# 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 ...# this provides the structure of the dataset# drop the id feature
wbcd <- wbcd[-1]
# drop a column# table of diagnosis
table(wbcd$diagnosis)##
## B M
## 357 212# show a table of the diagnosis column# recode diagnosis as a factor
wbcd$diagnosis <- factor(wbcd$diagnosis, levels = c("B", "M"),
labels = c("Benign", "Malignant"))
# change diagnosis from character to factor# table or proportions with more informative labels
round(prop.table(table(wbcd$diagnosis)) * 100, digits = 1)##
## Benign Malignant
## 62.7 37.3# calculate the percentage distribution of each unique value in the diagnosis variable# 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# provides a summary of the features# create normalization function
normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}
# normalize function takes a vector x as input, normalizes its values between 0 and 1, and returns the normalized vector.# test normalization function - result should be identical
normalize(c(1, 2, 3, 4, 5))## [1] 0.00 0.25 0.50 0.75 1.00normalize(c(10, 20, 30, 40, 50))## [1] 0.00 0.25 0.50 0.75 1.00# applying the normalize function to the above values# normalize the wbcd data
wbcd_n <- as.data.frame(lapply(wbcd[2:31], normalize))
# normalizes the numerical columns of the wbcd dataset, excluding the first column# confirm that normalization worked, output should be a value between 0 and 1
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[1:469, ]
wbcd_test <- wbcd_n[470:569, ]
# assigning the training data and the testing data to the above variables# create labels for training and test data
wbcd_train_labels <- wbcd[1:469, 1]
wbcd_test_labels <- wbcd[470:569, 1]
# these labels represent the target variable # load the "class" library
library(class)wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
cl = wbcd_train_labels, k = 21)
# will contain the predicted class labels for the test data based on the k-nearest neighbors algorithm.# load the "gmodels" library
library(gmodels)## Warning: package 'gmodels' was built under R version 4.3.2# 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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Out of the 100 observations, 2 were wrong. Based on the output, 2 people were informed that their cancer was benign when it was in fact malignant. Accuracy = Number of Correct Predictions / total number of predictions 98/100 = 98% Precision = True positive (TP) / True positive (TP) + False Positive (FP) 98/98+0 = 98% Recall = True positive (TP) / True positive (TP) + False negative (FN) 98/98+2 = 98% F-1 Score = 2 * (PrecisionRecall) / (Precision+Recall) 2 (1 * 0.98) / (1 + 0.98) = 0.989
## 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[1:469, ]
wbcd_test <- wbcd_z[470:569, ]
# Adjust the ratio of training/testing data
# 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: 100
##
##
## | wbcd_test_pred
## wbcd_test_labels | Benign | Malignant | Row Total |
## -----------------|-----------|-----------|-----------|
## Benign | 61 | 0 | 61 |
## | 1.000 | 0.000 | 0.610 |
## | 0.924 | 0.000 | |
## | 0.610 | 0.000 | |
## -----------------|-----------|-----------|-----------|
## Malignant | 5 | 34 | 39 |
## | 0.128 | 0.872 | 0.390 |
## | 0.076 | 1.000 | |
## | 0.050 | 0.340 | |
## -----------------|-----------|-----------|-----------|
## Column Total | 66 | 34 | 100 |
## | 0.660 | 0.340 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 95% Precision = 1 Recall = 90.5% F-1 Score = 95%
# try several different values of k
wbcd_train <- wbcd_n[1:469, ]
wbcd_test <- wbcd_n[470:569, ]#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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 97% Precision = 97% Recall = 99% F-1 Score = .975
#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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 99% Precision = 100% Recall = 98% F-1 Score = .98
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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Out of the 100 observations, 3 were wrong. Accuracy = 97% Precision = 100% Recall = 97% F-1 Score = .985
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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 97% Precision = 100% Recall = 97% F-1 Score = .985
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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 98% Precision = 100% Recall = 96.8% F-1 Score = .983
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: 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 | |
## -----------------|-----------|-----------|-----------|
##
## Accuracy = 96% Precision = 100% Recall = 93% F-1 Score = .963
Precision, accuracy, recall, and f1score only during classification In regression we talk about mean squared error, etc.
In my opinion, the best choice for k is 21 because of the significance of the F-1 Value. Although other k’s had less inaccurate values, the signifiance of the k value holds a lot of value.