def test_gmm_best_segment(self):
"""
Calculate the best segment
generated by the GMM and
compare the subsequent likelihood
of a reference segmentation.
Note: this test will take a while
to run.
returns:
best_seg = np.ndarray[np.ndarray[float]]
"""
image_file = 'images/party_spock.png'
image_matrix = image_to_matrix(image_file)
image_matrix_flat = flatten_image_matrix(image_matrix)
num_components = 3
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
iters = 10
# generate best segment from 10 iterations
# and extract its likelihood
best_seg = gmm.best_segment(iters)
matrix_to_image(best_seg, 'images/best_segment_spock.png')
best_likelihood = gmm.likelihood()
# extract likelihood from reference image
ref_image_file = 'images/party_spock%d_baseline.png' % num_components
ref_image = image_to_matrix(ref_image_file, grays=True)
gmm_ref = GaussianMixtureModel(ref_image, num_components)
ref_vals = ref_image.flatten()
ref_means = list(set(ref_vals))
ref_variances = np.zeros(num_components)
ref_mixing = np.zeros(num_components)
for i in range(num_components):
relevant_vals = ref_vals[ref_vals == ref_means[i]]
ref_mixing[i] = float(len(relevant_vals)) / float(len(ref_vals))
ref_mask = ref_vals == ref_means[i]
ref_variances[i] = np.mean(
(image_matrix_flat[ref_mask] - ref_means[i])**2)
gmm_ref.means = ref_means
gmm_ref.variances = ref_variances
gmm_ref.mixing_coefficients = ref_mixing
ref_likelihood = gmm_ref.likelihood()
# compare best likelihood and reference likelihood
likelihood_diff = best_likelihood - ref_likelihood
print "Reference"
print gmm_ref.means
print gmm_ref.variances
print gmm_ref.mixing_coefficients
print best_likelihood
print ref_likelihood
print likelihood_diff
likelihood_thresh = 8e4
self.assertTrue(likelihood_diff >= likelihood_thresh,
msg=("Image segmentation failed to improve baseline "
"by at least %.2f" % likelihood_thresh))
def test_gmm_train(self):
"""Test the training
procedure for GMM using
synthetic data.
returns:
gmm = GaussianMixtureModel
"""
num_components = 2
data_range = (1, 1000)
actual_means = np.array([2, 4])
actual_variances = np.ones(num_components)
actual_mixing = np.ones(num_components) / 2
dataset_1 = generate_test_mixture(data_range, actual_means,
actual_variances, actual_mixing)
gmm = GaussianMixtureModel(dataset_1, num_components)
gmm.initialize_training()
# start off with faulty means
gmm.means = np.array([1, 3])
initial_likelihood = gmm.likelihood()
gmm.train_model()
final_likelihood = gmm.likelihood()
likelihood_difference = final_likelihood - initial_likelihood
likelihood_thresh = 250
diff_check = likelihood_difference >= likelihood_thresh
self.assertTrue(diff_check,
msg=("Model likelihood increased by less"
" than %d for a two-mean mixture" %
likelihood_thresh))
num_components = 4
actual_means = np.array([2, 4, 6, 8])
actual_variances = np.ones(num_components)
actual_mixing = np.ones(num_components) / 4
dataset_1 = generate_test_mixture(data_range, actual_means,
actual_variances, actual_mixing)
gmm = GaussianMixtureModel(dataset_1, num_components)
gmm.initialize_training()
# start off with faulty means
gmm.means = np.array([1, 3, 5, 9])
initial_likelihood = gmm.likelihood()
gmm.train_model()
final_likelihood = gmm.likelihood()
# compare likelihoods
likelihood_difference = final_likelihood - initial_likelihood
likelihood_thresh = 190
diff_check = likelihood_difference >= likelihood_thresh
self.assertTrue(diff_check,
msg=("Model likelihood increased by less "
"than %d for a four-mean mixture" %
likelihood_thresh))
def test_gmm_segment(self):
"""
Apply the trained GMM
to unsegmented image and
generate a segmented image.
returns:
segmented_matrix = numpy.ndarray[numpy.ndarray[float]]
"""
image_file = 'images/party_spock.png'
image_matrix = image_to_matrix(image_file)
num_components = 3
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.train_model()
segment = gmm.segment()
segment_num_components = len(np.unique(segment))
self.assertTrue(segment_num_components == num_components,
msg="Incorrect number of image segments produced")
def test_gmm_joint_prob(self):
"""Testing the GMM method
for calculating the joint
log probability of a given point.
Should return -0.9413.
returns:
joint_prob = float
"""
image_file = 'images/self_driving.png'
image_matrix = image_to_matrix(image_file)
num_components = 5
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.array([0.03921569, 0.1764706, 0.06666667, 0.42745098, 0.2784314])
test_val = 0.03921569
joint_prob = gmm.joint_prob(test_val)
self.assertEqual(round(joint_prob, 4), -0.9413,
msg="Incorrect joint log probability")
def test_gmm_likelihood(self):
"""Testing the GMM method
for calculating the overall
model probability.
Should return -302844.
returns:
likelihood = float
"""
image_file = 'images/self_driving.png'
image_matrix = image_to_matrix(image_file)
num_components = 5
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.array([0.03921569, 0.1764706, 0.06666667, 0.42745098, 0.2784314])
likelihood = gmm.likelihood()
self.assertEqual(round(likelihood), -302844,
msg="Incorrect model probability")
def test_gmm_likelihood(self):
"""Testing the GMM method
for calculating the overall
model probability.
Should return -364370.
returns:
likelihood = float
"""
image_file = 'images/party_spock.png'
image_matrix = image_to_matrix(image_file)
num_components = 5
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = [0.4627451, 0.10196079, 0.027450981,
0.011764706, 0.1254902]
likelihood = gmm.likelihood()
self.assertEqual(round(likelihood), -364370,
msg="Incorrect model probability")
def test_bayes_info(self):
"""
Test for your
implementation of
BIC on fixed GMM values.
Should be about 610317.
returns:
BIC = float
"""
image_file = 'images/self_driving.png'
image_matrix = image_to_matrix(image_file)
num_components = 3
initial_means = np.array([0.4627451, 0.10196079, 0.027450981])
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.copy(initial_means)
b_i_c = bayes_info_criterion(gmm)
self.assertEqual(round(610317, -3), round(b_i_c, -3),
msg="BIC calculation incorrect.")
def test_gmm_joint_prob(self):
"""Testing the GMM method
for calculating the joint
log probability of a given point.
Should return -0.98196.
returns:
joint_prob = float
"""
image_file = 'images/party_spock.png'
image_matrix = image_to_matrix(image_file)
num_components = 5
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = [0.4627451, 0.10196079, 0.027450981,
0.011764706, 0.1254902]
test_val = 0.4627451
joint_prob = gmm.joint_prob(test_val)
self.assertEqual(round(joint_prob, 4), -0.982,
msg="Incorrect joint log probability")
def test_convergence_condition(self):
"""
Compare the performance of
the default convergence function
with the new convergence function.
return:
default_convergence_likelihood = float
new_convergence_likelihood = float
"""
image_file = 'images/party_spock.png'
image_matrix = image_to_matrix(image_file)
num_components = 3
initial_means = np.array([0.4627451, 0.10196079, 0.027450981])
# first test original model
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.copy(initial_means)
gmm.train_model()
default_convergence_likelihood = gmm.likelihood()
# now test new convergence model
gmm_new = GaussianMixtureModelConvergence(image_matrix, num_components)
gmm_new.initialize_training()
gmm_new.means = np.copy(initial_means)
gmm_new.train_model()
new_convergence_likelihood = gmm_new.likelihood()
# test convergence difference
convergence_diff = new_convergence_likelihood - \
default_convergence_likelihood
convergence_thresh = 8200
print new_convergence_likelihood
print default_convergence_likelihood
self.assertTrue(convergence_diff >= convergence_thresh,
msg=("Likelihood difference between"
" the original and converged"
" models less than %.2f" % convergence_thresh))
def test_gmm_improvement(self):
"""
Tests whether the new mixture
model is actually an improvement
over the previous one: if the
new model has a higher likelihood
than the previous model for the
provided initial means.
returns:
original_segment = numpy.ndarray[numpy.ndarray[float]]
improved_segment = numpy.ndarray[numpy.ndarray[float]]
"""
image_file = 'images/self_driving.png'
image_matrix = image_to_matrix(image_file)
num_components = 4
initial_means = np.array([0.4627451, 0.20392157, 0.36078432, 0.47254905])
# first train original model with fixed means
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.copy(initial_means)
gmm.train_model()
original_segment = gmm.segment()
original_likelihood = gmm.likelihood()
# then train improved model
gmm_improved = GaussianMixtureModelImproved(image_matrix,
num_components)
gmm_improved.initialize_training()
gmm_improved.train_model()
improved_segment = gmm_improved.segment()
improved_likelihood = gmm_improved.likelihood()
# then calculate likelihood difference
diff_thresh = 2.2e3
likelihood_diff = improved_likelihood - original_likelihood
print(improved_likelihood, original_likelihood, likelihood_diff)
self.assertTrue(likelihood_diff >= diff_thresh,
msg=("Model likelihood less than "
"%d higher than original model" % diff_thresh))
def test_convergence_condition(self):
"""
Compare the performance of
the default convergence function
with the new convergence function.
return:
default_convergence_likelihood = float
new_convergence_likelihood = float
"""
image_file = 'images/self_driving.png'
image_matrix = image_to_matrix(image_file)
num_components = 4
initial_means = np.array([0.25882354, 0.05686277, 0.75686275, 0.3882353])
# first test original model
gmm = GaussianMixtureModel(image_matrix, num_components)
gmm.initialize_training()
gmm.means = np.copy(initial_means)
gmm.train_model()
default_convergence_likelihood = gmm.likelihood()
# now test new convergence model
gmm_new = GaussianMixtureModelConvergence(image_matrix, num_components)
gmm_new.initialize_training()
gmm_new.means = np.copy(initial_means)
gmm_new.train_model()
new_convergence_likelihood = gmm_new.likelihood()
# test convergence difference
convergence_diff = new_convergence_likelihood - \
default_convergence_likelihood
convergence_thresh = 1800
self.assertTrue(convergence_diff >= convergence_thresh,
msg=("Likelihood difference between"
" the original and converged"
" models less than %.2f" % convergence_thresh))