Chapter 3 R Notebook

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Chapter 3: Classification using Nearest Neighbors

This is an R Notebook with the code from Machine Learning with R, Lantz.

Example: Classifying Cancer Samples

Step 2: Exploring and preparing the data

import the CSV file

wbcd <- read.csv("wisc_bc_data.csv", stringsAsFactors = FALSE)
wbcd

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 and table or proportions with more informative labels

wbcd$diagnosis <- factor(wbcd$diagnosis, levels = c("B", "M"),
                         labels = c("Benign", "Malignant"))
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 and test normalization function - result should be identical

normalize <- function(x) {
  return ((x - min(x)) / (max(x) - min(x)))
}
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 and confirm that normalization worked

wbcd_n <- as.data.frame(lapply(wbcd[2:31], normalize))
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

create labels for training and test data

wbcd_train <- wbcd_n[1:469, ]
wbcd_test <- wbcd_n[470:569, ]
wbcd_train_labels <- wbcd[1:469, 1]
wbcd_test_labels <- wbcd[470:569, 1]

visualize the data using labels

plot(wbcd$radius_mean,wbcd$texture_mean, 
     main = 'Scatterplot',
     xlab = 'randius mean',
     ylab = 'texture mean')

pairs(~radius_mean+texture_mean+perimeter_mean+area_mean+smoothness_mean, 
      data = wbcd,
      main = 'Scaterplot of many variables')

library(car)
scatterplot(texture_mean ~ radius_mean | diagnosis, data = wbcd,
     main = 'Scatterplot',
     xlab = 'randius mean',
     ylab = 'texture mean')

scatterplotMatrix(~radius_mean+texture_mean+perimeter_mean+area_mean+smoothness_mean | diagnosis, data=wbcd)

Step 3: Training a model on the data

library(class)
wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
                      cl = wbcd_train_labels, k = 21)
head(wbcd_test)

head(wbcd_test_pred)

[1] Benign    Benign    Benign    Benign    Malignant Benign   
Levels: Benign Malignant

Step 4: Evaluating model performance

Create the cross tabulation of predicted vs. actual

library(gmodels)
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 |           | 
-----------------|-----------|-----------|-----------|

 

Step 5: Improving model performance

use the scale() function to z-score standardize a data frame and confirm that the transformation was applied correctly

wbcd_z <- as.data.frame(scale(wbcd[-1]))
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, ]

re-classify test cases

wbcd_test_pred <- knn(train = wbcd_train, test = wbcd_test,
                      cl = wbcd_train_labels, k = 21)
head(wbcd_test)

head(wbcd_test_pred)

[1] Benign    Benign    Benign    Benign    Malignant Benign   
Levels: Benign Malignant

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 |           | 
-----------------|-----------|-----------|-----------|

 

try several different values of k

wbcd_train <- wbcd_n[1:469, ]
wbcd_test <- wbcd_n[470:569, ]
#start time
strt<-Sys.time()
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 |           | 
-----------------|-----------|-----------|-----------|

 

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 |           | 
-----------------|-----------|-----------|-----------|

 

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 |           | 
-----------------|-----------|-----------|-----------|

 

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 |           | 
-----------------|-----------|-----------|-----------|

 

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 |           | 
-----------------|-----------|-----------|-----------|

 

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 |           | 
-----------------|-----------|-----------|-----------|

 

#end time
print(Sys.time()-strt)

Time difference of 0.3308871 secs