Convolution Nets for MNIST¶

Deep Learning models can take quite a bit of time to run, particularly if GPU isn't used.

In the interest of time, you could sample a subset of observations (e.g. $1000$) that are a particular number of your choice (e.g. $6$) and $1000$ observations that aren't that particular number (i.e. $\neq 6$).

We will build a model using that and see how it performs on the test dataset

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#Import the required libraries
import numpy as np
np.random.seed(1338)

from keras.datasets import mnist

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from keras.models import Sequential
from keras.layers.core import Dense, Dropout, Activation, Flatten

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from keras.layers.convolutional import Conv2D
from keras.layers.pooling import MaxPooling2D

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from keras.utils import np_utils
from keras.optimizers import SGD

Loading Data¶

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#Load the training and testing data
(X_train, y_train), (X_test, y_test) = mnist.load_data()

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X_test_orig = X_test

Data Preparation¶

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from keras import backend as K

Very Important:¶

When dealing with images & convolutions, it is paramount to handle image_data_format properly

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img_rows, img_cols = 28, 28

if K.image_data_format() == 'channels_first':
    shape_ord = (1, img_rows, img_cols)
else:  # channel_last
    shape_ord = (img_rows, img_cols, 1)

Preprocess and Normalise Data¶

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X_train = X_train.reshape((X_train.shape[0],) + shape_ord)
X_test = X_test.reshape((X_test.shape[0],) + shape_ord)

X_train = X_train.astype('float32')
X_test = X_test.astype('float32')

X_train /= 255
X_test /= 255

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np.random.seed(1338)  # for reproducibilty!!

# Test data
X_test = X_test.copy()
Y = y_test.copy()

# Converting the output to binary classification(Six=1,Not Six=0)
Y_test = Y == 6
Y_test = Y_test.astype(int)

# Selecting the 5918 examples where the output is 6
X_six = X_train[y_train == 6].copy()
Y_six = y_train[y_train == 6].copy()

# Selecting the examples where the output is not 6
X_not_six = X_train[y_train != 6].copy()
Y_not_six = y_train[y_train != 6].copy()

# Selecting 6000 random examples from the data that 
# only contains the data where the output is not 6
random_rows = np.random.randint(0,X_six.shape[0],6000)
X_not_six = X_not_six[random_rows]
Y_not_six = Y_not_six[random_rows]

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# Appending the data with output as 6 and data with output as <> 6
X_train = np.append(X_six,X_not_six)

# Reshaping the appended data to appropraite form
X_train = X_train.reshape((X_six.shape[0] + X_not_six.shape[0],) + shape_ord)

# Appending the labels and converting the labels to 
# binary classification(Six=1,Not Six=0)
Y_labels = np.append(Y_six,Y_not_six)
Y_train = Y_labels == 6 
Y_train = Y_train.astype(int)

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print(X_train.shape, Y_labels.shape, X_test.shape, Y_test.shape)

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# Converting the classes to its binary categorical form
nb_classes = 2
Y_train = np_utils.to_categorical(Y_train, nb_classes)
Y_test = np_utils.to_categorical(Y_test, nb_classes)

A simple CNN¶

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# -- Initializing the values for the convolution neural network

nb_epoch = 2  # kept very low! Please increase if you have GPU

batch_size = 64
# number of convolutional filters to use
nb_filters = 32
# size of pooling area for max pooling
nb_pool = 2
# convolution kernel size
nb_conv = 3

sgd = SGD(lr=0.1, decay=1e-6, momentum=0.9, nesterov=True)

Step 1: Model Definition¶

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model = Sequential()

model.add(Conv2D(nb_filters, (nb_conv, nb_conv), padding='valid', 
                 input_shape=shape_ord))  # note: the very first layer **must** always specify the input_shape
model.add(Activation('relu'))

model.add(Flatten())
model.add(Dense(nb_classes))
model.add(Activation('softmax'))

Step 2: Compile¶

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model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])

Step 3: Fit¶

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hist = model.fit(X_train, Y_train, batch_size=batch_size, 
                 epochs=nb_epoch, verbose=1, 
                 validation_data=(X_test, Y_test))

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import matplotlib.pyplot as plt
%matplotlib inline

plt.figure()
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.plot(hist.history['loss'])
plt.plot(hist.history['val_loss'])
plt.legend(['Training', 'Validation'])

plt.figure()
plt.xlabel('Epochs')
plt.ylabel('Accuracy')
plt.plot(hist.history['acc'])
plt.plot(hist.history['val_acc'])
plt.legend(['Training', 'Validation'], loc='lower right')

Step 4: Evaluate¶

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print('Available Metrics in Model: {}'.format(model.metrics_names))

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# Evaluating the model on the test data    
loss, accuracy = model.evaluate(X_test, Y_test, verbose=0)
print('Test Loss:', loss)
print('Test Accuracy:', accuracy)

Let's plot our model Predictions!¶

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import matplotlib.pyplot as plt

%matplotlib inline

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slice = 15
predicted = model.predict(X_test[:slice]).argmax(-1)

plt.figure(figsize=(16,8))
for i in range(slice):
    plt.subplot(1, slice, i+1)
    plt.imshow(X_test_orig[i], interpolation='nearest')
    plt.text(0, 0, predicted[i], color='black', 
             bbox=dict(facecolor='white', alpha=1))
    plt.axis('off')

Adding more Dense Layers¶

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model = Sequential()
model.add(Conv2D(nb_filters, (nb_conv, nb_conv),
                 padding='valid', input_shape=shape_ord))
model.add(Activation('relu'))

model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu'))

model.add(Dense(nb_classes))
model.add(Activation('softmax'))

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model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])

model.fit(X_train, Y_train, batch_size=batch_size, 
          epochs=nb_epoch,verbose=1,
          validation_data=(X_test, Y_test))

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#Evaluating the model on the test data    
score, accuracy = model.evaluate(X_test, Y_test, verbose=0)
print('Test score:', score)
print('Test accuracy:', accuracy)

Adding Dropout¶

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model = Sequential()

model.add(Conv2D(nb_filters, (nb_conv, nb_conv),
                        padding='valid',
                        input_shape=shape_ord))
model.add(Activation('relu'))

model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu'))
model.add(Dropout(0.5))
model.add(Dense(nb_classes))
model.add(Activation('softmax'))

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model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])

model.fit(X_train, Y_train, batch_size=batch_size, 
          epochs=nb_epoch,verbose=1,
          validation_data=(X_test, Y_test))

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#Evaluating the model on the test data    
score, accuracy = model.evaluate(X_test, Y_test, verbose=0)
print('Test score:', score)
print('Test accuracy:', accuracy)

Adding more Convolution Layers¶

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model = Sequential()
model.add(Conv2D(nb_filters, (nb_conv, nb_conv),
                 padding='valid', input_shape=shape_ord))
model.add(Activation('relu'))
model.add(Convolution2D(nb_filters, (nb_conv, nb_conv)))
model.add(Activation('relu'))
model.add(MaxPooling2D(pool_size=(nb_pool, nb_pool)))
model.add(Dropout(0.25))
    
model.add(Flatten())
model.add(Dense(128))
model.add(Activation('relu'))
model.add(Dropout(0.5))
model.add(Dense(nb_classes))
model.add(Activation('softmax'))

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model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])

model.fit(X_train, Y_train, batch_size=batch_size, 
          epochs=nb_epoch,verbose=1,
          validation_data=(X_test, Y_test))

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#Evaluating the model on the test data    
score, accuracy = model.evaluate(X_test, Y_test, verbose=0)
print('Test score:', score)
print('Test accuracy:', accuracy)

Exercise¶

The above code has been written as a function.

Change some of the hyperparameters and see what happens.

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# Function for constructing the convolution neural network
# Feel free to add parameters, if you want

def build_model():
    """"""
    model = Sequential()
    model.add(Conv2D(nb_filters, (nb_conv, nb_conv), 
                     padding='valid',
                     input_shape=shape_ord))
    model.add(Activation('relu'))
    model.add(Conv2D(nb_filters, (nb_conv, nb_conv)))
    model.add(Activation('relu'))
    model.add(MaxPooling2D(pool_size=(nb_pool, nb_pool)))
    model.add(Dropout(0.25))
    
    model.add(Flatten())
    model.add(Dense(128))
    model.add(Activation('relu'))
    model.add(Dropout(0.5))
    model.add(Dense(nb_classes))
    model.add(Activation('softmax'))
    
    model.compile(loss='categorical_crossentropy',
              optimizer='sgd',
              metrics=['accuracy'])

    model.fit(X_train, Y_train, batch_size=batch_size, 
              epochs=nb_epoch,verbose=1,
              validation_data=(X_test, Y_test))
          

    #Evaluating the model on the test data    
    score, accuracy = model.evaluate(X_test, Y_test, verbose=0)
    print('Test score:', score)
    print('Test accuracy:', accuracy)

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#Timing how long it takes to build the model and test it.
%timeit -n1 -r1 build_model()

Batch Normalisation¶

Normalize the activations of the previous layer at each batch, i.e. applies a transformation that maintains the mean activation close to 0 and the activation standard deviation close to 1.

How to BatchNorm in Keras¶

from keras.layers.normalization import BatchNormalization

BatchNormalization(axis=-1, momentum=0.99, epsilon=0.001, center=True, scale=True, 
                   beta_initializer='zeros', gamma_initializer='ones', moving_mean_initializer='zeros',
                   moving_variance_initializer='ones', beta_regularizer=None, gamma_regularizer=None,
                   beta_constraint=None, gamma_constraint=None)

Arguments¶

axis: Integer, the axis that should be normalized (typically the features axis). For instance, after a Conv2D layer with data_format="channels_first", set axis=1 in BatchNormalization.
momentum: Momentum for the moving average.
epsilon: Small float added to variance to avoid dividing by zero.
center: If True, add offset of beta to normalized tensor. If False, beta is ignored.
scale: If True, multiply by gamma. If False, gamma is not used. When the next layer is linear (also e.g. nn.relu), this can be disabled since the scaling will be done by the next layer.
beta_initializer: Initializer for the beta weight.
gamma_initializer: Initializer for the gamma weight.
moving_mean_initializer: Initializer for the moving mean.
moving_variance_initializer: Initializer for the moving variance.
beta_regularizer: Optional regularizer for the beta weight.
gamma_regularizer: Optional regularizer for the gamma weight.
beta_constraint: Optional constraint for the beta weight.
gamma_constraint: Optional constraint for the gamma weight.

Excercise¶

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# Try to add a new BatchNormalization layer to the Model 
# (after the Dropout layer) - before or after the ReLU Activation