Decision tree

Data Set Information: 2126 fetal cardiotocograms (CTGs) were automatically processed and the respective diagnostic features measured. The CTGs were also classified by three expert obstetricians and a consensus classification label assigned to each of them. NSP: 1. Normal, 2. Suspected, 3. pathology.

data <- read.csv("file:///C:/Users/badal/Desktop/datset_/Cardiotocographic.csv")
head(data)

str(data)

'data.frame':   2126 obs. of  22 variables:
 $ LB      : int  120 132 133 134 132 134 134 122 122 122 ...
 $ AC      : num  0 0.00638 0.00332 0.00256 0.00651 ...
 $ FM      : num  0 0 0 0 0 0 0 0 0 0 ...
 $ UC      : num  0 0.00638 0.00831 0.00768 0.00814 ...
 $ DL      : num  0 0.00319 0.00332 0.00256 0 ...
 $ DS      : num  0 0 0 0 0 0 0 0 0 0 ...
 $ DP      : num  0 0 0 0 0 ...
 $ ASTV    : int  73 17 16 16 16 26 29 83 84 86 ...
 $ MSTV    : num  0.5 2.1 2.1 2.4 2.4 5.9 6.3 0.5 0.5 0.3 ...
 $ ALTV    : int  43 0 0 0 0 0 0 6 5 6 ...
 $ MLTV    : num  2.4 10.4 13.4 23 19.9 0 0 15.6 13.6 10.6 ...
 $ Width   : int  64 130 130 117 117 150 150 68 68 68 ...
 $ Min     : int  62 68 68 53 53 50 50 62 62 62 ...
 $ Max     : int  126 198 198 170 170 200 200 130 130 130 ...
 $ Nmax    : int  2 6 5 11 9 5 6 0 0 1 ...
 $ Nzeros  : int  0 1 1 0 0 3 3 0 0 0 ...
 $ Mode    : int  120 141 141 137 137 76 71 122 122 122 ...
 $ Mean    : int  137 136 135 134 136 107 107 122 122 122 ...
 $ Median  : int  121 140 138 137 138 107 106 123 123 123 ...
 $ Variance: int  73 12 13 13 11 170 215 3 3 1 ...
 $ Tendency: int  1 0 0 1 1 0 0 1 1 1 ...
 $ NSP     : int  2 1 1 1 1 3 3 3 3 3 ...

summary(data)

       LB              AC                 FM                 UC                 DL          
 Min.   :106.0   Min.   :0.000000   Min.   :0.000000   Min.   :0.000000   Min.   :0.000000  
 1st Qu.:126.0   1st Qu.:0.000000   1st Qu.:0.000000   1st Qu.:0.001876   1st Qu.:0.000000  
 Median :133.0   Median :0.001630   Median :0.000000   Median :0.004482   Median :0.000000  
 Mean   :133.3   Mean   :0.003170   Mean   :0.009474   Mean   :0.004357   Mean   :0.001885  
 3rd Qu.:140.0   3rd Qu.:0.005631   3rd Qu.:0.002512   3rd Qu.:0.006525   3rd Qu.:0.003264  
 Max.   :160.0   Max.   :0.019284   Max.   :0.480634   Max.   :0.014925   Max.   :0.015385  
       DS                  DP                 ASTV            MSTV            ALTV       
 Min.   :0.000e+00   Min.   :0.0000000   Min.   :12.00   Min.   :0.200   Min.   : 0.000  
 1st Qu.:0.000e+00   1st Qu.:0.0000000   1st Qu.:32.00   1st Qu.:0.700   1st Qu.: 0.000  
 Median :0.000e+00   Median :0.0000000   Median :49.00   Median :1.200   Median : 0.000  
 Mean   :3.585e-06   Mean   :0.0001566   Mean   :46.99   Mean   :1.333   Mean   : 9.847  
 3rd Qu.:0.000e+00   3rd Qu.:0.0000000   3rd Qu.:61.00   3rd Qu.:1.700   3rd Qu.:11.000  
 Max.   :1.353e-03   Max.   :0.0053476   Max.   :87.00   Max.   :7.000   Max.   :91.000  
      MLTV            Width             Min              Max           Nmax            Nzeros       
 Min.   : 0.000   Min.   :  3.00   Min.   : 50.00   Min.   :122   Min.   : 0.000   Min.   : 0.0000  
 1st Qu.: 4.600   1st Qu.: 37.00   1st Qu.: 67.00   1st Qu.:152   1st Qu.: 2.000   1st Qu.: 0.0000  
 Median : 7.400   Median : 67.50   Median : 93.00   Median :162   Median : 3.000   Median : 0.0000  
 Mean   : 8.188   Mean   : 70.45   Mean   : 93.58   Mean   :164   Mean   : 4.068   Mean   : 0.3236  
 3rd Qu.:10.800   3rd Qu.:100.00   3rd Qu.:120.00   3rd Qu.:174   3rd Qu.: 6.000   3rd Qu.: 0.0000  
 Max.   :50.700   Max.   :180.00   Max.   :159.00   Max.   :238   Max.   :18.000   Max.   :10.0000  
      Mode            Mean           Median         Variance         Tendency            NSP       
 Min.   : 60.0   Min.   : 73.0   Min.   : 77.0   Min.   :  0.00   Min.   :-1.0000   Min.   :1.000  
 1st Qu.:129.0   1st Qu.:125.0   1st Qu.:129.0   1st Qu.:  2.00   1st Qu.: 0.0000   1st Qu.:1.000  
 Median :139.0   Median :136.0   Median :139.0   Median :  7.00   Median : 0.0000   Median :1.000  
 Mean   :137.5   Mean   :134.6   Mean   :138.1   Mean   : 18.81   Mean   : 0.3203   Mean   :1.304  
 3rd Qu.:148.0   3rd Qu.:145.0   3rd Qu.:148.0   3rd Qu.: 24.00   3rd Qu.: 1.0000   3rd Qu.:1.000  
 Max.   :187.0   Max.   :182.0   Max.   :186.0   Max.   :269.00   Max.   : 1.0000   Max.   :3.000  

any(is.na(data))

[1] FALSE

data$NSP <- factor(data$NSP)

partition data into traning and validation sets

set.seed(1234)

index <- sample(2, nrow(data), replace = T, prob = c(0.80, 0.20))
train <- data[index==1,]
validate <- data[index==2,]

library(party)

package 㤼㸱party㤼㸲 was built under R version 3.6.1Loading required package: grid
Loading required package: mvtnorm
Loading required package: modeltools
Loading required package: stats4
Loading required package: strucchange
package 㤼㸱strucchange㤼㸲 was built under R version 3.6.1Loading required package: zoo
package 㤼㸱zoo㤼㸲 was built under R version 3.6.1
Attaching package: 㤼㸱zoo㤼㸲

The following objects are masked from 㤼㸱package:base㤼㸲:

    as.Date, as.Date.numeric

Loading required package: sandwich
package 㤼㸱sandwich㤼㸲 was built under R version 3.6.1

tree <- ctree(NSP~LB+AC+FM, data = train, controls = ctree_control(mincriterion=0.99, minsplit=500))
tree

     Conditional inference tree with 5 terminal nodes

Response:  NSP 
Inputs:  LB, AC, FM 
Number of observations:  1718 

1) AC <= 0.000834028; criterion = 1, statistic = 263.403
  2) LB <= 136; criterion = 1, statistic = 131.511
    3)*  weights = 416 
  2) LB > 136
    4)*  weights = 314 
1) AC > 0.000834028
  5) AC <= 0.002209945; criterion = 1, statistic = 52.155
    6)*  weights = 188 
  5) AC > 0.002209945
    7) LB <= 110; criterion = 1, statistic = 18.889
      8)*  weights = 18 
    7) LB > 110
      9)*  weights = 782 

plot(tree)

Predict

pred <- predict(tree,validate)
pred

  [1] 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 1 1 1 1 1 1
 [50] 1 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 1 1 1 2 2 1 1 2 2 2 1 2 2 1 2 2 1 2 2 1 1 1 2 2 1 1 1 1 1 1 1
 [99] 1 1 1 2 1 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 1 1 1
[148] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 2 2 1 2 2 2 2 1 2 1 2 2 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1
[197] 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1
[246] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 1 1 1 2 1 1 1 1 2 2 2
[295] 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[344] 1 1 1 1 1 1 2 2 1 1 2 2 2 1 1 1 1 1 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[393] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2
Levels: 1 2 3

Decision tree with R-part

library(rpart)
library(rpart.plot)

package 㤼㸱rpart.plot㤼㸲 was built under R version 3.6.1

tree1 <- rpart(NSP~LB+AC+FM, train)
rpart.plot(tree1)

rpart.plot(tree1, extra = 1)

rpart.plot(tree1, extra = 2)

pred2 <- predict(tree1, validate)
head(pred2,15)

           1          2          3
5  0.9453441 0.03340081 0.02125506
14 0.9453441 0.03340081 0.02125506
16 0.9453441 0.03340081 0.02125506
26 0.7111111 0.09135802 0.19753086
28 0.7111111 0.09135802 0.19753086
29 0.7111111 0.09135802 0.19753086
39 0.9453441 0.03340081 0.02125506
40 0.9453441 0.03340081 0.02125506
60 0.9453441 0.03340081 0.02125506
61 0.9453441 0.03340081 0.02125506
72 0.9453441 0.03340081 0.02125506
81 0.2584270 0.60674157 0.13483146
86 0.9453441 0.03340081 0.02125506
90 0.9453441 0.03340081 0.02125506
92 0.3523810 0.59047619 0.05714286

table <- table(predict(tree), train$NSP)
table

   
       1    2    3
  1 1222   70  112
  2  126  156   32
  3    0    0    0

sum(diag(table))/sum(table)

[1] 0.8020955

1-sum(diag(table))/sum(table)

[1] 0.1979045

misclassification in validation set

testpred <- predict(tree, newdata = validate)
tab <- table(testpred, validate$NSP)
tab

        
testpred   1   2   3
       1 274  21  28
       2  33  48   4
       3   0   0   0

1-sum(diag(tab))/sum(tab)

[1] 0.2107843