n_iter = 10 # Parameter of the alpha-stable distribution for the alpha-CSC model. # 0 < alpha < 2 # A value of 2 would correspond to the Gaussian noise model, as in vanilla CSC. alpha = 1.2 ############################################################################### # First, we fit a CSC model on the clean data. Interestingly, we obtain # prototypical waveforms of the signal on which we can clearly see the CFC. from alphacsc import learn_d_z, learn_d_z_weighted X = data_clean _, _, d_hat, z_hat, _ = learn_d_z(X, n_iter=n_iter, **common_params) plot_atoms(d_hat) ############################################################################### # Then, if we fit a CSC model on the dirty data, the model is strongly affected # by the artifacts, and we cannot see CFC anymore in the temporal waveforms. X = data_dirty _, _, d_hat, z_hat, _ = learn_d_z(X, n_iter=n_iter, **common_params) plot_atoms(d_hat) ############################################################################### # Finally, If we fit an alpha-CSC model on the dirty data, the model is less
###############################################################################
# Note that the atoms don't always have the same amplitude or occur at the
# same time instant.
#
# Now, we run vanilla CSC on the data.
from alphacsc import learn_d_z # noqa
random_state = 60
pobj, times, d_hat, z_hat, reg = learn_d_z(X,
n_atoms,
n_times_atom,
reg=reg,
n_iter=n_iter,
solver_d_kwargs=dict(factr=100),
random_state=random_state,
n_jobs=1,
verbose=1)
print('Vanilla CSC')
###############################################################################
# Finally, let's compare the results.
import matplotlib.pyplot as plt # noqa
plt.figure()
plt.plot(d_hat.T)
plt.plot(ds_true.T, 'k--')
from alphacsc import learn_d_z
params = dict(
n_atoms=3,
n_times_atom=int(sfreq * 1.0), # 1000. ms
reg=5.,
n_iter=10,
solver_z='l-bfgs',
solver_z_kwargs=dict(factr=1e9),
solver_d_kwargs=dict(factr=1e2),
random_state=42,
n_jobs=5,
verbose=1)
_, _, d_hat, z_hat, _ = learn_d_z(data, **params)
###############################################################################
# Plot the temporal patterns. Interestingly, we obtain prototypical
# waveforms of the signal on which we can clearly see the CFC.
n_atoms, n_times_atom = d_hat.shape
n_columns = min(6, n_atoms)
n_rows = int(np.ceil(n_atoms // n_columns))
figsize = (4 * n_columns, 3 * n_rows)
fig, axes = plt.subplots(n_rows, n_columns, figsize=figsize, sharey=True)
axes = axes.ravel()
for kk in range(n_atoms):
ax = axes[kk]
time = np.arange(n_times_atom) / sfreq
X_new -= np.mean(X_new)
X_new /= np.std(X_new)
###############################################################################
# The convolutions can result in edge artifacts at the edges of the trials.
# Therefore, we discount the contributions from the edges by windowing the
# trials.
from numpy import hamming
X_new *= hamming(n_times)[None, :]
###############################################################################
# Of course, in a data-limited setting we want to use as much of the data as
# possible. If this is the case, you can set `overlap` to non-zero (for example
# half the epoch length).
#
# Now, we run regular CSC since the trials are not too noisy
from alphacsc import learn_d_z
pobj, times, d_hat, z_hat, reg = learn_d_z(X_new,
n_atoms,
n_times_atom,
reg=reg,
n_iter=n_iter,
random_state=random_state,
n_jobs=1)
###############################################################################
# Let's look at the atoms now.
plt.figure()
plt.plot(d_hat.T)
plt.show()
###############################################################################
# Now, we run vanilla CSC on the data.
from functools import partial # noqa
from alphacsc import learn_d_z, update_d_block # noqa
random_state = 60
func = partial(update_d_block, projection='dual')
pobj, times, d_hat, Z_hat = learn_d_z(X,
n_atoms,
n_times_atom,
func_d=func,
reg=reg,
n_iter=n_iter,
solver_d_kwargs=dict(factr=100),
random_state=random_state,
n_jobs=1,
solver_z='l_bfgs',
verbose=1)
print('Vanilla CSC')
###############################################################################
# and then alpha CSC on the same data
from alphacsc import learn_d_z_weighted # noqa
d_hat_mcem, z_hat_mcem, Tau = learn_d_z_weighted(
X,
n_atoms,