Data 622- Final Project
Andreina Arias
2025-12-04
Modeling using decision tree and neural network.
Dataset from Kaggle: https://www.kaggle.com/datasets/yasserh/breast-cancer-dataset?resource=download&select=breast-cancer.csv License CC0: Public Domain
Breastdata<-read.csv("https://raw.githubusercontent.com/Andreina-A/Data-622/refs/heads/main/breast-cancer.csv")
head(Breastdata)## id diagnosis radius_mean texture_mean perimeter_mean area_mean
## 1 842302 M 17.99 10.38 122.80 1001.0
## 2 842517 M 20.57 17.77 132.90 1326.0
## 3 84300903 M 19.69 21.25 130.00 1203.0
## 4 84348301 M 11.42 20.38 77.58 386.1
## 5 84358402 M 20.29 14.34 135.10 1297.0
## 6 843786 M 12.45 15.70 82.57 477.1
## smoothness_mean compactness_mean concavity_mean concave.points_mean
## 1 0.11840 0.27760 0.3001 0.14710
## 2 0.08474 0.07864 0.0869 0.07017
## 3 0.10960 0.15990 0.1974 0.12790
## 4 0.14250 0.28390 0.2414 0.10520
## 5 0.10030 0.13280 0.1980 0.10430
## 6 0.12780 0.17000 0.1578 0.08089
## symmetry_mean fractal_dimension_mean radius_se texture_se perimeter_se
## 1 0.2419 0.07871 1.0950 0.9053 8.589
## 2 0.1812 0.05667 0.5435 0.7339 3.398
## 3 0.2069 0.05999 0.7456 0.7869 4.585
## 4 0.2597 0.09744 0.4956 1.1560 3.445
## 5 0.1809 0.05883 0.7572 0.7813 5.438
## 6 0.2087 0.07613 0.3345 0.8902 2.217
## area_se smoothness_se compactness_se concavity_se concave.points_se
## 1 153.40 0.006399 0.04904 0.05373 0.01587
## 2 74.08 0.005225 0.01308 0.01860 0.01340
## 3 94.03 0.006150 0.04006 0.03832 0.02058
## 4 27.23 0.009110 0.07458 0.05661 0.01867
## 5 94.44 0.011490 0.02461 0.05688 0.01885
## 6 27.19 0.007510 0.03345 0.03672 0.01137
## symmetry_se fractal_dimension_se radius_worst texture_worst perimeter_worst
## 1 0.03003 0.006193 25.38 17.33 184.60
## 2 0.01389 0.003532 24.99 23.41 158.80
## 3 0.02250 0.004571 23.57 25.53 152.50
## 4 0.05963 0.009208 14.91 26.50 98.87
## 5 0.01756 0.005115 22.54 16.67 152.20
## 6 0.02165 0.005082 15.47 23.75 103.40
## area_worst smoothness_worst compactness_worst concavity_worst
## 1 2019.0 0.1622 0.6656 0.7119
## 2 1956.0 0.1238 0.1866 0.2416
## 3 1709.0 0.1444 0.4245 0.4504
## 4 567.7 0.2098 0.8663 0.6869
## 5 1575.0 0.1374 0.2050 0.4000
## 6 741.6 0.1791 0.5249 0.5355
## concave.points_worst symmetry_worst fractal_dimension_worst
## 1 0.2654 0.4601 0.11890
## 2 0.1860 0.2750 0.08902
## 3 0.2430 0.3613 0.08758
## 4 0.2575 0.6638 0.17300
## 5 0.1625 0.2364 0.07678
## 6 0.1741 0.3985 0.12440Data Exploratory
The data set had 569 observations and 32 variables.
str(Breastdata)## 'data.frame': 569 obs. of 32 variables:
## $ id : int 842302 842517 84300903 84348301 84358402 843786 844359 84458202 844981 84501001 ...
## $ diagnosis : chr "M" "M" "M" "M" ...
## $ radius_mean : num 18 20.6 19.7 11.4 20.3 ...
## $ texture_mean : num 10.4 17.8 21.2 20.4 14.3 ...
## $ perimeter_mean : num 122.8 132.9 130 77.6 135.1 ...
## $ area_mean : num 1001 1326 1203 386 1297 ...
## $ smoothness_mean : num 0.1184 0.0847 0.1096 0.1425 0.1003 ...
## $ compactness_mean : num 0.2776 0.0786 0.1599 0.2839 0.1328 ...
## $ concavity_mean : num 0.3001 0.0869 0.1974 0.2414 0.198 ...
## $ concave.points_mean : num 0.1471 0.0702 0.1279 0.1052 0.1043 ...
## $ symmetry_mean : num 0.242 0.181 0.207 0.26 0.181 ...
## $ fractal_dimension_mean : num 0.0787 0.0567 0.06 0.0974 0.0588 ...
## $ radius_se : num 1.095 0.543 0.746 0.496 0.757 ...
## $ texture_se : num 0.905 0.734 0.787 1.156 0.781 ...
## $ perimeter_se : num 8.59 3.4 4.58 3.44 5.44 ...
## $ area_se : num 153.4 74.1 94 27.2 94.4 ...
## $ smoothness_se : num 0.0064 0.00522 0.00615 0.00911 0.01149 ...
## $ compactness_se : num 0.049 0.0131 0.0401 0.0746 0.0246 ...
## $ concavity_se : num 0.0537 0.0186 0.0383 0.0566 0.0569 ...
## $ concave.points_se : num 0.0159 0.0134 0.0206 0.0187 0.0188 ...
## $ symmetry_se : num 0.03 0.0139 0.0225 0.0596 0.0176 ...
## $ fractal_dimension_se : num 0.00619 0.00353 0.00457 0.00921 0.00511 ...
## $ radius_worst : num 25.4 25 23.6 14.9 22.5 ...
## $ texture_worst : num 17.3 23.4 25.5 26.5 16.7 ...
## $ perimeter_worst : num 184.6 158.8 152.5 98.9 152.2 ...
## $ area_worst : num 2019 1956 1709 568 1575 ...
## $ smoothness_worst : num 0.162 0.124 0.144 0.21 0.137 ...
## $ compactness_worst : num 0.666 0.187 0.424 0.866 0.205 ...
## $ concavity_worst : num 0.712 0.242 0.45 0.687 0.4 ...
## $ concave.points_worst : num 0.265 0.186 0.243 0.258 0.163 ...
## $ symmetry_worst : num 0.46 0.275 0.361 0.664 0.236 ...
## $ fractal_dimension_worst: num 0.1189 0.089 0.0876 0.173 0.0768 ...summary(Breastdata)## id diagnosis radius_mean texture_mean
## Min. : 8670 Length:569 Min. : 6.981 Min. : 9.71
## 1st Qu.: 869218 Class :character 1st Qu.:11.700 1st Qu.:16.17
## Median : 906024 Mode :character Median :13.370 Median :18.84
## Mean : 30371831 Mean :14.127 Mean :19.29
## 3rd Qu.: 8813129 3rd Qu.:15.780 3rd Qu.:21.80
## Max. :911320502 Max. :28.110 Max. :39.28
## perimeter_mean area_mean smoothness_mean compactness_mean
## Min. : 43.79 Min. : 143.5 Min. :0.05263 Min. :0.01938
## 1st Qu.: 75.17 1st Qu.: 420.3 1st Qu.:0.08637 1st Qu.:0.06492
## Median : 86.24 Median : 551.1 Median :0.09587 Median :0.09263
## Mean : 91.97 Mean : 654.9 Mean :0.09636 Mean :0.10434
## 3rd Qu.:104.10 3rd Qu.: 782.7 3rd Qu.:0.10530 3rd Qu.:0.13040
## Max. :188.50 Max. :2501.0 Max. :0.16340 Max. :0.34540
## concavity_mean concave.points_mean symmetry_mean fractal_dimension_mean
## Min. :0.00000 Min. :0.00000 Min. :0.1060 Min. :0.04996
## 1st Qu.:0.02956 1st Qu.:0.02031 1st Qu.:0.1619 1st Qu.:0.05770
## Median :0.06154 Median :0.03350 Median :0.1792 Median :0.06154
## Mean :0.08880 Mean :0.04892 Mean :0.1812 Mean :0.06280
## 3rd Qu.:0.13070 3rd Qu.:0.07400 3rd Qu.:0.1957 3rd Qu.:0.06612
## Max. :0.42680 Max. :0.20120 Max. :0.3040 Max. :0.09744
## radius_se texture_se perimeter_se area_se
## Min. :0.1115 Min. :0.3602 Min. : 0.757 Min. : 6.802
## 1st Qu.:0.2324 1st Qu.:0.8339 1st Qu.: 1.606 1st Qu.: 17.850
## Median :0.3242 Median :1.1080 Median : 2.287 Median : 24.530
## Mean :0.4052 Mean :1.2169 Mean : 2.866 Mean : 40.337
## 3rd Qu.:0.4789 3rd Qu.:1.4740 3rd Qu.: 3.357 3rd Qu.: 45.190
## Max. :2.8730 Max. :4.8850 Max. :21.980 Max. :542.200
## smoothness_se compactness_se concavity_se concave.points_se
## Min. :0.001713 Min. :0.002252 Min. :0.00000 Min. :0.000000
## 1st Qu.:0.005169 1st Qu.:0.013080 1st Qu.:0.01509 1st Qu.:0.007638
## Median :0.006380 Median :0.020450 Median :0.02589 Median :0.010930
## Mean :0.007041 Mean :0.025478 Mean :0.03189 Mean :0.011796
## 3rd Qu.:0.008146 3rd Qu.:0.032450 3rd Qu.:0.04205 3rd Qu.:0.014710
## Max. :0.031130 Max. :0.135400 Max. :0.39600 Max. :0.052790
## symmetry_se fractal_dimension_se radius_worst texture_worst
## Min. :0.007882 Min. :0.0008948 Min. : 7.93 Min. :12.02
## 1st Qu.:0.015160 1st Qu.:0.0022480 1st Qu.:13.01 1st Qu.:21.08
## Median :0.018730 Median :0.0031870 Median :14.97 Median :25.41
## Mean :0.020542 Mean :0.0037949 Mean :16.27 Mean :25.68
## 3rd Qu.:0.023480 3rd Qu.:0.0045580 3rd Qu.:18.79 3rd Qu.:29.72
## Max. :0.078950 Max. :0.0298400 Max. :36.04 Max. :49.54
## perimeter_worst area_worst smoothness_worst compactness_worst
## Min. : 50.41 Min. : 185.2 Min. :0.07117 Min. :0.02729
## 1st Qu.: 84.11 1st Qu.: 515.3 1st Qu.:0.11660 1st Qu.:0.14720
## Median : 97.66 Median : 686.5 Median :0.13130 Median :0.21190
## Mean :107.26 Mean : 880.6 Mean :0.13237 Mean :0.25427
## 3rd Qu.:125.40 3rd Qu.:1084.0 3rd Qu.:0.14600 3rd Qu.:0.33910
## Max. :251.20 Max. :4254.0 Max. :0.22260 Max. :1.05800
## concavity_worst concave.points_worst symmetry_worst fractal_dimension_worst
## Min. :0.0000 Min. :0.00000 Min. :0.1565 Min. :0.05504
## 1st Qu.:0.1145 1st Qu.:0.06493 1st Qu.:0.2504 1st Qu.:0.07146
## Median :0.2267 Median :0.09993 Median :0.2822 Median :0.08004
## Mean :0.2722 Mean :0.11461 Mean :0.2901 Mean :0.08395
## 3rd Qu.:0.3829 3rd Qu.:0.16140 3rd Qu.:0.3179 3rd Qu.:0.09208
## Max. :1.2520 Max. :0.29100 Max. :0.6638 Max. :0.20750Confirmed that there were no missing data.
sum(is.na(Breastdata))## [1] 0Data Preparation
Breastdata<-Breastdata|>
select(-id)Binary classification will be used, where Malignant will be 1 and bengin will be 0.
Breastdata$diagnosis<-ifelse(Breastdata$diagnosis == "M", 1,0)Used pairwise function to check for nonlinear relationships, based on the plot there are clouds and curved relationships showing evidence of non linearity.
pairs(Breastdata[,1:6], col=Breastdata$diagnosis+1)
Since I will be using neural network I have to scale the numeric features without scaling the target variable
predictors<-Breastdata[, names(Breastdata) !="diagnosis"]
scaled_predictor<-as.data.frame(scale(predictors))
scaled_breast<-cbind(diagnosis=Breastdata$diagnosis,scaled_predictor)Train-test split using 80% for training and 20% for testing
set.seed(123)
trainIndex<-createDataPartition(Breastdata$diagnosis, p=.8, list=FALSE)
train<-Breastdata[trainIndex, ]
test<-Breastdata[-trainIndex, ]
train_scaled<-scaled_breast[trainIndex, ]
test_scaled<-scaled_breast[-trainIndex, ]Decision Tree Model
DT_Model<-rpart(diagnosis~., data = train, method = "class")Decision Tree Plot
rpart.plot(DT_Model, main="Decision Tree for Breast Cancer Classification")
#Predictions
Tree_pred<-predict(DT_Model, test, type="class")Evaluation
Confusion Matrix
cat("\nDecision Tree Confusion Matrix\n")##
## Decision Tree Confusion MatrixConf_matrix_DT<-confusionMatrix(as.factor(Tree_pred), as.factor(test$diagnosis))
print(Conf_matrix_DT)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 56 4
## 1 4 49
##
## Accuracy : 0.9292
## 95% CI : (0.8653, 0.9689)
## No Information Rate : 0.531
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.8579
##
## Mcnemar's Test P-Value : 1
##
## Sensitivity : 0.9333
## Specificity : 0.9245
## Pos Pred Value : 0.9333
## Neg Pred Value : 0.9245
## Prevalence : 0.5310
## Detection Rate : 0.4956
## Detection Prevalence : 0.5310
## Balanced Accuracy : 0.9289
##
## 'Positive' Class : 0
## ROC Curve for the Decision Tree
Tree_prob<-predict(DT_Model, test, type="prob")[,2]
roc_DT<-roc(test$diagnosis, Tree_prob)## Setting levels: control = 0, case = 1## Setting direction: controls < casesplot(roc_DT, main="Decision Tree ROC Curve", print.auc=TRUE, col="blue", lwd=2)
auc_DT<-auc(roc_DT)
auc_DT## Area under the curve: 0.9585Neural Network Model
#Neuralnet would require formula syntax
features<-names(train_scaled)[names(train_scaled) != "diagnosis"]
formula_n<-as.formula(
paste("diagnosis~", paste(features, collapse= " + "))
)#training (with 2 hidden layers of 15 and 5 neurons as the dataset has many variables)
set.seed(123)
nn_model<-neuralnet(formula_n, data=train_scaled, hidden=c(15,5), linear.output=FALSE, lifesign = "minimal", stepma= 1e6)## hidden: 15, 5 thresh: 0.01 rep: 1/1 steps: 55 error: 0.50434 time: 0.1 secsNeural Network Plot
plot(nn_model, rep="best")
#prediction
nn_pred_prob<-compute(nn_model, test_scaled[, features])$net.result
nn_pred<- ifelse(nn_pred_prob> 0.5, 1, 0)Evaluation
Confusion Matrix for Neural Network
cat("\nNeural Network Confusion Matrix\n")##
## Neural Network Confusion MatrixConf_matrix_nn<-confusionMatrix(as.factor(nn_pred), as.factor(test$diagnosis))
print(Conf_matrix_nn)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 60 2
## 1 0 51
##
## Accuracy : 0.9823
## 95% CI : (0.9375, 0.9978)
## No Information Rate : 0.531
## P-Value [Acc > NIR] : <2e-16
##
## Kappa : 0.9644
##
## Mcnemar's Test P-Value : 0.4795
##
## Sensitivity : 1.0000
## Specificity : 0.9623
## Pos Pred Value : 0.9677
## Neg Pred Value : 1.0000
## Prevalence : 0.5310
## Detection Rate : 0.5310
## Detection Prevalence : 0.5487
## Balanced Accuracy : 0.9811
##
## 'Positive' Class : 0
## Neural Network ROC Curve
roc_nn<-roc(test$diagnosis, nn_pred_prob)## Setting levels: control = 0, case = 1## Warning in roc.default(test$diagnosis, nn_pred_prob): Deprecated use a matrix
## as predictor. Unexpected results may be produced, please pass a numeric vector.## Setting direction: controls < casesplot(roc_nn, main= "Neural Network ROC Curve", print.auc=TRUE, col="red", lwd=2)
auc_nn<-auc(roc_nn)
auc_nn## Area under the curve: 0.9994Combined Plot
A combined ROC plot was generated to compare the discriminative ability of both models visually. Each model’s ROC curve appears in a different color.
plot(roc_DT, col="blue", lwd=2, main="ROC: Decision Tree vs Neural Network")
plot(roc_nn, col="red", add=TRUE)
legend("bottomright", legend=c("Decision Tree", "Neural Network"), col = c("blue","red"), lwd=2)
AUC Results
AUC values provide a numerical summary of overall performance
cat("\n--- MODEL PERFORMANCE ---\n")##
## --- MODEL PERFORMANCE ---cat("Decision Tree AUC:", auc_DT, "\n")## Decision Tree AUC: 0.9584906cat("Neural Network AUC:", auc_nn, "\n")## Neural Network AUC: 0.9993711