        0.66241   0.9518  0.59497
## Neg Pred Value        0.95502   0.6402  0.99903
## Prevalence            0.09681   0.8696  0.03355
## Detection Rate        0.05561   0.8197  0.03263
## Detection Prevalence  0.08395   0.8612  0.05484
## Balanced Accuracy     0.77149   0.8121  0.97481

ROC(test=pred_tree_9, stat=test$target, plot="ROC", AUC=T)

2.1.2 연속형 변수에 대한 Decision Tree

c_thinkess 의 수를 예측한다.

autopart %>% 
  select(-prod_no) ->df2


#--------------------------------------
#  Train/Test 구분 
#---------------------------------------

sort(sample(nrow(df2), nrow(df2)*0.7)) -> fl

df2[fl,] -> train
df2[-fl,] -> test

#--------------------------------------
#  모델 생성 
#---------------------------------------

tree(c_thickness~fix_time+a_speed+b_speed+separation+s_separation+rate_terms+
           mpa+load_time+highpressure_time,data=train) -> df2_tree

plot(df2_tree)
text(df2_tree)

#--------------------------------------
#  예측
#---------------------------------------

predict(df2_tree, test) -> pred_df2

head(test$c_thickness)

## [1] 24.1 23.1 20.5 34.3 36.7 33.8

#--------------------------------------
#  Predict 
#---------------------------------------

new.data=data.frame(fix_time=c(87,85.6),a_speed=c(0.609,0.472),b_speed=c(1.715,1.685),separation=c(242.7,243.4),s_separation=c(657.5,657.9),rate_terms=c(95,95),mpa=c(78,28.8),load_time=c(18.1,18.2),highpressure_time=c(82,60))


predict(df2_tree, newdata=new.data)

## [1] 24.11343 24.11343

KNN

• 새로운 점이 주어졌을 때, 그 점으로부터 가까운 점 K개를 이용
• 오분류율이 낮은 K를 선정
• 범주, 연속형 변수 사용이 가능하지만, X가 연속형인것들

#--------------------------------------
# 1.  Data preparation  
#---------------------------------------


autopart %>% 
  filter(prod_no == "90784-76001") %>% 
  filter(c_thickness < 1000) %>% 
  filter(highpressure_time < 1000) %>%  
  mutate(target = ifelse(c_thickness<20| c_thickness>32,1 ,0) %>% 
           as.factor()) %>% 
  select(-prod_no, -c_thickness) -> df_knn

#--------------------------------------
#  2. Train/Test spereration 
#---------------------------------------

sort(sample(nrow(df_knn), nrow(df_knn)*0.7)) -> fl

df_knn[fl,] -> train
df_knn[-fl,] -> test

#--------------------------------------
#  3. Modelling 
#---------------------------------------

ctrl <- trainControl(method = "repeatedcv", repeats = 5)

customGrid <- expand.grid(k=1:10)

train(target~., 
      data=train, 
      method ="knn", 
      preProcess= c("center","scale"), 
      tuneGrid = customGrid,
      metric ="Accuracy") -> knn_fit


knn_fit

## k-Nearest Neighbors 
## 
## 15229 samples
##     9 predictor
##     2 classes: '0', '1' 
## 
## Pre-processing: centered (9), scaled (9) 
## Resampling: Bootstrapped (25 reps) 
## Summary of sample sizes: 15229, 15229, 15229, 15229, 15229, 15229, ... 
## Resampling results across tuning parameters:
## 
##   k   Accuracy   Kappa    
##    1  0.8865206  0.4733409
##    2  0.8819025  0.4517897
##    3  0.8850261  0.4539919
##    4  0.8872547  0.4541364
##    5  0.8912186  0.4596264
##    6  0.8930416  0.4608583
##    7  0.8949264  0.4620850
##    8  0.8952960  0.4589429
##    9  0.8965841  0.4591509
##   10  0.8963488  0.4546513
## 
## Accuracy was used to select the optimal model using the largest value.
## The final value used for the model was k = 9.

plot(knn_fit)

#--------------------------------------
#  3. optimal K 
#---------------------------------------

knn_fit$bestTune

##   k
## 9 9

#--------------------------------------
#  4. predict 
#---------------------------------------

predict(knn_fit, newdata = test) -> pred_knn

confusionMatrix(pred_knn, test$target)

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1
##          0 5574  471
##          1  108  375
##                                           
##                Accuracy : 0.9113          
##                  95% CI : (0.9041, 0.9181)
##     No Information Rate : 0.8704          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.519           
##                                           
##  Mcnemar's Test P-Value : < 2.2e-16       
##                                           
##             Sensitivity : 0.9810          
##             Specificity : 0.4433          
##          Pos Pred Value : 0.9221          
##          Neg Pred Value : 0.7764          
##              Prevalence : 0.8704          
##          Detection Rate : 0.8539          
##    Detection Prevalence : 0.9260          
##       Balanced Accuracy : 0.7121          
##                                           
##        'Positive' Class : 0               
## 

varImp(knn_fit, scale=FALSE) ->imp_knn
plot(imp_knn)

ROC(test=pred_knn, stat=test$target, plot="ROC")

i{r}