.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here ` to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_decomposition_plot_ica_blind_source_separation.py:
=====================================
Blind source separation using FastICA
=====================================
An example of estimating sources from noisy data.
:ref:`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.
.. image:: /auto_examples/decomposition/images/sphx_glr_plot_ica_blind_source_separation_001.png
:alt: Observations (mixed signal), True Sources, ICA recovered signals, PCA recovered signals
:class: sphx-glr-single-img
.. code-block:: default
print(__doc__)
import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
from sklearn.decomposition import FastICA, PCA
# #############################################################################
# Generate sample data
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
# Compute ICA
ica = FastICA(n_components=3)
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
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()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 0.342 seconds)
.. _sphx_glr_download_auto_examples_decomposition_plot_ica_blind_source_separation.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: binder-badge
.. image:: https://mybinder.org/badge_logo.svg
:target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.23.X?urlpath=lab/tree/notebooks/auto_examples/decomposition/plot_ica_blind_source_separation.ipynb
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_ica_blind_source_separation.py `
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_ica_blind_source_separation.ipynb `
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery `_