使用PCA去噪

2016-07-13 机器学习 PV:

使用PCA去噪

1 2	import numpy as np import matplotlib.pyplot as plt

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X = np.empty((100, 2))
X[:,0] = np.random.uniform(0., 100., size=100)
X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 5, size=100)

1 2	plt.scatter(X[:,0], X[:,1]) plt.show()

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from sklearn.decomposition import PCA

pca = PCA(n_components=1)
pca.fit(X)
X_reduction = pca.transform(X)
X_restore = pca.inverse_transform(X_reduction)

1 2	plt.scatter(X_restore[:,0], X_restore[:,1]) plt.show()

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降维的过程可以理解成是去噪。

手写识别的例子

from sklearn import datasets

digits = datasets.load_digits()
X = digits.data
y = digits.target

1	noisy_digits = X + np.random.normal(0, 4, size=X.shape)

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example_digits = noisy_digits[y==0,:][:10]
for num in range(1,10):
    example_digits = np.vstack([example_digits, noisy_digits[y==num,:][:10]])

1	example_digits.shape

(100, 64)

def plot_digits(data):
    fig, axes = plt.subplots(10, 10, figsize=(10, 10),
                             subplot_kw={'xticks':[], 'yticks':[]},
    gridspec_kw=dict(hspace=0.1, wspace=0.1)) 
    for i, ax in enumerate(axes.flat):
        ax.imshow(data[i].reshape(8, 8),
                  cmap='binary', interpolation='nearest',
                  clim=(0, 16))

    plt.show()
    
plot_digits(example_digits)

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1 2	pca = PCA(0.5).fit(noisy_digits) pca.n_components_

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components = pca.transform(example_digits)
filtered_digits = pca.inverse_transform(components)
plot_digits(filtered_digits)

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