Table of Contents
1. 基本信息查询
导入package
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn import linear_model, datasets, metrics
from sklearn.neural_network import BernoulliRBM
from sklearn.pipeline import Pipeline
# 显示中文
import matplotlib as mpl
mpl.rcParams["font.sans-serif"] = ["Microsoft YaHei"]
mpl.rcParams['axes.unicode_minus'] = False
from tensorflow.examples.tutorials.mnist import input_data
data_mnist = input_data.read_data_sets(r'C:\Users\Administrator\Documents\MNIST')
Extracting C:\Users\Administrator\Documents\MNIST\train-images-idx3-ubyte.gz
Extracting C:\Users\Administrator\Documents\MNIST\train-labels-idx1-ubyte.gz
Extracting C:\Users\Administrator\Documents\MNIST\t10k-images-idx3-ubyte.gz
Extracting C:\Users\Administrator\Documents\MNIST\t10k-labels-idx1-ubyte.gz
images_all = data_mnist.train.images
images = images_all[:6000,:]
images.shape
(6000, 784)
images_X, images_y = images, data_mnist.train.labels[:6000] # 这一步为何？
np.min(images_X), np.max(images_X)
(0.0, 1.0)
plt.imshow(images_X[0].reshape(28,28), cmap=plt.cm.gray_r)
<matplotlib.image.AxesImage at 0xf8990f0>
# images_X = images_X/255.0
images_X = (images_X > 0.5).astype(float)
plt.imshow(images_X[0].reshape(28,28), cmap=plt.cm.gray_r)
<matplotlib.image.AxesImage at 0xf98c400>
2. 提取PCA 成分
假设我们从784个变量中提取100个主成分，并观察.
from sklearn.decomposition import PCA
pca = PCA(n_components=100)
pca.fit(images_X)
PCA(copy=True, iterated_power='auto', n_components=100, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)
plt.figure(figsize=(10,10))
for i, comp in enumerate(pca.components_):
plt.subplot(10,10, i+1)
plt.imshow(comp.reshape((28,28)), cmap=plt.cm.gray_r)
plt.xticks(())
plt.yticks(())
plt.suptitle('100 components by PCA')
plt.show()
由各个特征的描述结果可以看到。前10个主成分，主要描述0，体现的是像素的一种整体形状。从后10个主成分，描述黑白像素的随机情况
pca.explained_variance_ratio_[:10].sum(),pca.explained_variance_ratio_[-10:].sum(),pca.explained_variance_ratio_[:30].sum()
(0.42493866841275713, 0.013189826871685456, 0.6406096747833725)
前30%的主成分解释了原有数据的64%的信息
full_pca = PCA(n_components=784)
full_pca.fit(images_X)
plt.plot(np.cumsum(full_pca.explained_variance_ratio_))
plt.xlabel('PCA 主成分数量')
<matplotlib.text.Text at 0x19c17eb8>
pca.transform(images_X[:1])
array([[ 0.52356293, 1.72349003, -2.14897954, 2.68673318, 0.47904816,
-1.23169352, 1.04362899, 1.41068746, 1.21128259, 0.74175855,
1.64123539, -3.34081047, -0.68832884, 0.03740046, -0.31612483,
0.95930869, 0.75656307, 0.85933748, 1.06149407, -0.10313465,
0.39483926, 1.68371086, -1.07682393, -0.257166 , -0.86288074,
1.71591167, -0.62275775, 1.10727832, 0.53435806, 1.46806889,
0.84523054, 0.71653435, 0.26125092, 0.65679105, 0.02417695,
0.54178825, 0.09140743, -0.47275769, 0.22448948, 1.32993595,
-1.36367223, 0.21807472, 0.93320535, -0.0499107 , -0.92103529,
-0.43783948, 0.24625445, 0.77436417, 0.59435984, -0.33551929,
-0.11900602, -0.94889884, -0.99956816, -0.43388146, 0.3136769 ,
-0.50563104, -0.57570834, -0.26703065, -0.28846614, -0.59134512,
-0.42216871, -0.70174101, -0.49465544, -0.14962569, 0.67165476,
0.03205398, 0.11720721, -0.33503693, 0.11959339, -0.56115567,
-0.16465967, -0.25587122, 0.48418026, -0.3838457 , -0.16103517,
0.52447191, -0.72697503, -0.26878197, 0.36217831, -0.27052404,
0.48639081, 0.39132248, -0.02694144, -0.33737552, 0.1130496 ,
-0.00843058, 0.29904734, 0.92900628, -0.07937508, -0.67891584,
-0.34406307, -0.24891354, -0.08196933, 0.17025649, -0.08947269,
0.01181867, -0.03082805, 0.55370055, 0.22111017, -0.1240324 ]])
3. 提取RBM主成分
成分数量100，迭代次数20，随机因子设定
rbm = BernoulliRBM(random_state=0, verbose=True, n_iter=20, n_components=100)
rbm.fit(images_X)
[BernoulliRBM] Iteration 1, pseudo-likelihood = -142.78, time = 4.39s
[BernoulliRBM] Iteration 2, pseudo-likelihood = -132.65, time = 4.83s
[BernoulliRBM] Iteration 3, pseudo-likelihood = -125.75, time = 3.94s
[BernoulliRBM] Iteration 4, pseudo-likelihood = -123.83, time = 3.84s
[BernoulliRBM] Iteration 5, pseudo-likelihood = -117.85, time = 4.77s
[BernoulliRBM] Iteration 6, pseudo-likelihood = -129.62, time = 8.42s
[BernoulliRBM] Iteration 7, pseudo-likelihood = -114.95, time = 5.17s
[BernoulliRBM] Iteration 8, pseudo-likelihood = -113.14, time = 5.54s
[BernoulliRBM] Iteration 9, pseudo-likelihood = -119.25, time = 5.78s
[BernoulliRBM] Iteration 10, pseudo-likelihood = -118.98, time = 3.98s
[BernoulliRBM] Iteration 11, pseudo-likelihood = -115.08, time = 4.07s
[BernoulliRBM] Iteration 12, pseudo-likelihood = -116.79, time = 4.02s
[BernoulliRBM] Iteration 13, pseudo-likelihood = -120.36, time = 5.32s
[BernoulliRBM] Iteration 14, pseudo-likelihood = -120.43, time = 3.83s
[BernoulliRBM] Iteration 15, pseudo-likelihood = -117.06, time = 3.75s
[BernoulliRBM] Iteration 16, pseudo-likelihood = -126.19, time = 3.73s
[BernoulliRBM] Iteration 17, pseudo-likelihood = -123.19, time = 3.82s
[BernoulliRBM] Iteration 18, pseudo-likelihood = -115.31, time = 3.89s
[BernoulliRBM] Iteration 19, pseudo-likelihood = -113.10, time = 3.83s
[BernoulliRBM] Iteration 20, pseudo-likelihood = -117.98, time = 3.80s
BernoulliRBM(batch_size=10, learning_rate=0.1, n_components=100, n_iter=20,
random_state=0, verbose=True)
plt.figure(figsize=(10,10))
for i, comp in enumerate(rbm.components_):
plt.subplot(10, 10, i+1)
plt.imshow(comp.reshape((28,28)), cmap=plt.cm.gray_r)
plt.xticks()
plt.yticks()
plt.suptitle('100 主成分 by RBM')
plt.show()
从上面观察的话，有部分的主成分是相似的，但真实值是有区别。
image_new_features = rbm.transform(images_X[:1]).reshape(100,)
image_new_features
array([ 7.76673604e-15, 1.49069292e-06, 9.55226339e-11,
9.99989771e-01, 7.57901771e-17, 1.28364972e-18,
1.16423303e-18, 1.85040066e-19, 1.64562339e-33,
9.99999965e-01, 1.00000000e+00, 1.30547116e-11,
2.25132935e-18, 3.92508207e-26, 9.99999994e-01,
1.43402544e-26, 1.46179051e-24, 2.40049579e-13,
6.08933225e-02, 5.49458550e-22, 1.39120674e-18,
9.99999959e-01, 1.00000000e+00, 7.54435384e-02,
5.68688998e-13, 1.00000000e+00, 1.40116926e-09,
1.32911930e-14, 1.66657538e-08, 1.01839668e-14,
6.20364773e-22, 4.80370202e-21, 1.00000000e+00,
9.99986780e-01, 9.68360209e-01, 1.00000000e+00,
8.72995544e-13, 3.00381851e-17, 9.99813915e-01,
2.36386359e-17, 7.22854123e-01, 4.08520026e-18,
9.99999867e-01, 1.67875177e-17, 6.99195965e-03,
9.99999980e-01, 9.99999354e-01, 4.09705958e-21,
6.29987342e-12, 9.99999945e-01, 8.19464506e-12,
5.72527937e-07, 1.04592638e-06, 2.06074887e-08,
2.08771197e-04, 4.46575921e-17, 5.15385587e-09,
9.07210343e-08, 1.30004168e-02, 1.15188762e-17,
4.72222949e-15, 4.09872360e-10, 9.99999895e-01,
9.99999995e-01, 4.59721307e-17, 9.99917857e-01,
1.00000000e+00, 1.09751419e-03, 2.10415770e-09,
9.99999990e-01, 1.45240705e-07, 4.22687339e-01,
9.99998734e-01, 1.53904429e-07, 3.75029784e-25,
1.62168712e-26, 9.99999999e-01, 6.24449101e-15,
9.99999795e-01, 2.08631558e-19, 2.33601220e-14,
4.63712966e-26, 9.99999875e-01, 9.99999984e-01,
1.00000000e+00, 7.02768473e-13, 3.34203731e-16,
9.99999632e-01, 9.99998566e-01, 5.20516733e-16,
2.77826938e-11, 8.65331812e-07, 1.14021791e-09,
1.12107682e-17, 9.99999829e-01, 8.97988679e-14,
1.13375304e-13, 4.73292411e-07, 4.15078855e-02,
9.86210789e-01])
np.dot(images_X[:1]-images_X.mean(axis=0), rbm.components_.T)
array([[ -4.35640343, 3.09815273, -8.96732465, 16.16171671,
-0.92552752, -11.3936493 , -17.66878685, -31.05364275,
-55.58072995, -3.33167638, 49.21657951, -15.98488937,
-11.66679346, -37.654284 , -3.40367975, -37.89639958,
-28.41722901, -10.87301095, -12.22387153, -17.46112116,
1.84502414, 20.26603895, 46.54081239, 8.3612151 ,
-2.25039004, 15.75994935, 0.92477231, -4.2922096 ,
3.67487237, -16.17087459, -18.88340271, -31.12333759,
59.82613022, 31.04368552, 35.17320636, 46.02308762,
-2.50456561, -25.90799767, 28.33256117, -18.1128016 ,
27.21562369, -11.60404548, -2.83829775, -7.10104947,
3.00935928, -2.89662714, 12.01018771, -19.25349294,
-21.81753662, -3.0530714 , 4.68355653, -14.13733712,
2.46498274, -10.74595849, 14.52808854, -2.79228021,
-9.30113454, 5.32310421, -1.07884352, -7.18723205,
-4.77835331, -0.88611728, -3.32560852, -3.57722757,
-7.94020713, 20.34851985, 32.38229912, 4.76989267,
-9.13085228, -3.3097796 , 6.96496308, -3.87208876,
30.98690441, 3.43280247, -32.71121127, -39.74467406,
38.33315289, -14.95538716, -3.02767468, -32.54087139,
-16.69611143, -37.44597534, -3.24721591, -3.1051272 ,
53.66291505, -14.494897 , -6.55842747, 31.50690171,
44.2169187 , -13.41007469, -12.01283844, 4.12374268,
-1.05586219, -15.06200184, -2.90743519, -4.20470404,
3.3775784 , 7.99768637, 7.28527442, 32.10640592]])
注意：RBM中的transform方法并未实现center的操作，有别与PCA中的。
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取出前20个最有代表性的特征
top_features = image_new_features.argsort()[-20:][::-1]
top_features
array([35, 10, 84, 22, 32, 66, 25, 76, 63, 14, 69, 83, 45, 9, 21, 49, 62,
82, 42, 94], dtype=int64)
image_new_features[top_features]
array([ 1. , 1. , 1. , 1. , 1. ,
1. , 1. , 1. , 1. , 0.99999999,
0.99999999, 0.99999998, 0.99999998, 0.99999996, 0.99999996,
0.99999995, 0.99999989, 0.99999988, 0.99999987, 0.99999983])
说明这里有9个特征具有100%的解释性
plt.figure(figsize=(25,25))
for i, comp in enumerate(top_features):
plt.subplot(5,4,i+1)
plt.imshow(rbm.components_[comp].reshape((28,28)), cmap=plt.cm.gray_r)
plt.title('component {}, feature value:{}'.format(comp, round(image_new_features[comp],2)), fontsize=20)
plt.xticks()
plt.yticks()
plt.suptitle('top20的主成分 by RBM')
plt.show()
63,14,69,83都希望能直接获取3的值
25获取底部的特征
35获取右下角的特征
提取后20个特征
least_features = image_new_features.argsort()[:20][::-1]
least_features
array([59, 93, 41, 12, 20, 5, 6, 79, 7, 31, 47, 30, 19, 16, 74, 81, 13,
75, 15, 8], dtype=int64)
image_new_features[least_features]
array([ 1.15188762e-17, 1.12107682e-17, 4.08520026e-18,
2.25132935e-18, 1.39120674e-18, 1.28364972e-18,
1.16423303e-18, 2.08631558e-19, 1.85040066e-19,
4.80370202e-21, 4.09705958e-21, 6.20364773e-22,
5.49458550e-22, 1.46179051e-24, 3.75029784e-25,
4.63712966e-26, 3.92508207e-26, 1.62168712e-26,
1.43402544e-26, 1.64562339e-33])
plt.figure(figsize=(25,25))
for i, comp in enumerate(least_features):
plt.subplot(5,4,i+1)
plt.imshow(rbm.components_[comp].reshape((28,28)), cmap=plt.cm.gray_r)
plt.title('component {}, feature value:{}'.format(comp, round(image_new_features[comp],2)), fontsize=20)
plt.xticks()
plt.yticks()
plt.suptitle('least20的主成分 by RBM')
plt.show()
从上面看，59、12都不是表示lable=3的信息。
4. RBM在machine learning中效果
直接用LR模型
# import packages
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import GridSearchCV
# create LR
lr = LogisticRegression()
params = {'C':[1e-2, 1e-1, 1e0, 1e1, 1e2]}
# grid-search
grid = GridSearchCV(lr, params)
grid.fit(images_X, images_y)
GridSearchCV(cv=None, error_score='raise',
estimator=LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False),
fit_params=None, iid=True, n_jobs=1,
param_grid={'C': [0.01, 0.1, 1.0, 10.0, 100.0]},
pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
scoring=None, verbose=0)
grid.best_estimator_, grid.best_score_
(LogisticRegression(C=0.1, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False), 0.88566666666666671)
采用PCA主成分的LR
lr = LogisticRegression()
pca = PCA()
params = {'clf__C':[1e-1, 1e0, 1e1], 'pca__n_components':[10, 100, 200]}
piplines = Pipeline([('pca', pca), ('clf', lr)])
grid_pca = GridSearchCV(piplines, params)
grid_pca.fit(images_X, images_y)
GridSearchCV(cv=None, error_score='raise',
estimator=Pipeline(memory=None,
steps=[('pca', PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)), ('clf', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))]),
fit_params=None, iid=True, n_jobs=1,
param_grid={'clf__C': [0.1, 1.0, 10.0], 'pca__n_components': [10, 100, 200]},
pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
scoring=None, verbose=0)
grid_pca.best_estimator_, grid_pca.best_params_,grid_pca.best_score_
(Pipeline(memory=None,
steps=[('pca', PCA(copy=True, iterated_power='auto', n_components=100, random_state=None,
svd_solver='auto', tol=0.0, whiten=False)), ('clf', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))]),
{'clf__C': 1.0, 'pca__n_components': 100},
0.88283333333333336)
pca的方法并未带来性能改善。
采用RBM主成分的LR
rbm = BernoulliRBM(random_state=0)
params = {'clf__C':[1e-1,1e0, 1e1], 'rbm__n_components':[10, 100, 200]}
pipeline = Pipeline([('rbm',rbm), ('clf',lr)])
grid_rbm = GridSearchCV(pipeline, params)
grid_rbm.fit(images_X, images_y)
GridSearchCV(cv=None, error_score='raise',
estimator=Pipeline(memory=None,
steps=[('rbm', BernoulliRBM(batch_size=10, learning_rate=0.1, n_components=256, n_iter=10,
random_state=0, verbose=0)), ('clf', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))]),
fit_params=None, iid=True, n_jobs=1,
param_grid={'clf__C': [0.1, 1.0, 10.0], 'rbm__n_components': [10, 100, 200]},
pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
scoring=None, verbose=0)
grid_rbm.best_params_, grid_rbm.best_score_
({'clf__C': 1.0, 'rbm__n_components': 200}, 0.91266666666666663)
对比结果表明，RBM提高了LR的性能。
rbm = BernoulliRBM(random_state=0)
params = {'clf__C':[1e0], 'rbm__n_components':[200,300]}
pipeline = Pipeline([('rbm',rbm), ('clf',lr)])
grid_rbm2 = GridSearchCV(pipeline, params)
grid_rbm2.fit(images_X, images_y)
GridSearchCV(cv=None, error_score='raise',
estimator=Pipeline(memory=None,
steps=[('rbm', BernoulliRBM(batch_size=10, learning_rate=0.1, n_components=256, n_iter=10,
random_state=0, verbose=0)), ('clf', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,
intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,
penalty='l2', random_state=None, solver='liblinear', tol=0.0001,
verbose=0, warm_start=False))]),
fit_params=None, iid=True, n_jobs=1,
param_grid={'clf__C': [1.0], 'rbm__n_components': [200, 300]},
pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
scoring=None, verbose=0)
grid_rbm2.best_params_, grid_rbm2.best_score_
({'clf__C': 1.0, 'rbm__n_components': 300}, 0.92016666666666669)
从上一会的结果看，RBM的components数量是200，意味着可以再考虑＞200的参数。故在上面试验了采用300的参数，结果表明采用300的参数的LR性能更优。