使用预计算字典的稀疏编码¶
将信号变换为Ricker小波的稀疏组合。这个例子直观地比较了不同的稀疏编码方法， 使用sklearn.decomposition.SparseCoder 估计器。Ricker(也称为Mexican hat或高斯的二阶导数)不是一个特别好的内核，可以表示像这样的分段常量信号。因此，我们可以看到增加了多少微量的不同宽度，并且因此它激发了学习字典，以最适合你的信号类型。
右边较丰富的字典的尺寸并不大，较重的子抽样是为了保持相同的数量级。
print(__doc__)
from distutils.version import LooseVersion
import numpy as np
import matplotlib.pyplot as plt
from sklearn.decomposition import SparseCoder
def ricker_function(resolution, center, width):
"""Discrete sub-sampled Ricker (Mexican hat) wavelet"""
x = np.linspace(0, resolution - 1, resolution)
x = ((2 / (np.sqrt(3 * width) * np.pi ** .25))
* (1 - (x - center) ** 2 / width ** 2)
* np.exp(-(x - center) ** 2 / (2 * width ** 2)))
return x
def ricker_matrix(width, resolution, n_components):
"""Dictionary of Ricker (Mexican hat) wavelets"""
centers = np.linspace(0, resolution - 1, n_components)
D = np.empty((n_components, resolution))
for i, center in enumerate(centers):
D[i] = ricker_function(resolution, center, width)
D /= np.sqrt(np.sum(D ** 2, axis=1))[:, np.newaxis]
return D
resolution = 1024
subsampling = 3 # subsampling factor
width = 100
n_components = resolution // subsampling
# Compute a wavelet dictionary
D_fixed = ricker_matrix(width=width, resolution=resolution,
n_components=n_components)
D_multi = np.r_[tuple(ricker_matrix(width=w, resolution=resolution,
n_components=n_components // 5)
for w in (10, 50, 100, 500, 1000))]
# Generate a signal
y = np.linspace(0, resolution - 1, resolution)
first_quarter = y < resolution / 4
y[first_quarter] = 3.
y[np.logical_not(first_quarter)] = -1.
# List the different sparse coding methods in the following format:
# (title, transform_algorithm, transform_alpha,
# transform_n_nozero_coefs, color)
estimators = [('OMP', 'omp', None, 15, 'navy'),
('Lasso', 'lasso_lars', 2, None, 'turquoise'), ]
lw = 2
# Avoid FutureWarning about default value change when numpy >= 1.14
lstsq_rcond = None if LooseVersion(np.__version__) >= '1.14' else -1
plt.figure(figsize=(13, 6))
for subplot, (D, title) in enumerate(zip((D_fixed, D_multi),
('fixed width', 'multiple widths'))):
plt.subplot(1, 2, subplot + 1)
plt.title('Sparse coding against %s dictionary' % title)
plt.plot(y, lw=lw, linestyle='--', label='Original signal')
# Do a wavelet approximation
for title, algo, alpha, n_nonzero, color in estimators:
coder = SparseCoder(dictionary=D, transform_n_nonzero_coefs=n_nonzero,
transform_alpha=alpha, transform_algorithm=algo)
x = coder.transform(y.reshape(1, -1))
density = len(np.flatnonzero(x))
x = np.ravel(np.dot(x, D))
squared_error = np.sum((y - x) ** 2)
plt.plot(x, color=color, lw=lw,
label='%s: %s nonzero coefs,\n%.2f error'
% (title, density, squared_error))
# Soft thresholding debiasing
coder = SparseCoder(dictionary=D, transform_algorithm='threshold',
transform_alpha=20)
x = coder.transform(y.reshape(1, -1))
_, idx = np.where(x != 0)
x[0, idx], _, _, _ = np.linalg.lstsq(D[idx, :].T, y, rcond=lstsq_rcond)
x = np.ravel(np.dot(x, D))
squared_error = np.sum((y - x) ** 2)
plt.plot(x, color='darkorange', lw=lw,
label='Thresholding w/ debiasing:\n%d nonzero coefs, %.2f error'
% (len(idx), squared_error))
plt.axis('tight')
plt.legend(shadow=False, loc='best')
plt.subplots_adjust(.04, .07, .97, .90, .09, .2)
plt.show()
脚本的总运行时间：(0分0.380秒)
