65 lines
1.9 KiB
Python
65 lines
1.9 KiB
Python
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"""
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=========================
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Kernel Density Estimation
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=========================
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This example shows how kernel density estimation (KDE), a powerful
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non-parametric density estimation technique, can be used to learn
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a generative model for a dataset. With this generative model in place,
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new samples can be drawn. These new samples reflect the underlying model
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of the data.
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"""
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import matplotlib.pyplot as plt
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import numpy as np
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from sklearn.datasets import load_digits
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from sklearn.decomposition import PCA
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from sklearn.model_selection import GridSearchCV
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from sklearn.neighbors import KernelDensity
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# load the data
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digits = load_digits()
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# project the 64-dimensional data to a lower dimension
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pca = PCA(n_components=15, whiten=False)
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data = pca.fit_transform(digits.data)
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# use grid search cross-validation to optimize the bandwidth
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params = {"bandwidth": np.logspace(-1, 1, 20)}
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grid = GridSearchCV(KernelDensity(), params)
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grid.fit(data)
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print("best bandwidth: {0}".format(grid.best_estimator_.bandwidth))
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# use the best estimator to compute the kernel density estimate
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kde = grid.best_estimator_
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# sample 44 new points from the data
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new_data = kde.sample(44, random_state=0)
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new_data = pca.inverse_transform(new_data)
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# turn data into a 4x11 grid
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new_data = new_data.reshape((4, 11, -1))
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real_data = digits.data[:44].reshape((4, 11, -1))
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# plot real digits and resampled digits
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fig, ax = plt.subplots(9, 11, subplot_kw=dict(xticks=[], yticks=[]))
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for j in range(11):
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ax[4, j].set_visible(False)
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for i in range(4):
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im = ax[i, j].imshow(
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real_data[i, j].reshape((8, 8)), cmap=plt.cm.binary, interpolation="nearest"
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)
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im.set_clim(0, 16)
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im = ax[i + 5, j].imshow(
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new_data[i, j].reshape((8, 8)), cmap=plt.cm.binary, interpolation="nearest"
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)
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im.set_clim(0, 16)
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ax[0, 5].set_title("Selection from the input data")
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ax[5, 5].set_title('"New" digits drawn from the kernel density model')
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plt.show()
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