GMM demo

# GMM model
# //
library(mvtnorm)

set.seed()
n1 =
n2 =
mu1 = c(,)
mu2 = c(-,-)
sigma1 = matrix(c(,.,.,),nrow=)
sigma2 = matrix(c(,.,.,),nrow=)
y1 = rep(,n1)
y2 = rep(,n2)
x1 = rmvnorm(n1, mean=mu1, sigma=sigma1)
x2 = rmvnorm(n2, mean=mu2, sigma=sigma2)

x = rbind(x1,x2)
y = rbind(y1,y2)

ns =
ngrid = 

mv.gauss = function(x,y,mu,sigma)
{
  nx = length(x)
  ny = length(y)
  z = matrix(,nrow=ny, ncol=nx)
  sigma_inv = solve(sigma)
  det_sigma = det(sigma)
  for (i in :nx){
    for (j in :ny){
      z[i,j] = /(*pi*sqrt(det_sigma)) * exp(-t(c(x[i], y[j]) - mu) %*% sigma_inv %*% t(t(c(x[i], y[j]) - mu)))
    }
  }
  return(z)
}
gauss_density = function(x,mu,sigma)
{
  nx = length(x)
  ny = length(y)
  z = matrix(,nrow=ny, ncol=nx)
  sigma_inv = solve(sigma)
  det_sigma = det(sigma)
  value = /(*pi*sqrt(det_sigma)) * exp(-/* t(x - mu) %*% sigma_inv %*% t(t(x - mu)))

  return(value)
}
plot_contour = function(ngrid, ns, mv.gauss, mu1,sigma1,mu2,sigma2){
  x.range1 = seq(mu1[]-ns*sigma1[],mu1[]+ns*sigma1[],length.out=ngrid)
  y.range1 = seq(mu1[]-ns*sigma1[],mu1[]+ns*sigma1[],length.out=ngrid)

  x.range2 = seq(mu2[]-ns*sigma2[],mu2[]+ns*sigma2[],length.out=ngrid)
  y.range2 = seq(mu2[]-ns*sigma2[],mu1[]+ns*sigma2[],length.out=ngrid)

  z1 = mv.gauss(x.range1, y.range1, mu1, sigma1)
  z2 = mv.gauss(x.range2, y.range2, mu2, sigma2)
  contour(x.range1, y.range1, z1, add=TRUE,col="red", lwd = )
  contour(x.range2, y.range2, z2, add=TRUE,col="blue", lwd = )
}
plot_iter = function(ngrid,x1,x2,mv.gauss, mu1,sigma1,mu2,sigma2, iter=){
  x = rbind(x1,x2)
  plot(x[,], x[,], type='p',
       main=sprintf("Iter %d: mu1=(%.2f, %.2f)/(-5,-6) mu2=(%.2f, %.2f)/(0,1)",
                    iter, mu1[],mu1[], mu2[], mu2[]))
  points(mu1[], mu1[], col='red', pch=)
  points(mu2[], mu2[], col='blue', pch=)
  plot_contour(ngrid,,mv.gauss, mu1,sigma1,mu2,sigma2)
}
obj_value = function(x,phi, mu1, sigma1, mu2, sigma2){
  n = dim(x)[]
  res =
  for (i in i:n){
    res = res + log(phi[]*gauss_density(x[i,], mu1, sigma1)+phi[]*gauss_density(x[i,], mu2, sigma2))
  }
  return(res)
}
plot_iter(ngrid,x1,x2,mv.gauss, mu1,sigma1,mu2,sigma2)

mu1_i = c(,)
mu2_i = c(,)
sigma1_i = matrix(c(,,,),nrow=)
sigma2_i = matrix(c(,,,),nrow=)
plot_iter(ngrid,x1,x2,mv.gauss, mu1_i,sigma1_i,mu2_i,sigma2_i,)

n = n1+n2
w = array(,dim=c(n,))
phi1 = 0.5
phi2 = 0.5
num_iter =
obj_val = rep(,num_iter)
for (ii in :num_iter){
  # E-step
  for (i in :n){
    w[i,] = phi1 * gauss_density(x[i,], mu1_i, sigma1_i)
    w[i,] = phi2 * gauss_density(x[i,], mu2_i, sigma2_i)
    tmp = sum(w[i,])
    w[i,] = w[i,] / tmp
    w[i,] = w[i,] / tmp
  }

  # M-step
  phi1 = mean(w[,])
  phi2 = mean(w[,])
  mu1_i = colSums(w[,]*x) / sum(w[,])
  mu2_i = colSums(w[,]*x) / sum(w[,])
  tmp = matrix(,nrow=,,ncol=)
  mu = mu1_i
  for (i in :n){
    tmp = tmp + w[i,] * (t(t(x[i,] - mu)) %*% t(x[i,] - mu))
  }
  sigma1_i = tmp / sum(w[,])
  tmp = matrix(,nrow=,ncol=)
  mu = mu2_i
  for (i in :n){
    tmp = tmp + w[i,] * (t(t(x[i,] - mu)) %*% t(x[i,] - mu))
  }
  sigma2_i = tmp / sum(w[,])
  plot_iter(ngrid,x1,x2,mv.gauss, mu1_i,sigma1_i,mu2_i,sigma2_i, ii)
  obj_val[ii] = obj_value(x,c(phi1,phi2), mu1_i,sigma1_i, mu2_i, sigma2_i)
}
plot(obj_val,type="l",main="Objective function: log likelihood",xlab="#Iteration")
print(c(phi1, phi2))
print(sigma1_i)
print(sigma2_i)