if __name__ == '__main__':
###############################################################################
# Generate sample data
S = np.random.standard_t(1.5, size=(2, 10000))
S[0] *= 2.
# Mix data
A = [[1, 1], [0, 2]] # Mixing matrix
X = np.dot(A, S) # Generate observations
pca = PCA()
S_pca_ = pca.fit(X.T).transform(X.T).T
ica = FastICA()
S_ica_ = ica.fit(X).transform(X) # Estimate the sources
S_ica_ /= S_ica_.std(axis=1)[:,np.newaxis]
###############################################################################
# Plot results
def plot_samples(S, axis_list=None):
pl.scatter(S[0], S[1], s=2, marker='o', linewidths=0, zorder=10)
if axis_list is not None:
colors = [(0, 0.6, 0), (0.6, 0, 0)]
for color, axis in zip(colors, axis_list):
axis /= axis.std()
x_axis, y_axis = axis
# Trick to get legend to work
from scikits.learn.fastica import FastICA
###############################################################################
# Generate sample data
S = np.random.standard_t(1.5, size=(2, 10000))
S[0] *= 2.
# Mix data
A = [[1, 1], [0, 2]] # Mixing matrix
X = np.dot(A, S) # Generate observations
pca = PCA()
S_pca_ = pca.fit(X.T).transform(X.T).T
ica = FastICA()
S_ica_ = ica.fit(X).transform(X) # Estimate the sources
S_ica_ /= S_ica_.std(axis=1)[:, np.newaxis]
###############################################################################
# Plot results
def plot_samples(S, axis_list=None):
pl.scatter(S[0], S[1], s=2, marker='o', linewidths=0, zorder=10)
if axis_list is not None:
colors = [(0, 0.6, 0), (0.6, 0, 0)]
for color, axis in zip(colors, axis_list):
axis /= axis.std()
x_axis, y_axis = axis
###############################################################################
# Generate sample data
np.random.seed(0)
n_samples = 2000
time = np.linspace(0, 10, n_samples)
s1 = np.sin(2*time) # Signal 1 : sinusoidal signal
s2 = np.sign(np.sin(3*time)) # Signal 2 : square signal
S = np.c_[s1,s2].T
S += 0.2*np.random.normal(size=S.shape) # Add noise
S /= S.std(axis=1)[:,np.newaxis] # Standardize data
# Mix data
A = [[1, 1], [0.5, 2]] # Mixing matrix
X = np.dot(A, S) # Generate observations
# Compute ICA
ica = FastICA()
S_ = ica.fit(X).transform(X) # Get the estimated sources
A_ = ica.get_mixing_matrix() # Get estimated mixing matrix
assert np.allclose(X, np.dot(A_, S_))
###############################################################################
# Plot results
pl.figure()
pl.subplot(3, 1, 1)
pl.plot(S.T)
pl.title('True Sources')
pl.subplot(3, 1, 2)
pl.plot(X.T)
pl.title('Observations (mixed signal)')
pl.subplot(3, 1, 3)
###############################################################################
# Generate sample data
np.random.seed(0)
n_samples = 2000
time = np.linspace(0, 10, n_samples)
s1 = np.sin(2 * time) # Signal 1 : sinusoidal signal
s2 = np.sign(np.sin(3 * time)) # Signal 2 : square signal
S = np.c_[s1, s2].T
S += 0.2 * np.random.normal(size=S.shape) # Add noise
S /= S.std(axis=1)[:, np.newaxis] # Standardize data
# Mix data
A = [[1, 1], [0.5, 2]] # Mixing matrix
X = np.dot(A, S) # Generate observations
# Compute ICA
ica = FastICA()
S_ = ica.fit(X).transform(X) # Get the estimated sources
A_ = ica.get_mixing_matrix() # Get estimated mixing matrix
assert np.allclose(X, np.dot(A_, S_))
###############################################################################
# Plot results
pl.figure()
pl.subplot(3, 1, 1)
pl.plot(S.T)
pl.title('True Sources')
pl.subplot(3, 1, 2)
pl.plot(X.T)
pl.title('Observations (mixed signal)')
pl.subplot(3, 1, 3)