def test_embedding(metric, eps, get_covmats):
"""Test Embedding."""
n_trials, n_channels, n_comp = 6, 3, 2
covmats = get_covmats(n_trials, n_channels)
embd = Embedding(metric=metric, n_components=n_comp, eps=eps)
covembd = embd.fit_transform(covmats)
assert covembd.shape == (n_trials, n_comp)
def plot_embedding(X,
y=None,
metric='riemann',
title='Spectral embedding of covariances'):
"""Plot 2D embedding of covariance matrices using Diffusion maps."""
lapl = Embedding(n_components=2, metric=metric)
embd = lapl.fit_transform(X)
if y is None:
y = np.ones(embd.shape[0])
fig, ax = plt.subplots(figsize=(7, 7), facecolor='white')
for label in np.unique(y):
idx = (y == label)
ax.scatter(embd[idx, 0], embd[idx, 1], s=36)
ax.set_xlabel(r'$\varphi_1$', fontsize=16)
ax.set_ylabel(r'$\varphi_2$', fontsize=16)
ax.set_title(title, fontsize=16)
ax.grid(False)
ax.set_xticks([-1.0, -0.5, 0.0, +0.5, 1.0])
ax.set_yticks([-1.0, -0.5, 0.0, +0.5, 1.0])
ax.legend(list(np.unique(y)))
return fig
def xdawn_embedding(data, use_xdawn):
"""Perform embedding of EEG data in 2D Euclidean space
with Laplacian Eigenmaps.
Parameters
----------
data : dict
A dictionary containing training and testing data
Returns
-------
array
Embedded
"""
if use_xdawn:
nfilter = 3
xdwn = XdawnCovariances(estimator='scm', nfilter=nfilter)
covs = xdwn.fit(data['train_x'],
data['train_y']).transform(data['test_x'])
lapl = Embedding(metric='riemann', n_components=3)
embd = lapl.fit_transform(covs)
else:
tangent_space = Pipeline([
('cov_transform', Covariances(estimator='lwf')),
('tangent_space', TangentSpace(metric='riemann'))
])
t_space = tangent_space.fit(data['train_x'],
data['train_y']).transform(data['test_x'])
reducer = umap.UMAP(n_neighbors=30, min_dist=1, spread=2)
embd = reducer.fit_transform(t_space)
return embd
def test_fit_independence(get_covmats):
n_trials, n_channels = 6, 3
covmats = get_covmats(n_trials, n_channels)
embd = Embedding()
embd.fit_transform(covmats)
# retraining with different size should erase previous fit
new_covmats = covmats[:, :-1, :-1]
embd.fit_transform(new_covmats)
def plot_embedding(X, y=None, metric='riemann',
title='Spectral embedding of covariances'):
"""Plot 2D embedding of covariance matrices using Diffusion maps."""
lapl = Embedding(n_components=2, metric=metric)
embd = lapl.fit_transform(X)
if y is None:
y = np.ones(embd.shape[0])
fig, ax = plt.subplots(figsize=(7, 7), facecolor='white')
for label in np.unique(y):
idx = (y == label)
ax.scatter(embd[idx, 0], embd[idx, 1], s=36)
ax.set_xlabel(r'$\varphi_1$', fontsize=16)
ax.set_ylabel(r'$\varphi_2$', fontsize=16)
ax.set_title(title, fontsize=16)
ax.grid(False)
ax.set_xticks([-1.0, -0.5, 0.0, +0.5, 1.0])
ax.set_yticks([-1.0, -0.5, 0.0, +0.5, 1.0])
ax.legend(list(np.unique(y)))
return fig
def xdawn_embedding(data):
"""Perform embedding of EEG data in 2D Euclidean space
with Laplacian Eigenmaps.
Parameters
----------
data : dict
A dictionary containing training and testing data
Returns
-------
array
Embedded
"""
nfilter = 3
xdwn = XdawnCovariances(estimator='scm', nfilter=nfilter)
covs = xdwn.fit(data['train_x'], data['train_y']).transform(data['test_x'])
lapl = Embedding(metric='riemann', n_components=3)
embd = lapl.fit_transform(covs)
return embd
samples_2 = sample_gaussian_spd(n_matrices=n_matrices,
mean=mean,
sigma=sigma / 2,
random_state=random_state)
samples_3 = sample_gaussian_spd(n_matrices=n_matrices,
mean=epsilon * mean,
sigma=sigma,
random_state=random_state)
# Stack all of the samples into one data array for the embedding
samples = np.concatenate([samples_1, samples_2, samples_3])
labels = np.array(n_matrices * [1] + n_matrices * [2] + n_matrices * [3])
###############################################################################
# Apply the spectral embedding over the SPD matrices
lapl = Embedding(metric='riemann', n_components=2)
embd = lapl.fit_transform(X=samples)
###############################################################################
# Plot the results
fig, ax = plt.subplots(figsize=(8, 6))
colors = {1: 'C0', 2: 'C1', 3: 'C2'}
for i in range(len(samples)):
ax.scatter(embd[i, 0], embd[i, 1], c=colors[labels[i]], s=50)
ax.scatter([], [], c='C0', s=50, label=r'$\varepsilon = 1.00, \sigma = 1.00$')
ax.scatter([], [], c='C1', s=50, label=r'$\varepsilon = 1.00, \sigma = 0.50$')
ax.scatter([], [], c='C2', s=50, label=r'$\varepsilon = 4.00, \sigma = 1.00$')
ax.set_xticks([-1, -0.5, 0, 0.5, 1.0])
ax.set_xticklabels([-1, -0.5, 0, 0.5, 1.0], fontsize=12)
def test_embedding():
"""Test Embedding."""
covmats, diags, A = generate_cov(100, 3)
embd = Embedding(metric='riemann', n_components=2).fit_transform(covmats)
assert_array_equal(embd.shape[1], 2)
# get trials and labels
X = epochs.get_data()
y = events[:, -1]
# cross validation
skf = StratifiedKFold(n_splits=5)
clf = make_pipeline(Covariances(estimator='lwf'), MDM())
scr = cross_val_score(clf, X, y, cv=skf)
# print results of classification
print('subject', subject)
print('mean accuracy :', scr.mean())
# get the spectral embedding of the epochs
C = Covariances(estimator='lwf').fit_transform(X)
emb = Embedding(metric='riemann').fit_transform(C)
# scatter plot of the embedded points
fig = plt.figure(facecolor='white', figsize=(5.6, 5.2))
colors = {1: 'r', 2: 'b'}
for embi, yi in zip(emb, y):
plt.scatter(embi[0], embi[1], s=120, c=colors[yi])
labels = {1: 'closed', 2: 'open'}
for yi in np.unique(y):
plt.scatter([], [], c=colors[yi], label=labels[yi])
plt.xticks([-1, -0.5, 0.0, +0.5, 1.0])
plt.yticks([-1, -0.5, 0.0, +0.5, 1.0])
plt.legend()
plt.title('Spectral embedding of the epochs from subject ' + str(subject),
fontsize=10)
epochs = mne.Epochs(raw, events, event_id, tmin, tmax, proj=False,
picks=picks, baseline=None, preload=True, verbose=False)
X = epochs.get_data()
y = epochs.events[:, -1]
###############################################################################
# Embedding the Xdawn covariance matrices with Laplacian Eigenmaps
nfilter = 4
xdwn = XdawnCovariances(estimator='scm', nfilter=nfilter)
split = train_test_split(X, y, train_size=0.25, random_state=42)
Xtrain, Xtest, ytrain, ytest = split
covs = xdwn.fit(Xtrain, ytrain).transform(Xtest)
lapl = Embedding(metric='riemann', n_components=2)
embd = lapl.fit_transform(covs)
###############################################################################
# Plot the three first components of the embedded points
fig, ax = plt.subplots(figsize=(7, 8), facecolor='white')
for cond, label in event_id.items():
idx = (ytest == label)
ax.scatter(embd[idx, 0], embd[idx, 1], s=36, label=cond)
ax.set_xlabel(r'$\varphi_1$', fontsize=16)
ax.set_ylabel(r'$\varphi_2$', fontsize=16)
ax.set_title('Spectral embedding of ERP recordings', fontsize=16)
ax.set_xticks([-1.0, -0.5, 0.0, +0.5, 1.0])