In [1]:

    

from IPython.display import Image, SVG
import matplotlib.pyplot as plt

%matplotlib inline

import numpy as np
import keras
from keras.datasets import mnist
from keras.utils import np_utils
from keras.models import Sequential
from keras.layers import Dense

from keras.utils.vis_utils import model_to_dot


    

    




Using TensorFlow backend.

In [2]:

    

# Loads the training and test data sets
(X_train, y_train), (X_test, y_test) = mnist.load_data()


    

In [3]:

    

first_image = X_train[0, :, :]


    

In [4]:

    

# To interpret the values as a 28x28 image, we need to reshape
# the numpy array, which is one dimensional.
plt.imshow(first_image, cmap=plt.cm.Greys);


    

In [5]:

    

num_classes = len(np.unique(y_train))
num_classes


    

    
Out[5]:





10

In [6]:

    

# 60K training 28 x 28 (pixel) images
X_train.shape


    

    
Out[6]:





(60000, 28, 28)

In [7]:

    

# 10K test 28 x 28 (pixel) images
X_test.shape


    

    
Out[7]:





(10000, 28, 28)

In [8]:

    

input_dim = np.prod(X_train.shape[1:])
input_dim


    

    
Out[8]:





784

In [9]:

    

# The training and test data sets are integers, ranging from 0 to 255.
# We reshape the training and test data sets to be matrices with 784 (= 28 * 28) features.
X_train = X_train.reshape(60000, input_dim).astype('float32')
X_test = X_test.reshape(10000, input_dim).astype('float32')


    

In [10]:

    

# Scales the training and test data to range between 0 and 1.
max_value = X_train.max()
X_train /= max_value
X_test /= max_value


    

In [11]:

    

# The training and test labels are integers from 0 to 9 indicating the class label
(y_train, y_test)


    

    
Out[11]:





(array([5, 0, 4, ..., 5, 6, 8], dtype=uint8),
 array([7, 2, 1, ..., 4, 5, 6], dtype=uint8))

In [12]:

    

# We convert the class labels to binary class matrices
y_train = np_utils.to_categorical(y_train, num_classes)
y_test = np_utils.to_categorical(y_test, num_classes)


    

In [13]:

    

# All the logic to build a (multinomial) logistic regression classifier
model = Sequential()
model.add(Dense(num_classes, input_dim=input_dim, activation='softmax'))


    

In [14]:

    

model.summary()


    

    




_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_1 (Dense)              (None, 10)                7850      
=================================================================
Total params: 7,850
Trainable params: 7,850
Non-trainable params: 0
_________________________________________________________________

In [15]:

    

SVG(model_to_dot(model).create(prog='dot', format='svg'))


    

    
Out[15]:

In [16]:

    

# Trains the model, iterating on the training data in batches of 32 in 10 epochs.
# The optimizer is stochastic gradient descent (SGD).
model.compile(optimizer='sgd', loss='categorical_crossentropy', metrics=['accuracy'])
model.fit(X_train, y_train, batch_size=32, epochs=10, verbose=1)


    

    




Epoch 1/10
60000/60000 [==============================] - 2s - loss: 0.7714 - acc: 0.8208     
Epoch 2/10
60000/60000 [==============================] - 2s - loss: 0.4548 - acc: 0.8821     - ETA: 0s - loss: 0.4631 - a
Epoch 3/10
60000/60000 [==============================] - 2s - loss: 0.4029 - acc: 0.8921     
Epoch 4/10
60000/60000 [==============================] - 2s - loss: 0.3767 - acc: 0.8973     
Epoch 5/10
60000/60000 [==============================] - 1s - loss: 0.3600 - acc: 0.9013     
Epoch 6/10
60000/60000 [==============================] - ETA: 0s - loss: 0.3485 - acc: 0.903 - 2s - loss: 0.3483 - acc: 0.9038     
Epoch 7/10
60000/60000 [==============================] - 2s - loss: 0.3393 - acc: 0.9063     
Epoch 8/10
60000/60000 [==============================] - 1s - loss: 0.3320 - acc: 0.9078     
Epoch 9/10
60000/60000 [==============================] - 2s - loss: 0.3263 - acc: 0.9095     
Epoch 10/10
60000/60000 [==============================] - 2s - loss: 0.3214 - acc: 0.9110     






    
Out[16]:





<keras.callbacks.History at 0x7f31942ebf50>

In [17]:

    

# Test accuracy is ~92%.
model.evaluate(X_test, y_test, verbose=False)


    

    
Out[17]:





[0.3067630158960819, 0.91539999999999999]

In [18]:

    

first_test_image = X_test[0, :]
plt.imshow(first_test_image.reshape(28, 28), cmap=plt.cm.Greys);


    

In [19]:

    

second_test_image = X_test[1, :]
plt.imshow(second_test_image.reshape(28, 28), cmap=plt.cm.Greys);


    

In [20]:

    

model.predict_classes(X_test[[0, 1], :])


    

    




2/2 [==============================] - 0s






    
Out[20]:





array([7, 2])

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