特征聚合与单变量选择#

本示例比较了 2 种降维策略

使用 Anova 进行单变量特征选择
使用 Ward 层次聚类进行特征聚合

在使用贝叶斯岭回归作为监督估计器的回归问题中比较了这两种方法。

# Author: Alexandre Gramfort <[email protected]>
# License: BSD 3 clause

import shutil
import tempfile

import matplotlib.pyplot as plt
import numpy as np
from joblib import Memory
from scipy import linalg, ndimage

from sklearn import feature_selection
from sklearn.cluster import FeatureAgglomeration
from sklearn.feature_extraction.image import grid_to_graph
from sklearn.linear_model import BayesianRidge
from sklearn.model_selection import GridSearchCV, KFold
from sklearn.pipeline import Pipeline

设置参数

n_samples = 200
size = 40  # image size
roi_size = 15
snr = 5.0
np.random.seed(0)

生成数据

coef = np.zeros((size, size))
coef[0:roi_size, 0:roi_size] = -1.0
coef[-roi_size:, -roi_size:] = 1.0

X = np.random.randn(n_samples, size**2)
for x in X:  # smooth data
    x[:] = ndimage.gaussian_filter(x.reshape(size, size), sigma=1.0).ravel()
X -= X.mean(axis=0)
X /= X.std(axis=0)

y = np.dot(X, coef.ravel())

添加噪声

noise = np.random.randn(y.shape[0])
noise_coef = (linalg.norm(y, 2) / np.exp(snr / 20.0)) / linalg.norm(noise, 2)
y += noise_coef * noise

使用 GridSearch 计算贝叶斯岭回归的系数

cv = KFold(2)  # cross-validation generator for model selection
ridge = BayesianRidge()
cachedir = tempfile.mkdtemp()
mem = Memory(location=cachedir, verbose=1)

Ward 聚合，然后是贝叶斯岭回归

connectivity = grid_to_graph(n_x=size, n_y=size)
ward = FeatureAgglomeration(n_clusters=10, connectivity=connectivity, memory=mem)
clf = Pipeline([("ward", ward), ("ridge", ridge)])
# Select the optimal number of parcels with grid search
clf = GridSearchCV(clf, {"ward__n_clusters": [10, 20, 30]}, n_jobs=1, cv=cv)
clf.fit(X, y)  # set the best parameters
coef_ = clf.best_estimator_.steps[-1][1].coef_
coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_)
coef_agglomeration_ = coef_.reshape(size, size)

________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[-0.451933, ..., -0.675318],
       ...,
       [ 0.275706, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
        with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.1s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[ 0.905206, ...,  0.161245],
       ...,
       [-0.849835, ..., -1.091621]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
        with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.1s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.cluster._agglomerative.ward_tree...
ward_tree(array([[ 0.905206, ..., -0.675318],
       ...,
       [-0.849835, ..., -1.085711]]), connectivity=<1600x1600 sparse matrix of type '<class 'numpy.int64'>'
        with 7840 stored elements in COOrdinate format>, n_clusters=None, return_distance=False)
________________________________________________________ward_tree - 0.1s, 0.0min

Anova 单变量特征选择，然后是贝叶斯岭回归

f_regression = mem.cache(feature_selection.f_regression)  # caching function
anova = feature_selection.SelectPercentile(f_regression)
clf = Pipeline([("anova", anova), ("ridge", ridge)])
# Select the optimal percentage of features with grid search
clf = GridSearchCV(clf, {"anova__percentile": [5, 10, 20]}, cv=cv)
clf.fit(X, y)  # set the best parameters
coef_ = clf.best_estimator_.steps[-1][1].coef_
coef_ = clf.best_estimator_.steps[0][1].inverse_transform(coef_.reshape(1, -1))
coef_selection_ = coef_.reshape(size, size)

________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[-0.451933, ...,  0.275706],
       ...,
       [-0.675318, ..., -1.085711]]),
array([ 25.267703, ..., -25.026711]))
_____________________________________________________f_regression - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[ 0.905206, ..., -0.849835],
       ...,
       [ 0.161245, ..., -1.091621]]),
array([ -27.447268, ..., -112.638768]))
_____________________________________________________f_regression - 0.0s, 0.0min
________________________________________________________________________________
[Memory] Calling sklearn.feature_selection._univariate_selection.f_regression...
f_regression(array([[ 0.905206, ..., -0.849835],
       ...,
       [-0.675318, ..., -1.085711]]),
array([-27.447268, ..., -25.026711]))
_____________________________________________________f_regression - 0.0s, 0.0min

反转变换以在图像上绘制结果

plt.close("all")
plt.figure(figsize=(7.3, 2.7))
plt.subplot(1, 3, 1)
plt.imshow(coef, interpolation="nearest", cmap=plt.cm.RdBu_r)
plt.title("True weights")
plt.subplot(1, 3, 2)
plt.imshow(coef_selection_, interpolation="nearest", cmap=plt.cm.RdBu_r)
plt.title("Feature Selection")
plt.subplot(1, 3, 3)
plt.imshow(coef_agglomeration_, interpolation="nearest", cmap=plt.cm.RdBu_r)
plt.title("Feature Agglomeration")
plt.subplots_adjust(0.04, 0.0, 0.98, 0.94, 0.16, 0.26)
plt.show()

True weights, Feature Selection, Feature Agglomeration

尝试删除临时缓存目录，但如果失败也不用担心

shutil.rmtree(cachedir, ignore_errors=True)

脚本总运行时间：（0 分 0.566 秒）