Chapter 3: Classification using Nearest Neighbors
Example: Classifying Cancer Samples
Step 2: Exploring and preparing the data
# import the CSV file
wbcd <- read.csv("C:/Users/User/OneDrive/Desktop/1 - STU - DATA ANALYTICS/7 - DMML/CA#12/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
wbcd <- wbcd[-1]
# table of diagnosis
table(wbcd$diagnosis)
##
## B M
## 357 212
# recode diagnosis as a factor
wbcd$diagnosis <- factor(wbcd$diagnosis, levels = c("B", "M"),
labels = c("Benign", "Malignant"))
# table or proportions with more informative labels
round(prop.table(table(wbcd$diagnosis)) * 100, digits = 1)
##
## Benign Malignant
## 62.7 37.3
# summarize three numeric features
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
normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}
# test normalization function - result should be identical
normalize(c(1, 2, 3, 4, 5))
## [1] 0.00 0.25 0.50 0.75 1.00
normalize(c(10, 20, 30, 40, 50))
## [1] 0.00 0.25 0.50 0.75 1.00
# normalize the wbcd data
wbcd_n <- as.data.frame(lapply(wbcd[2:31], normalize))
# confirm that normalization worked
summary(wbcd_n$area_mean)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0000 0.1174 0.1729 0.2169 0.2711 1.0000
# create training and test data
wbcd_train <- wbcd_n[1:369, ]
wbcd_test <- wbcd_n[370:569, ]
# create labels for training and test data
wbcd_train_labels <- wbcd[1:369, 1]
wbcd_test_labels <- wbcd[370:569, 1]
Step 3: Training a model on the data
# load the "class" library
library(class)
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
cl = wbcd_train_labels, k = 21)
Step 4: Evaluating model performance
# load the "gmodels" library
library(gmodels)
## Warning: package 'gmodels' was built under R version 4.2.3
# Create the cross tabulation of predicted vs. actual
CrossTable(x = wbcd_test_labels, y = wbcd_test_pred,
prop.chisq = FALSE)
##
##
## Cell Contents
## |-------------------------|
## | N |
## | N / Row Total |
## | N / Col Total |
## | N / Table Total |
## |-------------------------|
##
##
## Total Observations in Table: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 127 | 1 | 128 |
## | 0.992 | 0.008 | 0.640 |
## | 0.948 | 0.015 | |
## | 0.635 | 0.005 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 7 | 65 | 72 |
## | 0.097 | 0.903 | 0.360 |
## | 0.052 | 0.985 | |
## | 0.035 | 0.325 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 134 | 66 | 200 |
## | 0.670 | 0.330 | |
## -----------------|-----------|-----------|-----------|
##
##
## Step 5: Improving model performance
# use the scale() function to z-score standardize a data frame
wbcd_z <- as.data.frame(scale(wbcd[-1]))
# confirm that the transformation was applied correctly
summary(wbcd_z$area_mean)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.4532 -0.6666 -0.2949 0.0000 0.3632 5.2459
# create training and test datasets
wbcd_train <- wbcd_z[1:369, ]
wbcd_test <- wbcd_z[370:569, ]
# re-classify test cases
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
cl = wbcd_train_labels, k = 21)
# Create the cross tabulation of predicted vs. actual
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 128 | 0 | 128 |
## | 1.000 | 0.000 | 0.640 |
## | 0.928 | 0.000 | |
## | 0.640 | 0.000 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 10 | 62 | 72 |
## | 0.139 | 0.861 | 0.360 |
## | 0.072 | 1.000 | |
## | 0.050 | 0.310 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 138 | 62 | 200 |
## | 0.690 | 0.310 | |
## -----------------|-----------|-----------|-----------|
##
##
# try several different values of k
wbcd_train <- wbcd_n[1:369, ]
wbcd_test <- wbcd_n[370:569, ]
#K=1
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=1)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 124 | 4 | 128 |
## | 0.969 | 0.031 | 0.640 |
## | 0.976 | 0.055 | |
## | 0.620 | 0.020 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 3 | 69 | 72 |
## | 0.042 | 0.958 | 0.360 |
## | 0.024 | 0.945 | |
## | 0.015 | 0.345 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 127 | 73 | 200 |
## | 0.635 | 0.365 | |
## -----------------|-----------|-----------|-----------|
##
##
#k=5
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=5)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 127 | 1 | 128 |
## | 0.992 | 0.008 | 0.640 |
## | 0.977 | 0.014 | |
## | 0.635 | 0.005 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 3 | 69 | 72 |
## | 0.042 | 0.958 | 0.360 |
## | 0.023 | 0.986 | |
## | 0.015 | 0.345 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 130 | 70 | 200 |
## | 0.650 | 0.350 | |
## -----------------|-----------|-----------|-----------|
##
##
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=11)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 128 | 0 | 128 |
## | 1.000 | 0.000 | 0.640 |
## | 0.962 | 0.000 | |
## | 0.640 | 0.000 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 5 | 67 | 72 |
## | 0.069 | 0.931 | 0.360 |
## | 0.038 | 1.000 | |
## | 0.025 | 0.335 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 133 | 67 | 200 |
## | 0.665 | 0.335 | |
## -----------------|-----------|-----------|-----------|
##
##
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=15)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 127 | 1 | 128 |
## | 0.992 | 0.008 | 0.640 |
## | 0.962 | 0.015 | |
## | 0.635 | 0.005 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 5 | 67 | 72 |
## | 0.069 | 0.931 | 0.360 |
## | 0.038 | 0.985 | |
## | 0.025 | 0.335 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 132 | 68 | 200 |
## | 0.660 | 0.340 | |
## -----------------|-----------|-----------|-----------|
##
##
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=21)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 127 | 1 | 128 |
## | 0.992 | 0.008 | 0.640 |
## | 0.948 | 0.015 | |
## | 0.635 | 0.005 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 7 | 65 | 72 |
## | 0.097 | 0.903 | 0.360 |
## | 0.052 | 0.985 | |
## | 0.035 | 0.325 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 134 | 66 | 200 |
## | 0.670 | 0.330 | |
## -----------------|-----------|-----------|-----------|
##
##
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test, cl = wbcd_train_labels, k=27)
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: 200
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 128 | 0 | 128 |
## | 1.000 | 0.000 | 0.640 |
## | 0.934 | 0.000 | |
## | 0.640 | 0.000 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 9 | 63 | 72 |
## | 0.125 | 0.875 | 0.360 |
## | 0.066 | 1.000 | |
## | 0.045 | 0.315 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 137 | 63 | 200 |
## | 0.685 | 0.315 | |
## -----------------|-----------|-----------|-----------|
##
##
# CALCULATE: PRECISION, ACCURACY, RECALL, F1
# Example actual and predicted classifications
wbcd_test_labels <- c('Yes', 'No', 'No', 'Yes', 'Yes', 'No', 'Yes', 'No', 'Yes', 'No')
wbcd_test_pred <- c('Yes', 'Yes', 'No', 'No', 'Yes', 'Yes', 'No', 'No', 'Yes', 'No')
# Create a confusion matrix
conf_matrix <- table(Predicted = wbcd_test_pred, Actual = wbcd_test_labels)
# Calculate metrics
accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)
precision <- conf_matrix['Yes', 'Yes'] / sum(conf_matrix['Yes', ])
recall <- conf_matrix['Yes', 'Yes'] / sum(conf_matrix[, 'Yes'])
F1 <- 2 * ((precision * recall) / (precision + recall))
# Print the results
cat("Confusion Matrix:\n")
## Confusion Matrix:
print(conf_matrix)
## Actual
## Predicted No Yes
## No 3 2
## Yes 2 3
cat("Accuracy:", accuracy, "\n")
## Accuracy: 0.6
cat("Precision:", precision, "\n")
## Precision: 0.6
cat("Recall:", recall, "\n")
## Recall: 0.6
cat("F1 Score:", F1, "\n")
## F1 Score: 0.6