D Solutions ch. 5 - Nearest neighbours

Solutions to exercises of chapter 5.

D.1 Exercise 1

Load libraries

library(caret)
## Loading required package: lattice
## Loading required package: ggplot2
library(RColorBrewer)
library(doMC)
## Loading required package: foreach
## Loading required package: iterators
## Loading required package: parallel
library(corrplot)

Prepare for parallel processing

registerDoMC()

Load data

load("data/wheat_seeds/wheat_seeds.Rda")

Partition data

set.seed(42)
trainIndex <- createDataPartition(y=variety, times=1, p=0.7, list=F)
varietyTrain <- variety[trainIndex]
morphTrain <- morphometrics[trainIndex,]
varietyTest <- variety[-trainIndex]
morphTest <- morphometrics[-trainIndex,]

summary(varietyTrain)
## Canadian     Kama     Rosa 
##       49       49       49
summary(varietyTest)
## Canadian     Kama     Rosa 
##       21       21       21

Data check: zero and near-zero predictors

nzv <- nearZeroVar(morphTrain, saveMetrics=T)
nzv
##              freqRatio percentUnique zeroVar   nzv
## area               1.5      93.87755   FALSE FALSE
## perimeter          1.0      85.03401   FALSE FALSE
## compactness        1.0      93.19728   FALSE FALSE
## kernLength         1.5      91.83673   FALSE FALSE
## kernWidth          1.5      91.15646   FALSE FALSE
## asymCoef           1.0      98.63946   FALSE FALSE
## grooveLength       1.0      77.55102   FALSE FALSE

Data check: are all predictors on same scale?

summary(morphTrain)
##       area         perimeter      compactness       kernLength   
##  Min.   :10.74   Min.   :12.57   Min.   :0.8081   Min.   :4.902  
##  1st Qu.:12.28   1st Qu.:13.46   1st Qu.:0.8571   1st Qu.:5.253  
##  Median :14.29   Median :14.28   Median :0.8735   Median :5.504  
##  Mean   :14.86   Mean   :14.56   Mean   :0.8712   Mean   :5.632  
##  3rd Qu.:17.45   3rd Qu.:15.74   3rd Qu.:0.8880   3rd Qu.:5.979  
##  Max.   :21.18   Max.   :17.25   Max.   :0.9108   Max.   :6.675  
##    kernWidth        asymCoef       grooveLength  
##  Min.   :2.630   Min.   :0.7651   Min.   :4.605  
##  1st Qu.:2.947   1st Qu.:2.5965   1st Qu.:5.028  
##  Median :3.212   Median :3.5970   Median :5.222  
##  Mean   :3.258   Mean   :3.6679   Mean   :5.406  
##  3rd Qu.:3.563   3rd Qu.:4.6735   3rd Qu.:5.878  
##  Max.   :4.033   Max.   :8.4560   Max.   :6.550
featurePlot(x = morphTrain, 
            y = varietyTrain, 
            plot = "box", 
            ## Pass in options to bwplot() 
            scales = list(y = list(relation="free"),
                          x = list(rot = 90)),  
            layout = c(3,3))
Boxplots of the 7 geometric parameters in the wheat data set

Figure D.1: Boxplots of the 7 geometric parameters in the wheat data set

Data check: pairwise correlations between predictors

corMat <- cor(morphTrain)
corrplot(corMat, order="hclust", tl.cex=1)
Correlogram of the wheat seed data set.

Figure D.2: Correlogram of the wheat seed data set.

highCorr <- findCorrelation(corMat, cutoff=0.75)
length(highCorr)
## [1] 4
names(morphTrain)[highCorr]
## [1] "area"       "kernWidth"  "perimeter"  "kernLength"

Data check: skewness

featurePlot(x = morphTrain, 
            y = varietyTrain,
            plot = "density", 
            ## Pass in options to xyplot() to 
            ## make it prettier
            scales = list(x = list(relation="free"), 
                          y = list(relation="free")), 
            adjust = 1.5, 
            pch = "|", 
            layout = c(3, 3), 
            auto.key = list(columns = 3))
Density plots of the 7 geometric parameters in the wheat data set

Figure D.3: Density plots of the 7 geometric parameters in the wheat data set

Create a ‘grid’ of values of k for evaluation:

tuneParam <- data.frame(k=seq(1,50,2))

Generate a list of seeds for reproducibility (optional) based on grid size

set.seed(42)
seeds <- vector(mode = "list", length = 101)
for(i in 1:100) seeds[[i]] <- sample.int(1000, length(tuneParam$k))
seeds[[101]] <- sample.int(1000,1)

Set training parameters. In the example in chapter 5 pre-processing was performed outside the cross-validation process to save time for the purposes of the demonstration. Here we have a relatively small data set, so we can do pre-processing within each iteration of the cross-validation process. We specify the option preProcOptions=list(cutoff=0.75) to set a value for the pairwise correlation coefficient cutoff.

train_ctrl <- trainControl(method="repeatedcv",
                   number = 10,
                   repeats = 10,
                   preProcOptions=list(cutoff=0.75),
                   seeds = seeds)

Run training

knnFit <- train(morphTrain, varietyTrain, 
                method="knn",
                preProcess = c("center", "scale", "corr"),
                tuneGrid=tuneParam,
                trControl=train_ctrl)
knnFit
## k-Nearest Neighbors 
## 
## 147 samples
##   7 predictor
##   3 classes: 'Canadian', 'Kama', 'Rosa' 
## 
## Pre-processing: centered (3), scaled (3), remove (4) 
## Resampling: Cross-Validated (10 fold, repeated 10 times) 
## Summary of sample sizes: 133, 132, 132, 132, 132, 132, ... 
## Resampling results across tuning parameters:
## 
##   k   Accuracy   Kappa    
##    1  0.8429963  0.7644190
##    3  0.9060916  0.8591664
##    5  0.8809414  0.8214171
##    7  0.8764249  0.8145913
##    9  0.8840989  0.8260932
##   11  0.8900989  0.8350932
##   13  0.8974799  0.8461701
##   15  0.8981465  0.8471701
##   17  0.8981465  0.8471701
##   19  0.8941465  0.8411868
##   21  0.8955751  0.8433490
##   23  0.8934322  0.8400932
##   25  0.8920989  0.8381099
##   27  0.8921465  0.8381868
##   29  0.8928132  0.8391868
##   31  0.8907656  0.8360598
##   33  0.8893370  0.8339060
##   35  0.8819560  0.8228372
##   37  0.8813370  0.8219221
##   39  0.8853370  0.8279221
##   41  0.8880513  0.8319908
##   43  0.8893846  0.8339908
##   45  0.8921465  0.8381614
##   47  0.8934799  0.8401614
##   49  0.8920513  0.8379992
## 
## Accuracy was used to select the optimal model using  the largest value.
## The final value used for the model was k = 3.

Plot cross validation accuracy as a function of k

plot(knnFit)
Accuracy (repeated cross-validation) as a function of neighbourhood size for the wheat seeds data set.

Figure D.4: Accuracy (repeated cross-validation) as a function of neighbourhood size for the wheat seeds data set.

Predict the class (wheat variety) of the observations in the test set.

test_pred <- predict(knnFit, morphTest)
confusionMatrix(test_pred, varietyTest)
## Confusion Matrix and Statistics
## 
##           Reference
## Prediction Canadian Kama Rosa
##   Canadian       18    4    0
##   Kama            3   16    2
##   Rosa            0    1   19
## 
## Overall Statistics
##                                           
##                Accuracy : 0.8413          
##                  95% CI : (0.7274, 0.9212)
##     No Information Rate : 0.3333          
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.7619          
##  Mcnemar's Test P-Value : NA              
## 
## Statistics by Class:
## 
##                      Class: Canadian Class: Kama Class: Rosa
## Sensitivity                   0.8571      0.7619      0.9048
## Specificity                   0.9048      0.8810      0.9762
## Pos Pred Value                0.8182      0.7619      0.9500
## Neg Pred Value                0.9268      0.8810      0.9535
## Prevalence                    0.3333      0.3333      0.3333
## Detection Rate                0.2857      0.2540      0.3016
## Detection Prevalence          0.3492      0.3333      0.3175
## Balanced Accuracy             0.8810      0.8214      0.9405