This is a basic example of machine learning. The algorithm is a perceptron learning algorithm. The data set to learn is artificially created.

perceptron.R

# creating an artificial target function
# in a real machine learning application this would, of course, be unkown
target <- function(x) {
  if (x[1] + x[2] > -5) {
    return(-1)
  } else {
    return(1)
  }
}

# size of data set
N <- 100

# creating dataset with random coords and precomputed y
D <- data.frame()
for (i in 1:N) {
  D[i,1] <- sample(-10:10, 1)
  D[i,2] <- sample(-10:10, 1)
  D[i,"y"] <- target(D[i,])
}

# plot the data set, color indicated the two categories
plot(D[c(1,2)], col = ifelse(D$y < 0, 'red', 'green'), pch=19)

# initializing random weights
w <- c(runif(3))

# this is our function that should approximate the target function
# key to solving is finding the right weigths
hypothesis <- function(x) {
  input <- c(1, unlist(x))
  if (input[1] * w[1] + input[2] * w[2] + input[3] * w[3] > 0) {
    return(1)
  } else {
    return(-1)
  }
}

# for counting the necessary iterations to find the weights
counter <- 1

# while there are misclassified data points...
while (nrow(D[apply(D, c(1), hypothesis) != D['y'],]) > 0) {
  # retrieve all elements that are misclassified with the current hypothesis
  m <- D[apply(D, c(1), hypothesis) != D['y'],]
  m.length <- nrow(m)
  
  # choose a random misclassified data point
  random <- sample(1:m.length, 1)
  e <- m[random,]
  
  # adjust the weigths to match the random missmatch
  w <- w + e$y * c(1, as.numeric(e[1:2]))
  
  # plot current hypothesis curve
  k <- -(w[2]/w[3])
  d <- -(w[1]/w[3])
  curve(x*k+d, add=TRUE)
  
  # for transparency
  Sys.sleep(0.5)
  print(paste('iteration:', counter))
  counter <- counter + 1
}