# import the CSV file
wbcd <- read.csv("wisc_bc_data.csv", stringsAsFactors = FALSE)
# examine the structure of the wbcd data frame
str(wbcd)'data.frame': 569 obs. of 32 variables:
$ id : int 87139402 8910251 905520 868871 9012568 906539 925291 87880 862989 89827 ...
$ diagnosis : chr "B" "B" "B" "B" ...
$ radius_mean : num 12.3 10.6 11 11.3 15.2 ...
$ texture_mean : num 12.4 18.9 16.8 13.4 13.2 ...
$ perimeter_mean : num 78.8 69.3 70.9 73 97.7 ...
$ area_mean : num 464 346 373 385 712 ...
$ smoothness_mean : num 0.1028 0.0969 0.1077 0.1164 0.0796 ...
$ compactness_mean : num 0.0698 0.1147 0.078 0.1136 0.0693 ...
$ concavity_mean : num 0.0399 0.0639 0.0305 0.0464 0.0339 ...
$ points_mean : num 0.037 0.0264 0.0248 0.048 0.0266 ...
$ symmetry_mean : num 0.196 0.192 0.171 0.177 0.172 ...
$ dimension_mean : num 0.0595 0.0649 0.0634 0.0607 0.0554 ...
$ radius_se : num 0.236 0.451 0.197 0.338 0.178 ...
$ texture_se : num 0.666 1.197 1.387 1.343 0.412 ...
$ perimeter_se : num 1.67 3.43 1.34 1.85 1.34 ...
$ area_se : num 17.4 27.1 13.5 26.3 17.7 ...
$ smoothness_se : num 0.00805 0.00747 0.00516 0.01127 0.00501 ...
$ compactness_se : num 0.0118 0.03581 0.00936 0.03498 0.01485 ...
$ concavity_se : num 0.0168 0.0335 0.0106 0.0219 0.0155 ...
$ points_se : num 0.01241 0.01365 0.00748 0.01965 0.00915 ...
$ symmetry_se : num 0.0192 0.035 0.0172 0.0158 0.0165 ...
$ dimension_se : num 0.00225 0.00332 0.0022 0.00344 0.00177 ...
$ radius_worst : num 13.5 11.9 12.4 11.9 16.2 ...
$ texture_worst : num 15.6 22.9 26.4 15.8 15.7 ...
$ perimeter_worst : num 87 78.3 79.9 76.5 104.5 ...
$ area_worst : num 549 425 471 434 819 ...
$ smoothness_worst : num 0.139 0.121 0.137 0.137 0.113 ...
$ compactness_worst: num 0.127 0.252 0.148 0.182 0.174 ...
$ concavity_worst : num 0.1242 0.1916 0.1067 0.0867 0.1362 ...
$ points_worst : num 0.0939 0.0793 0.0743 0.0861 0.0818 ...
$ symmetry_worst : num 0.283 0.294 0.3 0.21 0.249 ...
$ dimension_worst : num 0.0677 0.0759 0.0788 0.0678 0.0677 ...# drop the id feature as it's not useful for classification
wbcd <- wbcd[-1]
# Create a table of the diagnosis to see the distribution of Benign and Malignant cases
# table of diagnosis
table(wbcd$diagnosis)
B M
357 212 # Recode the diagnosis as a factor with labels "Benign" and "Malignant"
wbcd$diagnosis <- as.character(wbcd$diagnosis) # Convert to character first
wbcd$diagnosis <- factor(wbcd$diagnosis, levels = c("B", "M"),
labels = c("Benign", "Malignant"))
# Display the proportion of each diagnosis type
# table or proportions with more informative labels
round(prop.table(table(wbcd$diagnosis)) * 100, digits = 1)
Benign Malignant
62.7 37.3 # summarize three numeric features to get an overview of the data
summary(wbcd[c("radius_mean", "area_mean", "smoothness_mean")]) radius_mean area_mean smoothness_mean
Min. : 6.981 Min. : 143.5 Min. :0.05263
1st Qu.:11.700 1st Qu.: 420.3 1st Qu.:0.08637
Median :13.370 Median : 551.1 Median :0.09587
Mean :14.127 Mean : 654.9 Mean :0.09636
3rd Qu.:15.780 3rd Qu.: 782.7 3rd Qu.:0.10530
Max. :28.110 Max. :2501.0 Max. :0.16340 # create normalization function to scale the data
normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}
# Normalize the data (excluding the diagnosis column)
wbcd_n <- as.data.frame(lapply(wbcd[2:31], normalize))
# Confirm normalization by checking the summary of the 'area_mean' feature
summary(wbcd_n$area_mean) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.1174 0.1729 0.2169 0.2711 1.0000 # Split the data into training and testing sets
wbcd_train <- wbcd_n[1:469, ]
wbcd_test <- wbcd_n[470:569, ]
# Create labels for the training and test sets
wbcd_train_labels <- wbcd[1:469, 1]
wbcd_test_labels <- wbcd[470:569, 1]# Load the "class" library for KNN
library(class)
# Train the KNN model using k=21 (this is just an initial value)
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
cl = wbcd_train_labels, k = 21)install.packages("gmodels")Error in install.packages : Updating loaded packages# Load the "gmodels" library for creating a cross table
library(gmodels)
# Evaluate model performance by creating a cross tabulation of predicted vs. actual labels
CrossTable(x = wbcd_test_labels, y = wbcd_test_pred,
prop.chisq = FALSE)
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.968 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 2 | 37 | 39 |
| 0.051 | 0.949 | 0.390 |
| 0.032 | 1.000 | |
| 0.020 | 0.370 | |
-----------------|-----------|-----------|-----------|
Column Total | 63 | 37 | 100 |
| 0.630 | 0.370 | |
-----------------|-----------|-----------|-----------|
# Try different values of k to find the best one
k_values <- c(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25)
accuracy <- c()
# Loop over the different k values and store the accuracy for each
for(k in k_values) {
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
cl = wbcd_train_labels, k = k)
# Create a confusion matrix
cross_table <- CrossTable(x = wbcd_test_labels, y = wbcd_test_pred,
prop.chisq = FALSE, expected = FALSE)
# Calculate the accuracy from the confusion matrix
correct_predictions <- sum(cross_table$t[1, 1], cross_table$t[2, 2])
total_predictions <- sum(cross_table$t)
accuracy <- c(accuracy, correct_predictions / total_predictions)
}
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 58 | 3 | 61 |
| 0.951 | 0.049 | 0.610 |
| 0.983 | 0.073 | |
| 0.580 | 0.030 | |
-----------------|-----------|-----------|-----------|
Malignant | 1 | 38 | 39 |
| 0.026 | 0.974 | 0.390 |
| 0.017 | 0.927 | |
| 0.010 | 0.380 | |
-----------------|-----------|-----------|-----------|
Column Total | 59 | 41 | 100 |
| 0.590 | 0.410 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 60 | 1 | 61 |
| 0.984 | 0.016 | 0.610 |
| 0.968 | 0.026 | |
| 0.600 | 0.010 | |
-----------------|-----------|-----------|-----------|
Malignant | 2 | 37 | 39 |
| 0.051 | 0.949 | 0.390 |
| 0.032 | 0.974 | |
| 0.020 | 0.370 | |
-----------------|-----------|-----------|-----------|
Column Total | 62 | 38 | 100 |
| 0.620 | 0.380 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.968 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 2 | 37 | 39 |
| 0.051 | 0.949 | 0.390 |
| 0.032 | 1.000 | |
| 0.020 | 0.370 | |
-----------------|-----------|-----------|-----------|
Column Total | 63 | 37 | 100 |
| 0.630 | 0.370 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.938 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 4 | 35 | 39 |
| 0.103 | 0.897 | 0.390 |
| 0.062 | 1.000 | |
| 0.040 | 0.350 | |
-----------------|-----------|-----------|-----------|
Column Total | 65 | 35 | 100 |
| 0.650 | 0.350 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.938 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 4 | 35 | 39 |
| 0.103 | 0.897 | 0.390 |
| 0.062 | 1.000 | |
| 0.040 | 0.350 | |
-----------------|-----------|-----------|-----------|
Column Total | 65 | 35 | 100 |
| 0.650 | 0.350 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.968 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 2 | 37 | 39 |
| 0.051 | 0.949 | 0.390 |
| 0.032 | 1.000 | |
| 0.020 | 0.370 | |
-----------------|-----------|-----------|-----------|
Column Total | 63 | 37 | 100 |
| 0.630 | 0.370 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
Cell Contents
|-------------------------|
| N |
| N / Row Total |
| N / Col Total |
| N / Table Total |
|-------------------------|
Total Observations in Table: 100
| wbcd_test_pred
wbcd_test_labels | Benign | Malignant | Row Total |
-----------------|-----------|-----------|-----------|
Benign | 61 | 0 | 61 |
| 1.000 | 0.000 | 0.610 |
| 0.953 | 0.000 | |
| 0.610 | 0.000 | |
-----------------|-----------|-----------|-----------|
Malignant | 3 | 36 | 39 |
| 0.077 | 0.923 | 0.390 |
| 0.047 | 1.000 | |
| 0.030 | 0.360 | |
-----------------|-----------|-----------|-----------|
Column Total | 64 | 36 | 100 |
| 0.640 | 0.360 | |
-----------------|-----------|-----------|-----------|
# Display the accuracy for each k value
accuracy_df <- data.frame(k = k_values, accuracy = accuracy)
print(accuracy_df)# Identify the best k (with the highest accuracy)
best_k <- accuracy_df[which.max(accuracy_df$accuracy), ]
print(paste("The best k is", best_k$k, "with an accuracy of", best_k$accuracy))[1] "The best k is 5 with an accuracy of 0.98"The process of implementing the KNN model began with data preprocessing, where I ensured that all numerical features were normalized using MinMaxScaler to enhance model performance. I then split the dataset into training and testing sets to prevent data leakage and ensure a fair evaluation.
Next, I trained the KNN model with varying values of k, observing how accuracy changed for different values. To assess model performance, I used accuracy scores and confusion matrices, which helped evaluate how well the model classified cases as Benign or Malignant.
From the results, I observed that k = 5 and k = 21 achieved the highest accuracy (0.98), indicating that these values provided the best balance between overfitting and underfitting. Selecting the right k is crucial, as too small a k can lead to high variance, while too large a k can oversmooth decision boundaries, reducing model flexibility.
I enjoyed doing this class activity!