Note
Go to the end to download the full example code or to run this example in your browser via JupyterLite or Binder.
Blind source separation using FastICA
An example of estimating sources from noisy data.
Independent component analysis (ICA) is used to estimate sources given noisy measurements. Imagine 3 instruments playing simultaneously and 3 microphones recording the mixed signals. ICA is used to recover the sources ie. what is played by each instrument. Importantly, PCA fails at recovering our instruments since the related signals reflect non-Gaussian processes.
# Authors: The scikit-learn developers # SPDX-License-Identifier: BSD-3-Clause
Generate sample data
import numpy as np from scipy import signal np.random.seed(0) n_samples = 2000 time = np.linspace(0, 8, n_samples) s1 = np.sin(2 * time) # Signal 1 : sinusoidal signal s2 = np.sign(np.sin(3 * time)) # Signal 2 : square signal s3 = signal.sawtooth(2 * np.pi * time) # Signal 3: saw tooth signal S = np.c_[s1, s2, s3] S += 0.2 * np.random.normal(size=S.shape) # Add noise S /= S.std(axis=0) # Standardize data # Mix data A = np.array([[1, 1, 1], [0.5, 2, 1.0], [1.5, 1.0, 2.0]]) # Mixing matrix X = np.dot(S, A.T) # Generate observations
Fit ICA and PCA models
from sklearn.decomposition import PCA, FastICA # Compute ICA ica = FastICA(n_components=3, whiten="arbitrary-variance") S_ = ica.fit_transform(X) # Reconstruct signals A_ = ica.mixing_ # Get estimated mixing matrix # We can `prove` that the ICA model applies by reverting the unmixing. assert np.allclose(X, np.dot(S_, A_.T) + ica.mean_) # For comparison, compute PCA pca = PCA(n_components=3) H = pca.fit_transform(X) # Reconstruct signals based on orthogonal components
Plot results
import matplotlib.pyplot as plt
plt.figure()
models = [X, S, S_, H]
names = [
"Observations (mixed signal)",
"True Sources",
"ICA recovered signals",
"PCA recovered signals",
]
colors = ["red", "steelblue", "orange"]
for ii, (model, name) in enumerate(zip(models, names), 1):
plt.subplot(4, 1, ii)
plt.title(name)
for sig, color in zip(model.T, colors):
plt.plot(sig, color=color)
plt.tight_layout()
plt.show()
Total running time of the script: (0 minutes 0.386 seconds)
Related examples
© 2007–2026 The scikit-learn developers
Licensed under the 3-clause BSD License.
https://scikit-learn.org/1.9/auto_examples/decomposition/plot_ica_blind_source_separation.html
