gradientDescent.r

##GRADIENT DESCENT ALGORITHM FOR ONE VARIABLE REGRESSION ANALYSIS

#Data is from an online course taught by Andrew Ng of Stanford University 
#provided by Coursea
#https://github.com/ahawker/machine-learning-coursera

############## Cevrimici (online) bir kaynaktan veri seti okutma ##############
URL_subs <-"https://goo.gl/zEVbcU"
data <- read.table(URL_subs, header=FALSE, sep=",")

x.test = data[,1] #bagimsiz degisken
y.test = data[,2] #bagimli degisken
m = length(y.test); # egitim kumesinde bulunan veri noktalarinin sayisi

############## Verinin sacilim grafigini cizdirme ##############
library(ggplot2) #grafik cizdirmek icin kullanilan en iyi R paketlerden biri

data = data.frame(x=x.test, y=y.test)
g <- ggplot(data, aes(x=x.test, y=y.test))  + 
  geom_point(alpha=1/3, size=4) +
  geom_smooth(method="lm", se=F, col="steelblue") +
  labs(title = "Doğrusal Regresyon – Örnek Veri")
g

#x girdi degiskenine 1'lerden olusan kolon ekleyelim (Sabit degisken olan
#theta_{0}'u hesaplayabilmek icin)
x.test <- matrix(c(rep(1,length(x.test)),x.test), ncol=2)
head(x.test)

############## Gradyan Inis yontemi ##############
theta <- c(0, 0) #theta parametresi icin baslangic degerleri
iterations <- 1500 # iterasyon sayisi
alpha <- 0.01

# Maliyet fonksiyonunu tanimlama
CostFunction <- function(X, Y, theta){
  m <- length(Y); #number of observations in the model
  J =0;
  J <- 1/(2*m) * sum(((X %*% theta) - Y)^2);
}

# tek degisken icin Gradyan Inis yontemini tanimlama
GradientDescent <- function(X, Y, theta, alpha, num_iters){
  m <- length(Y) 
  J_history = rep(0, num_iters);
for (i in 1:num_iters){
  predictions <-  X %*% theta;
  updates = t(X) %*% (predictions - Y);
  theta = theta - alpha * (1/m) * updates;
  J_history[i] <- CostFunction(X, Y, theta);
}
  list("theta" = theta, "J_history" = J_history)  
}

#Sonuclar
result.test <- GradientDescent(x.test, y.test, theta, alpha, iterations)
theta <- result.test$theta
theta
#Bu yontem ile elde edilen theta degerleri asagidaki gibidir.
#          [,1]
#[1,] -3.630291  #thetea_{0}
#[2,]  1.166362  #theta_{1}

#Tahmin denklemi y = -3.630291 + 1.166362 x

# Elde edilen tahmin denklemini kullanarak tahmini y degerlerini hesaplama ve
# grafigini cizdirme
data = data.frame(x=x.test[,2], y=y.test, y.hat = x.test%*%theta)

ggplot(data, aes(x=x.test[,2], y=y.test, test=y.hat))  + 
  geom_point(alpha=1/3, size=4) +
  stat_smooth(method = "lm", formula = test~ x, size = 1, se = FALSE,
              aes(color="Gradyan İniş")) +
  geom_smooth(method="lm", se=F, aes(color="Eğitim Kümesi")) +
  scale_colour_manual(name="Method", values=c("red", "steelblue")) +
  theme(legend.position = "bottom") +
  labs(title = "Gradyan İniş - Sonuçlar")

#Her iterasyon da elde edilen maliyet fonksiyonu degerlerini cizdirme
data <- data.frame(x=seq(1, length(result.test$J_history)),
                   y=result.test$J_history)
ggplot(data, aes(x=x, y=y)) +
  geom_line() +
  labs(title="Gradyan İniş iterasyonları",
       x="İterasyonlar", y="Maliyet J")