xs = [mnorm.rvs(mu[k], sigma[k], size=n) for k in range(3)]
z = np.random.multinomial(1, mix, size=n).astype('Bool')
x = xs[0].copy()
x[z[:,1]] = xs[1][z[:,1]]
x[z[:,2]] = xs[2][z[:,2]]
z_ind = np.zeros(n, dtype=int)
z_ind[z[:,1]] = 1
z_ind[z[:,2]] = 2
init_mu = np.array([[0., 0.], [1., 1.], [2., 2.]])
init_sigma = [np.identity(2) for i in range(3)]
init_mix = np.array([1., 1., 1.])/3
niter = 500
_, (logliks_em, _) = em_alg(
x, init_mu, init_sigma, init_mix, num_iter=niter)
i=0
run_storage = np.zeros(((niter+1)*2, 3))
run_storage[i*(niter+1):(i+1)*(niter+1), 0] = i
run_storage[i*(niter+1):(i+1)*(niter+1), 1] = np.arange(niter+1)
run_storage[i*(niter+1):(i+1)*(niter+1), 2] = logliks_em
# More overlapping
np.random.seed(29643)
mu = np.array([[0., 2.], [2., 0.], [3., 4.]])
xs = [mnorm.rvs(mu[k], sigma[k], size=n) for k in range(3)]
z = np.random.multinomial(1, mix, size=n).astype('Bool')
x = xs[0].copy()
# Plot data
cmap, norm = colors.from_levels_and_colors(
levels=[0, 1, 2], colors=['magenta', 'cyan', 'green'], extend='max')
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.scatter(x[:,0], x[:,1], c=z_ind, cmap=cmap, norm=norm)
fig.savefig('./sim_data.pdf')
# Estimate
init_mu = np.array([[0., 0.], [1., 1.], [2., 2.]])
init_sigma = [np.identity(2) for i in range(3)]
init_mix = np.array([1., 1., 1.])/3
res_em, (logliks_em, times_em) = em_alg(
x, init_mu, init_sigma, init_mix, num_iter=250)
res_da, (logliks_da, times_da) = em_alg(
x, init_mu, init_sigma, init_mix, num_iter=250,
beta_func=lambda i: 1.-np.exp(-(i+1)/5))
res_sa, (logliks_sa, times_sa) = sim_anneal(
x, init_mu, init_sigma, init_mix, num_iter=250, seed=29624,
temp_func=lambda i: max(1e-4, 100*.992**i))
# Save results
colnames = \
'logliks_em, times_em, logliks_da, times_da, logliks_sa, times_sa'
np.savetxt(
'./intermediate_data/singlerun_results.csv',
np.column_stack((logliks_em, times_em,
z_ind = np.zeros(n, dtype=int)
z_ind[z[:,1]] = 1
z_ind[z[:,2]] = 2
# Run SA
# Note that some runs for small sample sizes run have issues with
# singular covariance matrices, so I simply try a couple times
# if there is an issue.
res_sa, _ = sim_anneal(
x, init_mu, init_sigma, init_mix, num_iter=iter_num,
temp_func=lambda i: max(1e-4, 100*.992**i))
# Run EM
res_em, _ = em_alg(
x, init_mu, init_sigma, init_mix, num_iter=iter_num)
# Run DA
res_da, _ = em_alg(
x, init_mu, init_sigma, init_mix, num_iter=iter_num,
beta_func=lambda i: 1.-np.exp(-(i+1)/5))
distances = np.array([cluster_dist(mu, res_sa[0]),
cluster_dist(mu, res_em[0]),
cluster_dist(mu, res_da[0])])
# Store results
run_storage[(j*3):((j+1)*3), 0] = j
run_storage[(j*3):((j+1)*3), 1] = methods
run_storage[(j*3):((j+1)*3), 2] = distances
colors=['magenta', 'cyan', 'green'],
extend='max')
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.scatter(x[:, 0], x[:, 1], c=z_ind, cmap=cmap, norm=norm)
fig.savefig('./sim_data.pdf')
# Estimate
init_mu = np.array([[0., 0.], [1., 1.], [2., 2.]])
init_sigma = [np.identity(2) for i in range(3)]
init_mix = np.array([1., 1., 1.]) / 3
res_em, (logliks_em, times_em) = em_alg(x,
init_mu,
init_sigma,
init_mix,
num_iter=250)
res_da, (logliks_da,
times_da) = em_alg(x,
init_mu,
init_sigma,
init_mix,
num_iter=250,
beta_func=lambda i: 1. - np.exp(-(i + 1) / 5))
res_sa, (logliks_sa,
times_sa) = sim_anneal(x,
init_mu,
init_sigma,
