Homework1.R

# Homework 1 - Jake Mathews

# Utility methods
edistance <- function(x, y) {
  n = length(x)
  d = 0
  for (i in 1:n) {
    d = d + (x[,i] - y[,i]) ^ 2
  }
  d = sqrt(d)
  return(d)
}

######## Problem 1 ########
knn = 3
data("iris")
colnames(iris)[5] <- "Species.Name"

# Map species to a value
speciesNames = c("setosa", "versicolor", "virginica")
speciesCount = length(speciesNames)
for (speciesIndex in 1:speciesCount) {
  name = speciesNames[speciesIndex]
  iris$Species.Int[iris$Species.Name == name] <- speciesIndex
}

# Seperate training and test sets
trainIrisIndex <- sample(1:nrow(iris), as.integer(.7 * nrow(iris)), replace = FALSE)
trainIris <- iris[trainIrisIndex,]
testIris <- iris[-trainIrisIndex,]

# Remove species as a column to calculate distance
trainIris.no_species <- trainIris[,-5]
testIris.no_species <- testIris[,-5]

predictions <- numeric()
for (testIndex in 1:nrow(testIris)) {
  distances <- numeric()
  test <- testIris.no_species[testIndex,]
  for (trainIndex in 1:nrow(trainIris)) {
    train <- trainIris.no_species[trainIndex,]
    distance <- edistance(test, train)
    distances[trainIndex] = distance
  }
  
  # Create a sorted data frame with distances mapped to species
  distances <- data.frame(distances, trainIris$Species.Int)
  colnames(distances) <- c("distance", "species")
  distances.sorted <- distances[order(distances$distance),]
  
  # The occurance of each species is tallied
  occurance <- numeric(speciesCount)
  for (neighborIndex in 1:knn) {
    speciesIndex = distances.sorted[neighborIndex,]$species
    occurance[speciesIndex] <- occurance[speciesIndex] + 1
  }
  
  # Which ever species occured the most in the k nearest neighbors wins
  # In the event of a tie, the first species in this order wins (setosa, versicolor, virginica)
  predictedSpecies = which.max(occurance)
  predictions[testIndex] = predictedSpecies
}

# Load result into a data frame
results <- data.frame(predictions, testIris$Species.Int)
colnames(results) <- c("predicted", "actual")

# Create confusion matrix
matrixSize = speciesCount ^ 2
confusionMatrix = matrix(numeric(matrixSize), nrow = speciesCount, ncol = speciesCount)
rownames(confusionMatrix) <- speciesNames
colnames(confusionMatrix) <- speciesNames

# Fill confusion matrix
for (resultIndex in 1:nrow(results)) {
  result <- results[resultIndex,]
  confusionMatrix[result$actual, result$predicted] = confusionMatrix[result$actual, result$predicted] + 1
}

matrixDiaganol <- diag(confusionMatrix)
sumTotal <- sum(confusionMatrix)
sumDiagnanol <- sum(matrixDiaganol)

#calculate accuracy
overallAccuracy <- sumDiagnanol/sumTotal
#calculate realtive error
overallError <- (sumTotal-sumDiagnanol)/sumTotal
overall <- data.frame(overallAccuracy, overallError)
colnames(overall) <- c("Accuracy", "Error")
rownames(overall) <- c("Overall")

# Print results
accuracyTable <- matrix(nrow = speciesCount, ncol = 4)
colnames(accuracyTable) <- c("TP", "FN", "FP", "TN")
rownames(accuracyTable) <- speciesNames
for (species in 1:speciesCount) {
  TP = confusionMatrix[species,species]
  FN = sum(confusionMatrix[species,]) - TP
  FP = sum(confusionMatrix[,species]) - TP
  TN = FN + FP
  accuracyTable[species,] = c(TP, FN, FP, TN)
}

print("Problem 1")
print(results)
print(accuracyTable)
print(overall)



######## Problem 2 ########
library(Matrix)
library(DMwR)
library(class)
library(TTR)
acc <- numeric()
err <- numeric()
n <- integer()
datatr <- read.csv(file="pendigits_tra.csv",as.is=TRUE)
datate <- read.csv(file="pendigits_tes.csv",as.is=TRUE)
for (i in 1:100) {
  n[i]=i
  knear <- kNN(digit~.,datatr, datate, k=i)
  #confusion matrix
  t <- table(datate[,'digit'],knear)
  #print(t)
  #get diagonal elements of matrix
  td <- diag(t)
  #sum all the elements of the matrix t which gives 
  #the examples tested
  sumt <- sum(t)
  #some the diagonal to see how many we got correct
  sumtd <- sum(td)
  #calculate accuracy
  acc[i] <- sumtd/sumt
  #calculate realtive error
  err[i] <- (sumt-sumtd)/sumt
  #print(acc[i])
  #print(err[i])
  
}
resultsknn <- cbind(n,acc,err)
colnames(resultsknn) <- c("k","Accuracy","Error")