def test_fit(self):
"""Test the fit method."""
X_train_a = gs.array([[[EULER**2, 0], [0, 1]], [[1, 0], [0, 1]]])
X_train_b = gs.array([[[EULER**8, 0], [0, 1]], [[1, 0], [0, 1]]])
X_train = gs.concatenate([X_train_a, X_train_b])
y_train = gs.array([0, 0, 1, 1])
for metric in METRICS:
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
metric(n=2), n_classes=2, point_type="matrix")
MDMEstimator.fit(X_train, y_train)
bary_a_fit = MDMEstimator.mean_estimates_[0]
bary_b_fit = MDMEstimator.mean_estimates_[1]
if metric in [SPDMetricAffine, SPDMetricLogEuclidean]:
bary_a_expected = gs.array([[EULER, 0], [0, 1]])
bary_b_expected = gs.array([[EULER**4, 0], [0, 1]])
elif metric in [SPDMetricEuclidean]:
bary_a_expected = gs.array([[0.5 * EULER**2 + 0.5, 0], [0, 1]])
bary_b_expected = gs.array([[0.5 * EULER**8 + 0.5, 0], [0, 1]])
else:
raise ValueError("Invalid metric: {}".format(metric))
self.assertAllClose(bary_a_fit, bary_a_expected)
self.assertAllClose(bary_b_fit, bary_b_expected)
def main():
"""Execute illustration of MDM supervised classifier."""
n_samples = 100
n_features = 2
n_classes = 3
# generate toy dataset of 2D SPD matrices
dataset_generator = geomstats.datasets.sample_sdp_2d.DatasetSPD2D(
n_samples, n_features, n_classes)
data, labels = dataset_generator.generate_sample_dataset()
# plot dataset as ellipses
ellipsis = visualization.Ellipsis2D()
for i in range(n_samples):
x = data[i]
y = geomstats.datasets.sample_sdp_2d.get_label_at_index(i, labels)
ellipsis.draw(x, color=ellipsis.colors[y], alpha=.1)
# define and fit MDM classifier to data
metric = SPDMetricAffine(n=n_features)
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
metric, n_classes, point_type='matrix')
MDMEstimator.fit(data, labels)
# plot Frechet means computed in the MDM
for i in range(n_classes):
ellipsis.draw(MDMEstimator.mean_estimates_[i],
color=ellipsis.colors_alt[i],
linewidth=5,
label='Barycenter of class ' + str(i))
# generate random test samples, and predict with MDM classifier
data_test = SPDMatrices(n=n_features).random_uniform(n_samples=3)
predictions = MDMEstimator.predict(data_test)
for i in range(data_test.shape[0]):
c = list(predictions[i] == 1).index(True)
x_from, y_from = ellipsis.draw(data_test[i],
color=ellipsis.colors[c],
linewidth=5)
_, _, x_to, y_to = ellipsis.compute_coordinates(
MDMEstimator.mean_estimates_[c])
arrow = visualization.DataArrow(ellipsis.fig)
arrow.draw(x_from, y_from, x_to, y_to)
ellipsis.fig.axes[0].set_title(
'Example plot of the MDM classifier in dimension 2\n'
'3-class fit and 3 test sample prediction\n'
'(black arrows denote assignement)')
ellipsis.plot()
def test_predict(self):
"""Test the predict method."""
X_train_a = gs.array([[EULER, 0], [0, 1]])[None, ...]
X_train_b = gs.array([[EULER**4, 0], [0, 1]])[None, ...]
X_train = gs.concatenate([X_train_a, X_train_b])
y_train = gs.array([42, 17])
X_test = gs.array([[EULER**2, 0], [0, 1]])[None, ...]
y_expected = gs.array([42])
for metric in METRICS:
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
metric(n=2), n_classes=2, point_type="matrix")
MDMEstimator.fit(X_train, y_train)
y_test = MDMEstimator.predict(X_test)
self.assertAllClose(y_test, y_expected)
def test_predict(self):
"""Test the predict method."""
n_clusters = 2
bary_a = gs.array([[EULER, 0], [0, 1]])
bary_b = gs.array([[EULER**4, 0], [0, 1]])
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
SPDMetricAffine(n=2), n_clusters, point_type='matrix')
MDMEstimator.mean_estimates_ = gs.concatenate(
[bary_a[None, ...], bary_b[None, ...]])
X = gs.array([[EULER**3, 0], [0, 1]])[None, ...]
y_expected = gs.array([[0, 1]])
y_result = MDMEstimator.predict(X)
self.assertAllClose(y_result, y_expected)
def test_score(self):
"""Test the score method."""
X_train_a = gs.array([[EULER, 0], [0, 1]])[None, ...]
X_train_b = gs.array([[EULER**4, 0], [0, 1]])[None, ...]
X_train = gs.concatenate([X_train_a, X_train_b])
y_train = gs.array([-1, 1])
X_test = gs.array([[[EULER**3, 0], [0, 1]], [[EULER**2, 0], [0, 1]]])
for metric in METRICS:
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
metric(n=2), n_classes=2, point_type="matrix")
MDMEstimator.fit(X_train, y_train)
if metric in [SPDMetricAffine, SPDMetricLogEuclidean]:
y_expected = gs.array([1, -1])
elif metric in [SPDMetricEuclidean]:
y_expected = gs.array([-1, -1])
else:
raise ValueError("Invalid metric: {}".format(metric))
accuracy = MDMEstimator.score(X_test, y_expected)
self.assertAllClose(accuracy, 1.0)
def test_predict_proba(self):
"""Test the predict_proba method."""
X_train_a = gs.array([[1.0, 0], [0, 1]])[None, ...]
X_train_b = gs.array([[EULER**10, 0], [0, 1]])[None, ...]
X_train = gs.concatenate([X_train_a, X_train_b])
y_train = gs.array([1, 2])
X_test = gs.array([[[1.0, 0], [0, 1]], [[EULER**5, 0], [0, 1]]])
for metric in METRICS:
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
metric(n=2), n_classes=2, point_type="matrix")
MDMEstimator.fit(X_train, y_train)
proba_test = MDMEstimator.predict_proba(X_test)
if metric in [SPDMetricAffine, SPDMetricLogEuclidean]:
proba_expected = gs.array([[1.0, 0.0], [0.5, 0.5]])
elif metric in [SPDMetricEuclidean]:
proba_expected = gs.array([[1.0, 0.0], [1.0, 0.0]])
else:
raise ValueError("Invalid metric: {}".format(metric))
self.assertAllClose(proba_test, proba_expected)
def test_fit(self):
"""Test the fit method."""
n_clusters = 2
MDMEstimator = RiemannianMinimumDistanceToMeanClassifier(
SPDMetricAffine(n=2), n_clusters, point_type='matrix')
points_a = gs.array([[[EULER**2, 0], [0, 1]], [[1, 0], [0, 1]]])
labels_a = gs.array([[1, 0], [1, 0]])
bary_a_expected = gs.array([[EULER, 0], [0, 1]])
points_b = gs.array([[[EULER**8, 0], [0, 1]], [[1, 0], [0, 1]]])
labels_b = gs.array([[0, 1], [0, 1]])
bary_b_expected = gs.array([[EULER**4, 0], [0, 1]])
train_data = gs.concatenate([points_a, points_b])
train_labels = gs.concatenate([labels_a, labels_b])
MDMEstimator.fit(train_data, train_labels)
bary_a_result = MDMEstimator.mean_estimates_[0]
bary_b_result = MDMEstimator.mean_estimates_[1]
self.assertAllClose(bary_a_result, bary_a_expected)
self.assertAllClose(bary_b_result, bary_b_expected)