assignment4.R

library(neuralnet)

set.seed(1234567890)

# ----1.----

Var <- runif(500, 0, 10)

mydata <- data.frame(Var, Sin = sin(Var))


tr <- mydata[1:25, ] # Training
te <- mydata[26:500, ] # Test


# Random initialization of the weights in the interval [-1, 1]
winit <- runif(10, -1, 1)
formula <- Sin ~ Var
nn <- neuralnet(
  formula ,
  data = tr,
  hidden = c(10),
  startweights = winit
)

# Plot of the training data (black), test data (blue), and predictions (red)
plot(
  tr,
  cex = 2,
  ylab = "sin(x)",
  xlab = "x",
  main = "NN with logistic activation function"
)
points(te, col = "blue", cex = 1)
points(te[, 1], predict(nn, te), col = "red", cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Test data", "Predicted test data"),
  col = c("black", "blue", "red"),
  pch = 1,
  pt.cex = c(2, 1, 1),
  cex = 1
)


# ----2.----

h1 <- function(x) {
  x
}


h2 <- function(x) {
  ifelse(x > 0, x, 0)
}

h3 <- function(x)  {
  log(1 + exp(x))
}

nn_h1 <- neuralnet(
  formula ,
  data = tr,
  hidden = c(10),
  startweights = t(winit),
  act.fct = h1
)

plot(tr,
     cex = 2,
     xlab = "x",
     "sin(x)",
     main = "NN with linear activation function (h1)")
points(te, col = "blue", cex = 1)
points(te[, 1], predict(nn_h1, te), col = "red", cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Test data", "Predicted test data"),
  col = c("black", "blue", "red"),
  pch = 1,
  pt.cex = c(2, 1, 1),
  cex = 1
)

nn_h2 <- neuralnet(
  formula ,
  data = tr,
  hidden = c(10),
  startweights = t(winit),
  act.fct = h2
)

plot(
  tr,
  cex = 2,
  xlab = "x",
  ylab = "sin(x)",
  main = "NN with ReLU activation function (h2)"
)
points(te, col = "blue", cex = 1)
points(te[, 1], predict(nn_h2, te), col = "red", cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Test data", "Predicted test data"),
  col = c("black", "blue", "red"),
  pch = 1,
  pt.cex = c(2, 1, 1),
  cex = 1
)

nn_h3 <- neuralnet(
  formula ,
  data = tr,
  hidden = c(10),
  startweights = t(winit),
  act.fct = h3
)

plot(
  tr,
  cex = 2,
  xlab = "x",
  ylab = "sin(x)",
  main = "NN with softplus activation function (h3)"
)
points(te, col = "blue", cex = 1)
points(te[, 1], predict(nn_h3, te), col = "red", cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Test data", "Predicted test data"),
  col = c("black", "blue", "red"),
  pch = 1,
  pt.cex = c(2, 1, 1),
  cex = 1
)


# ----3.----
Var1 <- runif(500, 0, 50)

mydata1 <- data.frame(Var = Var1, Sin = sin(Var1))

pred1 <- predict(nn, mydata1)

plot(
  mydata1,
  cex = 2,
  main = "NN with logistic activation",
  ylim = c(-10, 2),
  xlab = "x",
  ylab = "sin(x)"
)
points(mydata1, col = "blue", cex = 1)
points(mydata1[, 1], pred1, col = "red", cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Test data", "Predicted test data"),
  col = c("black", "blue", "red"),
  pch = 1,
  pt.cex = c(2, 1, 1),
  cex = 1
)

# ----4.----

pred1[order(pred1)][1]

nn$weights

# ----5.----

Var2 <- runif(500, 0, 10)

mydata2 <- data.frame(Sin2 = sin(Var2), Var2)

formula2 <- Var2 ~ Sin2

nn2 <- neuralnet(
  formula2 ,
  data = mydata2,
  hidden = c(10),
  startweights = winit,
  threshold = 0.1
)


plot(
  mydata2,
  col = "blue",
  cex = 1,
  main = "NN with logistic activation function",
  xlab = "sin(x)",
  ylab = "x",
)
points(mydata2[, 1],
       predict(nn2, mydata2),
       col = "red",
       cex = 1)
grid()
legend(
  "bottomleft",
  legend = c("Training data", "Predicted training data"),
  col = c("blue", "red"),
  pch = 1,
  pt.cex = c(1, 1),
  cex = 1
)