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52 lines
1.7 KiB
Markdown
52 lines
1.7 KiB
Markdown
Sure! Here's a Python script that demonstrates Independent Component Analysis (ICA) using the scikit-learn library:
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```python
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import numpy as np
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from sklearn.decomposition import FastICA
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import matplotlib.pyplot as plt
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# Generate data
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np.random.seed(0)
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n_samples = 2000
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time = np.linspace(0, 8, n_samples)
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s1 = np.sin(2 * time) # Signal 1: sinusoidal signal
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s2 = np.sign(np.sin(3 * time)) # Signal 2: square signal
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S = np.c_[s1, s2]
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S += 0.2 * np.random.normal(size=S.shape) # Add noise
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# Mix data
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A = np.array([[1, 1], [0.5, 2]]) # Mixing matrix
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X = np.dot(S, A.T) # Generate observations
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# ICA
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ica = FastICA(n_components=2)
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S_ = ica.fit_transform(X) # Reconstruct signals
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A_ = ica.mixing_ # Estimated mixing matrix
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# Plot results
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plt.figure(figsize=(8, 6))
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models = [X, S, S_]
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names = ['Observations (mixed signals)',
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'True Sources',
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'ICA estimated sources']
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colors = ['red', 'steelblue']
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for i, (model, name) in enumerate(zip(models, names), 1):
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plt.subplot(3, 1, i)
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plt.title(name)
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for sig, color in zip(model.T, colors):
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plt.plot(sig, color=color)
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plt.tight_layout()
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plt.show()
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```
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This script demonstrates ICA by generating two mixed signals, `s1` and `s2`, adding noise, and then applying ICA to separate the original signals. The original signals are represented by the `S` matrix, and the observed mixed signals are stored in the `X` matrix. The `FastICA` class from scikit-learn is used to perform ICA.
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The script plots three subplots: the observed mixed signals, the true sources, and the estimated sources achieved through ICA.
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Make sure to install required dependencies (scikit-learn, numpy, matplotlib) before running the script. |