Reference link: https://www.missshi.cn/api/view/blog/59bbcb46e519f50d04000206
When using the Tensorflow framework, the usual steps are as follows:
1. Initialize variables2. Start a Session
3. Train the algorithm
4. Complete the neural network
1. Tensorflow library
import tensorflow as tf from tensorflow.python.framework import ops
2. A point to note:
3. Linear function:
def linear_function():
np.random.seed(1)
X = tf.constant(np.random.randn(3,1), name = "X")
W = tf.constant(np.random.randn(4,3), name = "X")
b = tf.constant(np.random.randn(4,1), name = "X")
Y = tf.matmul(W, X) + b
# Create the session using tf.Session() and run it with sess.run(...) on the variable you want to calculate
sex = tf.Session ()
result = sess.run(Y)
sess.close() # close the session
return result
4. sigmod function:
def sigmoid(z):
# Create a placeholder for x. Name it 'x'.
x = tf.placeholder(tf.float32, name = "x")
# compute sigmoid(x)
sigmoid = tf.sigmoid(x)
# Create a session, and run it. Please use the method 2 explained above.
# You should use a feed_dict to pass z's value to x.
with tf.Session() as sess:
# Run session and call the output "result"
result = sess.run(sigmoid, feed_dict = {x: z})
return result
5. Cost function calculation:
def cost(logits, labels):
"""
Computes the cost using the sigmoid cross entropy
Arguments:
logits -- vector containing z, output of the last linear unit (before the final sigmoid activation)
labels -- vector of labels y (1 or 0)
Note: What we've been calling "z" and "y" in this class are respectively called "logits" and "labels"
in the TensorFlow documentation. So logits will feed into z, and labels into y.
Returns:
cost -- runs the session of the cost (formula (2))
"""
### START CODE HERE ###
# Create the placeholders for "logits" (z) and "labels" (y) (approx. 2 lines)
z = tf.placeholder(tf.float32, name = "logits")
y = tf.placeholder(tf.float32, name = "labels")
# Use the loss function (approx. 1 line)6666666666666666666666666666666666666666666666666666666666666666666666666
cost = tf.nn.sigmoid_cross_entropy_with_logits(logits = z, labels = y)
# Create a session (approx. 1 line). See method 1 above.
sex = tf.Session ()
# Run the session (approx. 1 line).
cost = sess.run(cost, feed_dict = {z: logits, y:labels})
# Close the session (approx. 1 line). See method 1 above.
sess.close()
### END CODE HERE ###
return cost
6. Perform 0,1 encoding:
When the multi-class problem labels are some integers from 0 to C-1, we need to convert the integers directly from 0 to C-1 to a C-dimensional vector before training.
def one_hot_matrix(labels, C):
# Create a tf.constant equal to C (depth), name it 'C'. (approx. 1 line)
C = tf.constant(C, name = "C")
# Use tf.one_hot, be careful with the axis (approx. 1 line)
one_hot_matrix = tf.one_hot(labels, C, 1)
# Create the session (approx. 1 line)
sex = tf.Session ()
one_hot = sess.run(one_hot_matrix).T
sess.close()
return one_hot
7. All 0 initialization and all 1 initialization
def zeros(shape):
"""
Creates an array of ones of dimension shape
Arguments:
shape -- shape of the array you want to create
Returns:
ones -- array containing only ones
"""
### START CODE HERE ###
# Create "zeros" tensor using tf.zeros(...). (approx. 1 line)
ones = tf.zeros(shape)
# Create the session (approx. 1 line)
sex = tf.Session ()
# Run the session to compute 'zeros' (approx. 1 line)
zeros = sess.run(zeros)
# Close the session (approx. 1 line). See method 1 above.
sess.close()
### END CODE HERE ###
return zeros
def ones(shape):
"""
Creates an array of ones of dimension shape
Arguments:
shape -- shape of the array you want to create
Returns:
ones -- array containing only ones
"""
### START CODE HERE ###
# Create "ones" tensor using tf.ones(...). (approx. 1 line)
ones = tf.ones(shape)
# Create the session (approx. 1 line)
sex = tf.Session ()
# Run the session to compute 'ones' (approx. 1 line)
ones = sess.run(ones)
# Close the session (approx. 1 line). See method 1 above.
sess.close()
### END CODE HERE ###
return ones
8. Build a neural network model with Tensorflow
# read dataset X_train_orig, Y_train_orig, X_test_orig, Y_test_orig, classes = load_dataset()
Let's test an image:
# Example of a picture
index = 0
plt.imshow(X_train_orig[index])
print ("y = " + str(np.squeeze(Y_train_orig[:, index])))
Next, we need to preprocess the read dataset:
Including normalization and the previously mentioned zeroing.
X_train_flatten = X_train_orig.reshape(X_train_orig.shape[0], -1).T X_test_flatten = X_test_orig.reshape(X_test_orig.shape[0], -1).T # Normalize image vectors X_train = X_train_flatten/255. X_test = X_test_flatten/255. # Convert training and test labels to one hot matrices Y_train = convert_to_one_hot(Y_train_orig, 6) Y_test = convert_to_one_hot(Y_test_orig, 6)
ef create_placeholders(n_x, n_y):
"""
Creates the placeholders for the tensorflow session.
Arguments:
n_x -- scalar, size of an image vector (num_px * num_px = 64 * 64 * 3 = 12288)
n_y -- scalar, number of classes (from 0 to 5, so -> 6)
Returns:
X -- placeholder for the data input, of shape [n_x, None] and dtype "float"
Y -- placeholder for the input labels, of shape [n_y, None] and dtype "float"
Tips:
- You will use None because it let's us be flexible on the number of examples you will for the placeholders.
In fact, the number of examples during test/train is different.
"""
### START CODE HERE ### (approx. 2 lines)
X = tf.placeholder(tf.float32, [n_x, None], name = "X")
Y = tf.placeholder(tf.float32, [n_y, None], name = "Y")
### END CODE HERE ###
return X, Y
Next, we need to initialize the parameters:
def initialize_parameters():
"""
Initializes parameters to build a neural network with tensorflow. The shapes are:
W1 : [25, 12288]
b1 : [25, 1]
W2 : [12, 25]
b2 : [12, 1]
W3 : [6, 12]
b3: [6, 1]
Returns:
parameters -- a dictionary of tensors containing W1, b1, W2, b2, W3, b3
"""
tf.set_random_seed(1) # so that your "random" numbers match ours
### START CODE HERE ### (approx. 6 lines of code)
W1 = tf.get_variable("W1", [25,12288], initializer = tf.contrib.layers.xavier_initializer(seed = 1))
b1 = tf.get_variable("b1", [25,1], initializer = tf.zeros_initializer())
W2 = tf.get_variable("W2", [12,25], initializer = tf.contrib.layers.xavier_initializer(seed = 1))
b2 = tf.get_variable("b2", [12,1], initializer = tf.zeros_initializer())
W3 = tf.get_variable("W3", [6,12], initializer = tf.contrib.layers.xavier_initializer(seed = 1))
b3 = tf.get_variable("b3", [6,1], initializer = tf.zeros_initializer())
### END CODE HERE ###
parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2,
"W3": W3,
"b3": b3}
return parameters
Implement the forward propagation calculation:
def forward_propagation(X, parameters):
"""
Implements the forward propagation for the model: LINEAR -> RELU -> LINEAR -> RELU -> LINEAR -> SOFTMAX
Arguments:
X -- input dataset placeholder, of shape (input size, number of examples)
parameters -- python dictionary containing your parameters "W1", "b1", "W2", "b2", "W3", "b3"
the shapes are given in initialize_parameters
Returns:
Z3 -- the output of the last LINEAR unit
"""
# Retrieve the parameters from the dictionary "parameters"
W1 = parameters['W1']
b1 = parameters['b1']
W2 = parameters['W2']
b2 = parameters['b2']
W3 = parameters['W3']
b3 = parameters ['b3']
### START CODE HERE ### (approx. 5 lines) # Numpy Equivalents:
Z1 = tf.matmul(W1, X) + b1 # Z1 = np.dot(W1, X) + b1
A1 = tf.nn.relu (Z1) # A1 = relu (Z1)
Z2 = tf.matmul(W2, A1) + b2 # Z2 = np.dot(W2, a1) + b2
A2 = tf.nn.relu (Z2) # A2 = relu (Z2)
Z3 = tf.matmul (W3, A2) + b3 # Z3 = np.dot (W3, Z2) + b3
### END CODE HERE ###
return Z3
Calculate the cost function:
ef compute_cost(Z3, Y):
"""
Computes the cost
Arguments:
Z3 -- output of forward propagation (output of the last LINEAR unit), of shape (6, number of examples)
Y -- "true" labels vector placeholder, same shape as Z3
Returns:
cost - Tensor of the cost function
"""
# to fit the tensorflow requirement for tf.nn.softmax_cross_entropy_with_logits(...,...)
logits = tf.transpose(Z3)
labels = tf.transpose(Y)
### START CODE HERE ### (1 line of code)
cost = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits(logits = logits, labels = labels))
### END CODE HERE ###
return cost
It should be noted that for the two steps of backpropagation calculation and parameter update, in frameworks such as Tensorflow, it has been automatically completed according to the forward propagation calculation and cost function we wrote, and we do not need to write it ourselves.
Now, let's build our model based on some of the methods we just implemented:
def model(X_train, Y_train, X_test, Y_test, learning_rate = 0.0001,
num_epochs = 1500, minibatch_size = 32, print_cost = True):
"""
Implements a three-layer tensorflow neural network: LINEAR->RELU->LINEAR->RELU->LINEAR->SOFTMAX.
Arguments:
X_train -- training set, of shape (input size = 12288, number of training examples = 1080)
Y_train -- test set, of shape (output size = 6, number of training examples = 1080)
X_test -- training set, of shape (input size = 12288, number of training examples = 120)
Y_test -- test set, of shape (output size = 6, number of test examples = 120)
learning_rate -- learning rate of the optimization
num_epochs -- number of epochs of the optimization loop
minibatch_size -- size of a minibatch
print_cost -- True to print the cost every 100 epochs
Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""
ops.reset_default_graph() # to be able to rerun the model without overwriting tf variables
tf.set_random_seed(1) # to keep consistent results
seed = 3 # to keep consistent results
(n_x, m) = X_train.shape # (n_x: input size, m : number of examples in the train set)
n_y = Y_train.shape[0] # n_y : output size
costs = [] # To keep track of the cost
# Create Placeholders of shape (n_x, n_y)
### START CODE HERE ### (1 line)
X, Y = create_placeholders(n_x, n_y)
### END CODE HERE ###
# Initialize parameters
### START CODE HERE ### (1 line)
parameters = initialize_parameters()
### END CODE HERE ###
# Forward propagation: Build the forward propagation in the tensorflow graph
### START CODE HERE ### (1 line)
Z3 = forward_propagation(X, parameters)
### END CODE HERE ###
# Cost function: Add cost function to tensorflow graph
### START CODE HERE ### (1 line)
cost = compute_cost(Z3, Y)
### END CODE HERE ###
# Backpropagation: Define the tensorflow optimizer. Use an AdamOptimizer.
### START CODE HERE ### (1 line)
optimizer = tf.train.AdamOptimizer(learning_rate = learning_rate).minimize(cost)
### END CODE HERE ###
# Initialize all the variables
init = tf.global_variables_initializer()
# Start the session to compute the tensorflow graph
with tf.Session() as sess:
# Run the initialization
sess.run(init)
# Do the training loop
for epoch in range(num_epochs):
epoch_cost = 0. # Defines a cost related to an epoch
num_minibatches = int(m / minibatch_size) # number of minibatches of size minibatch_size in the train set
seed = seed + 1
minibatches = random_mini_batches(X_train, Y_train, minibatch_size, seed)
for minibatch in minibatches:
# Select a minibatch
(minibatch_X, minibatch_Y) = minibatch
# IMPORTANT: The line that runs the graph on a minibatch.
# Run the session to execute the "optimizer" and the "cost", the feedict should contain a minibatch for (X,Y).
### START CODE HERE ### (1 line)
_ , minibatch_cost = sess.run([optimizer, cost], feed_dict={X: minibatch_X, Y: minibatch_Y})
### END CODE HERE ###
epoch_cost += minibatch_cost / num_minibatches
# Print the cost every epoch
if print_cost == True and epoch % 100 == 0:
print ("Cost after epoch %i: %f" % (epoch, epoch_cost))
if print_cost == True and epoch % 5 == 0:
costs.append(epoch_cost)
# plot the cost
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per tens)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()
# lets save the parameters in a variable
parameters = sess.run(parameters)
print ("Parameters have been trained!")
# Calculate the correct predictions
correct_prediction = tf.equal(tf.argmax(Z3), tf.argmax(Y))
# Calculate accuracy on the test set
accuracy = tf.reduce_mean(tf.cast(correct_prediction, "float"))
print ("Train Accuracy:", accuracy.eval({X: X_train, Y: Y_train}))
print ("Test Accuracy:", accuracy.eval({X: X_test, Y: Y_test}))
return parameters
Let's test it with our model:
parameters = model(X_train, Y_train, X_test, Y_test)
There is a certain amount of overfitting!
