GD_multivarite.R

GradientDescent <- function(data, alpha, iteration, epsilon){
  
  data <- matrix(unlist(data), ncol=ncol(data), byrow=FALSE)
  
  # bagimli degiskeni ve bagimsiz degiskenleri ayiralim.
  #Veridaki en son kolon, bagimli degiskene ait olmalidir.
  independent.variable<- data[,1:ncol(data)-1]
  dependent.variable<- data[,ncol(data)]
                 
  # girdi degiskenlerine z-değeri normalleştirmesi uygulayalim.
  # Her degiskene ait ortalama ve standart sapma bilgisini kaydedelim.
  normalized <- function(x) ( x - mean(x) ) / sd(x)
  independent.variable.mean <- apply(independent.variable, 2, mean)
  independent.variable.sd <- apply(independent.variable, 2, sd)
  independent.variable <- apply(independent.variable, 2,normalized)
  
  # Sabit terimi (theta0) hesaplayabilmek icin bagimsiz degiskenlerden olusan matrise
  #1'lerden olusan bir kolon ekleyelim.
  independent.variable <- cbind(theta0 = 1, independent.variable)
  
  # theta_new : baslangic degerleri 
  # theta_old 
  theta_new <- matrix( 1, ncol = ncol(independent.variable))
  theta_old <- matrix( 2, ncol = ncol(independent.variable))
  
  #Maliyet fonksiyonu
  CostFunction <- function (independent.variable, dependent.variable, theta){
    1/(2*(NROW(dependent.variable))) * sum(((independent.variable %*% t(theta)) - dependent.variable)^2);
  }
  
  # her iterasyondaki theta degerlerini ve bu degerlere kasilik gelen maliyet
  #fonksiyonu degerlerini kaydedelim. Bu iki vektorun ilk degelerini atayalim.
  thetas <- vector( mode = "list", length = iteration ) 
  thetas[[1]] <- theta_new
  J <- numeric( length = iteration )
  J[1] <- CostFunction(independent.variable, dependent.variable, theta_old )
  
  #Gradyan inis algoritmasindaki kismi turev islemini yapan fonksiyon
  derivative <- function(independent.variable, dependent.variable, theta)
  {
    descent <- (t(independent.variable) %*% ((independent.variable %*% t(theta)) - dependent.variable))/ NROW(dependent.variable)
    return( t(descent) )
  }
  
  #Durdurma kriterlerini tanımlayalım.
  step <- 1 
  while(any(abs(theta_new - theta_old) > epsilon) & step <= iteration )
  {
    step <- step + 1
    
    # gradient descent 
    theta_old <- theta_new
    theta_new <- theta_old - alpha * derivative(independent.variable, dependent.variable, theta_old)
    
    # record keeping 
    thetas[[step]] <- theta_new
    J[step] <- CostFunction(independent.variable, dependent.variable, theta_new)
    
  }
  
  # Sonuclari yazdiralim. 
  costs <- data.frame( costs = J )
  theta <- data.frame( do.call( rbind, thetas ), row.names = NULL )
  norm  <- data.frame( input_mean = independent.variable.mean, input_sd = independent.variable.sd)
  
  return( list( costs = costs, theta = theta, norm = norm))
}