INTRODUCTION: Features are computed from a digitized image of a fine needle aspirate (FNA) of a breast mass. They describe characteristics of the cell nuclei present in the image. n the 3-dimensional space is that described in: [K. P. Bennett and O. L. Mangasarian: “Robust Linear Programming Discrimination of Two Linearly Inseparable Sets”, Optimization Methods and Software 1, 1992, 23-34]. This database is also available through the UW CS ftp server: ftp ftp.cs.wisc.edu cd math-prog/cpo-dataset/machine-learn/WDBC/ Also can be found on UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29 Attribute Information: 1) ID number 2) Diagnosis (M = malignant, B = benign) 3-32) Ten real-valued features are computed for each cell nucleus: a) radius (mean of distances from center to points on the perimeter) b) texture (standard deviation of gray-scale values) c) perimeter d) area e) smoothness (local variation in radius lengths) f) compactness (perimeter^2 / area - 1.0) g) concavity (severity of concave portions of the contour) h) concave points (number of concave portions of the contour) i) symmetry j) fractal dimension (“coastline approximation” - 1)
largest values) of these features were computed for each image, resulting in 30 features. For instance, field 3 is Mean Radius, field 13 is Radius SE, field 23 is Worst Radius. All feature values are recoded with four significant digits. Missing attribute values: none Class distribution: 357 benign, 212 malignant
GOAL: Predict the status of breast cancer using predictive modeling
bcd <- read.csv("data.csv", stringsAsFactors = FALSE)
#print(bcd)view the top few rows of the dataset.
head(bcd)## 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 X
## 1 0.2654 0.4601 0.11890 NA
## 2 0.1860 0.2750 0.08902 NA
## 3 0.2430 0.3613 0.08758 NA
## 4 0.2575 0.6638 0.17300 NA
## 5 0.1625 0.2364 0.07678 NA
## 6 0.1741 0.3985 0.12440 NAsince we will not be needing the ID column, let’s drop it
bcd <- bcd[-1 ]For our predicted variables, we set the B and M as factors with labels as Benign and Malignant
bcd$diagnosis <- factor(bcd$diagnosis, levels = c("B","M"), labels = c("Benign", "Malignant"))Since KNN is a distance-based algorithm, it is a good idea to scale all our numeric features. That way a few features won’t dominate in the distance calculations. We first create a function and then apply that function to all our features (column 2 to 31).
normalize<-function(x)
{
return((x-min(x))/max(x)-min(x))
}
bcd_n<-as.data.frame(lapply(bcd[,2:31], normalize))To implement KNN, we need to install a package called class.
library("class")## Warning: package 'class' was built under R version 4.0.5To check the performance of the model, our data is divided into training and test set. We train the model on the training set and validate the test set.
bcd_train<-bcd_n[1:469,]
dim(bcd_train)## [1] 469 30bcd_test<-bcd_n[470:569,]
dim(bcd_test)## [1] 100 30bcd_train_label <- bcd[1:469,1]
bcd_test_label <- bcd[470:569,1]As you can see, 469 points are used in the training set and the rest in the test set. Finally, we can generate the predictions
bcd_pred<-knn(bcd_train,bcd_test,bcd_train_label,k=21)Here, the model is trained on the bcd_train and bcd_train_label and predictions are generated on bcd_test. The number of neighbors or K is set to 21. The performance of the model is evaluated then.
library("class")
library("gmodels")## Warning: package 'gmodels' was built under R version 4.0.5CrossTable(bcd_test_label,bcd_pred,prop.chisq = FALSE)##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 100
##
##
## | bcd_pred
## bcd_test_label | Benign | Malignant | Row Total |
## ---------------|-----------|-----------|-----------|
## Benign | 77 | 0 | 77 |
## | 1.000 | 0.000 | 0.770 |
## | 0.975 | 0.000 | |
## | 0.770 | 0.000 | |
## ---------------|-----------|-----------|-----------|
## Malignant | 2 | 21 | 23 |
## | 0.087 | 0.913 | 0.230 |
## | 0.025 | 1.000 | |
## | 0.020 | 0.210 | |
## ---------------|-----------|-----------|-----------|
## Column Total | 79 | 21 | 100 |
## | 0.790 | 0.210 | |
## ---------------|-----------|-----------|-----------|
##
## The results are tabulated above. As we can see, out of 77 actual Benign, 0 were misclassified as Malignant. For the 23 actual Malignant, 2 were misclassified as Benign. You can tweak the value of K and check if the results are getting better