You will use use the functions you'd implemented in the previous assignment to build a deep network, and apply it to cat vs non-cat classification.
After this assignment you will be able to:
Build and apply a deep neural network to supervised learning.
1 - pakage
import time
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
from scipy import ndimage
from dnn_app_utils_v2 import *
%matplotlib inline
plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'
%load_ext autoreload
%autoreload 2
np.random.seed(1)
2 - Dataset
Problem Statement: You are given a dataset ("data.h5") containing:
- a training set of m_train images labelled as cat (1) or non-cat (0)
- a test set of m_test images labelled as cat and non-cat
- each image is of shape (num_px, num_px, 3) where 3 is for the 3 channels (RGB).
train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
Handle Dataset
# Reshape the training and test examples
train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T # The "-1" makes reshape flatten the remaining dimensions
test_x_flatten = test_x_orig.reshape(test_x_orig.shape[0], -1).T
# Standardize data to have feature values between 0 and 1.
train_x = train_x_flatten/255.
test_x = test_x_flatten/255.
print ("train_x's shape: " + str(train_x.shape))
print ("test_x's shape: " + str(test_x.shape))
3 - Architecture of your model
to build a deep neural network to distinguish cat images from non-cat images.
You will build two different models:
A 2-layer neural network
An L-layer deep neural network
3.1 - 2 - layer neural network
2-layer neural network.png
The model can be summarized as: INPUT -> LINEAR -> RELU -> LINEAR -> SIGMOID -> OUTPUT.
3.2 - L - layer neural network
It is hard to represent an L-layer deep neural network with the above representation. However, here is a simplified network representation:
L-layer deep neural network.png
3.3 - General methodology
As usual you will follow the Deep Learning methodology to build the model:
- Initialize parameters / Define hyperparameters
- Loop for num_iterations:
a. Forward propagation
b. Compute cost function
c. Backward propagation
d. Update parameters (using parameters, and grads from backprop) - Use trained parameters to predict labels
4 - Two-layer neural network
Question: Use the helper functions you have implemented in the previous assignment to build a 2-layer neural network with the following structure: LINEAR -> RELU -> LINEAR -> SIGMOID. The functions you may need and their inputs are:
def initialize_parameters(n_x, n_h, n_y):
...
return parameters
def linear_activation_forward(A_prev, W, b, activation):
...
return A, cache
def compute_cost(AL, Y):
...
return cost
def linear_activation_backward(dA, cache, activation):
...
return dA_prev, dW, db
def update_parameters(parameters, grads, learning_rate):
...
return parameters
### CONSTANTS DEFINING THE MODEL ####
n_x = 12288 # num_px * num_px * 3
n_h = 7 # hidden layer
n_y = 1 # output layer
layers_dims = (n_x, n_h, n_y)
# GRADED FUNCTION: two_layer_model
def two_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
"""
Implements a two-layer neural network: LINEAR->RELU->LINEAR->SIGMOID.
Arguments:
X -- input data, of shape (n_x, number of examples)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
layers_dims -- dimensions of the layers (n_x, n_h, n_y)
num_iterations -- number of iterations of the optimization loop
learning_rate -- learning rate of the gradient descent update rule
print_cost -- If set to True, this will print the cost every 100 iterations
Returns:
parameters -- a dictionary containing W1, W2, b1, and b2
"""
np.random.seed(1)
grads = {}
costs = [] # to keep track of the cost
m = X.shape[1] # number of examples
(n_x, n_h, n_y) = layers_dims
# Initialize parameters dictionary, by calling one of the functions you'd previously implemented
parameters = initialize_parameters(n_x, n_h, n_y)
# Get W1, b1, W2 and b2 from the dictionary parameters.
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: LINEAR -> RELU -> LINEAR -> SIGMOID. Inputs: "X, W1, b1". Output: "A1, cache1, A2, cache2".
A1, cache1 = linear_activation_forward(X, W1, b1, activation = "relu")
A2, cache2 = linear_activation_forward(A1, W2, b2, activation = "sigmoid")
# Compute cost
cost = compute_cost(A2, Y)
# Initializing backward propagation
dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
# Backward propagation. Inputs: "dA2, cache2, cache1". Outputs: "dA1, dW2, db2; also dA0 (not used), dW1, db1".
dA1, dW2, db2 = linear_activation_backward(dA2, cache2, activation = "sigmoid")
dA0, dW1, db1 = linear_activation_backward(dA1, cache1, activation = "relu")
# Set grads['dWl'] to dW1, grads['db1'] to db1, grads['dW2'] to dW2, grads['db2'] to db2
grads['dW1'] = dW1
grads['db1'] = db1
grads['dW2'] = dW2
grads['db2'] = db2
# Update parameters.
parameters = update_parameters(parameters, grads, learning_rate= 0.0075)
# Retrieve W1, b1, W2, b2 from parameters
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Print the cost every 100 training example
if print_cost and i % 100 == 0:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if print_cost and i % 100 == 0:
costs.append(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()
return parameters
5 - L-layer Neural Network
Question: Use the helper functions you have implemented previously to build an 𝐿L -layer neural network with the following structure: [LINEAR -> RELU] ×× (L-1) -> LINEAR -> SIGMOID. The functions you may need and their inputs are:
def initialize_parameters_deep(layer_dims):
...
return parameters
def L_model_forward(X, parameters):
...
return AL, caches
def compute_cost(AL, Y):
...
return cost
def L_model_backward(AL, Y, caches):
...
return grads
def update_parameters(parameters, grads, learning_rate):
...
return parameters
### CONSTANTS ###
layers_dims = [12288, 20, 7, 5, 1] # 5-layer model
# GRADED FUNCTION: L_layer_model
def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009
"""
Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
Arguments:
X -- data, numpy array of shape (number of examples, num_px * num_px * 3)
Y -- true "label" vector (containing 0 if cat, 1 if non-cat), of shape (1, number of examples)
layers_dims -- list containing the input size and each layer size, of length (number of layers + 1).
learning_rate -- learning rate of the gradient descent update rule
num_iterations -- number of iterations of the optimization loop
print_cost -- if True, it prints the cost every 100 steps
Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""
np.random.seed(1)
costs = [] # keep track of cost
# Parameters initialization.
parameters = initialize_parameters_deep(layers_dims)
# Loop (gradient descent)
for i in range(0, num_iterations):
# Forward propagation: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID.
AL, caches = L_model_forward(X, parameters)
# Compute cost.
cost = compute_cost(AL, Y)
# Backward propagation.
grads = L_model_backward(AL, Y, caches)
# Update parameters.
parameters = update_parameters(parameters, grads, learning_rate)
# Print the cost every 100 training example
if print_cost and i % 100 == 0:
print ("Cost after iteration %i: %f" %(i, cost))
if print_cost and i % 100 == 0:
costs.append(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()
return parameters
6- Results Analysis
7- Test with your own image (optional/ungraded exercise)
## START CODE HERE ##
my_image = "my_image.jpg" # change this to the name of your image file
my_label_y = [1] # the true class of your image (1 -> cat, 0 -> non-cat)
## END CODE HERE ##
fname = "images/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((num_px*num_px*3,1))
my_predicted_image = predict(my_image, my_label_y, parameters)
plt.imshow(image)
print ("y = " + str(np.squeeze(my_predicted_image)) + ", your L-layer model predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") + "\" picture.")
