# Ex 2: Restricted Boltzmann Machine features for digit classification

<http://scikit-learn.org/stable/auto_examples/neural_networks/plot_rbm_logistic_classification.html#sphx-glr-auto-examples-neural-networks-plot-rbm-logistic-classification-py>

此範例將使用BernoulliRBM特徵選取方法，提升手寫數字識別的精確率，伯努利限制玻爾茲曼機器模型（\`BernoulliRBM

\`）將可以對數據做有效的非線性 特徵提取的處理。 為了讓此模型訓練出來更為強健，將輸入的圖檔，分別做上左右下，一像素的平移，用以增加更多訓練資料， 訓練網路的參數是使用grid search演算法，但此訓練太耗費時間，因此不再這重現，。 此範例結果將比較， 1.使用原本的像素值做的邏輯回歸 2.使用BernoulliRBM做特徵選取的邏輯回歸 結果將顯示:使用BernoulliRBM將可以提升分類的準確度。

## (一)引入函式庫與資料

```python
from __future__ import print_function

print(__doc__)

# Authors: Yann N. Dauphin, Vlad Niculae, Gabriel Synnaeve
# License: BSD

import numpy as np
import matplotlib.pyplot as plt

from scipy.ndimage import convolve
from sklearn import linear_model, datasets, metrics
from sklearn.model_selection import train_test_split
from sklearn.neural_network import BernoulliRBM
from sklearn.pipeline import Pipeline
```

## (二)資料前處理、讀取資料、選取模型

```python
def nudge_dataset(X, Y):
    """
    此副函式是用來將輸入資料的數字圖形，分別做上左右下一像素的平移，目的是製造更多的訓練資料讓模型訓練出來更強健
    """
    direction_vectors = [
        [[0, 1, 0],
         [0, 0, 0],
         [0, 0, 0]],

        [[0, 0, 0],
         [1, 0, 0],
         [0, 0, 0]],

        [[0, 0, 0],
         [0, 0, 1],
         [0, 0, 0]],

        [[0, 0, 0],
         [0, 0, 0],
         [0, 1, 0]]]

    shift = lambda x, w: convolve(x.reshape((8, 8)), mode='constant',
                                  weights=w).ravel()
    X = np.concatenate([X] +
                       [np.apply_along_axis(shift, 1, X, vector)
                        for vector in direction_vectors])
    Y = np.concatenate([Y for _ in range(5)], axis=0)
    return X, Y

# Load Data
digits = datasets.load_digits()
X = np.asarray(digits.data, 'float32')
X, Y = nudge_dataset(X, digits.target)
X = (X - np.min(X, 0)) / (np.max(X, 0) + 0.0001)  # 將灰階影像降尺度降到[0,1]
# 將資料切割成訓練集與測試集
X_train, X_test, Y_train, Y_test = train_test_split(X, Y,
                                                    test_size=0.2,
                                                    random_state=0)

# Models we will use
logistic = linear_model.LogisticRegression()
rbm = BernoulliRBM(random_state=0, verbose=True)

classifier = Pipeline(steps=[('rbm', rbm), ('logistic', logistic)])
```

## (三)設定模型參數與訓練模型

```python
# 參數選擇需使用cross-validation去比較
# 此參數是使用GridSearchCV找出來的. Here we are not performing cross-validation to save time.
#GridSratch 就是將參數設定好，跑過全部參數後去找結果最好的一組參數
rbm.learning_rate = 0.06
rbm.n_iter = 20
#.n_components = 100 表示隱藏層單元為100，即表示萃取出100個特徵，特徵萃取的越多準確率會越高，但越耗時間
rbm.n_components = 100
logistic.C = 6000.0

# Training RBM-Logistic Pipeline
classifier.fit(X_train, Y_train)

# Training Logistic regression
logistic_classifier = linear_model.LogisticRegression(C=100.0)
logistic_classifier.fit(X_train, Y_train)
```

## (四)評估模型的分辨準確率

```python
print()
print("Logistic regression using RBM features:\n%s\n" % (
    metrics.classification_report(
        Y_test,
        classifier.predict(X_test))))

print("Logistic regression using raw pixel features:\n%s\n" % (
    metrics.classification_report(
        Y_test,
        logistic_classifier.predict(X_test))))
```

![](/files/-LVfZZr42rBAsOsJ6kkG)

圖1:使用RBM演算法後準確率為0.95

![](/files/-LVfZZr69hVK_9ytIOS4)

圖2:不使用任何特徵選取方法做的做的邏輯回歸準確率0.77

## (五)畫出100個RBM萃取出的特徵

```python
plt.figure(figsize=(4.2, 4))
for i, comp in enumerate(rbm.components_):
    plt.subplot(10, 10, i + 1)
    plt.imshow(comp.reshape((8, 8)), cmap=plt.cm.gray_r,
               interpolation='nearest')
    plt.xticks(())
    plt.yticks(())
plt.suptitle('100 components extracted by RBM', fontsize=16)
plt.subplots_adjust(0.08, 0.02, 0.92, 0.85, 0.08, 0.23)

plt.show()
```

![](/files/-LVfZZr81vsgVQeUyUkN)

圖3:使用RBM演算法，尋找出來的特徵

## (六)完整程式碼

```python
from __future__ import print_function

print(__doc__)

# Authors: Yann N. Dauphin, Vlad Niculae, Gabriel Synnaeve
# License: BSD

import numpy as np
import matplotlib.pyplot as plt

from scipy.ndimage import convolve
from sklearn import linear_model, datasets, metrics
from sklearn.model_selection import train_test_split
from sklearn.neural_network import BernoulliRBM
from sklearn.pipeline import Pipeline


###############################################################################
# Setting up

def nudge_dataset(X, Y):
    """
    This produces a dataset 5 times bigger than the original one,
    by moving the 8x8 images in X around by 1px to left, right, down, up
    """
    direction_vectors = [
        [[0, 1, 0],
         [0, 0, 0],
         [0, 0, 0]],

        [[0, 0, 0],
         [1, 0, 0],
         [0, 0, 0]],

        [[0, 0, 0],
         [0, 0, 1],
         [0, 0, 0]],

        [[0, 0, 0],
         [0, 0, 0],
         [0, 1, 0]]]

    shift = lambda x, w: convolve(x.reshape((8, 8)), mode='constant',
                                  weights=w).ravel()
    X = np.concatenate([X] +
                       [np.apply_along_axis(shift, 1, X, vector)
                        for vector in direction_vectors])
    Y = np.concatenate([Y for _ in range(5)], axis=0)
    return X, Y

# Load Data
digits = datasets.load_digits()
X = np.asarray(digits.data, 'float32')
X, Y = nudge_dataset(X, digits.target)
X = (X - np.min(X, 0)) / (np.max(X, 0) + 0.0001)  # 0-1 scaling

X_train, X_test, Y_train, Y_test = train_test_split(X, Y,
                                                    test_size=0.2,
                                                    random_state=0)

# Models we will use
logistic = linear_model.LogisticRegression()
rbm = BernoulliRBM(random_state=0, verbose=True)

classifier = Pipeline(steps=[('rbm', rbm), ('logistic', logistic)])

###############################################################################
# Training

# Hyper-parameters. These were set by cross-validation,
# using a GridSearchCV. Here we are not performing cross-validation to
# save time.
rbm.learning_rate = 0.06
rbm.n_iter = 20
# More components tend to give better prediction performance, but larger
# fitting time
rbm.n_components = 100
logistic.C = 6000.0

# Training RBM-Logistic Pipeline
classifier.fit(X_train, Y_train)

# Training Logistic regression
logistic_classifier = linear_model.LogisticRegression(C=100.0)
logistic_classifier.fit(X_train, Y_train)

###############################################################################
# Evaluation

print()
print("Logistic regression using RBM features:\n%s\n" % (
    metrics.classification_report(
        Y_test,
        classifier.predict(X_test))))

print("Logistic regression using raw pixel features:\n%s\n" % (
    metrics.classification_report(
        Y_test,
        logistic_classifier.predict(X_test))))

###############################################################################
# Plotting

plt.figure(figsize=(4.2, 4))
for i, comp in enumerate(rbm.components_):
    plt.subplot(10, 10, i + 1)
    plt.imshow(comp.reshape((8, 8)), cmap=plt.cm.gray_r,
               interpolation='nearest')
    plt.xticks(())
    plt.yticks(())
plt.suptitle('100 components extracted by RBM', fontsize=16)
plt.subplots_adjust(0.08, 0.02, 0.92, 0.85, 0.08, 0.23)

plt.show()
```


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