import time
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
from scipy import ndimage
from utils 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)train_x_orig, train_y, test_x_orig, test_y, classes = load_data()## Visualize an image in our dataset
index = 19
plt.imshow(train_x_orig[index])
print ("y = " + str(train_y[0,index]) + ". It's a " + classes[train_y[0,index]].decode("utf-8") + " picture.")y = 1. It's a cat picture.
m_train = train_x_orig.shape[0]
num_px = train_x_orig.shape[1]
m_test = test_x_orig.shape[0]
print ("Number of training examples: " + str(m_train))
print ("Number of testing examples: " + str(m_test))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_x_orig shape: " + str(train_x_orig.shape))
print ("train_y shape: " + str(train_y.shape))
print ("test_x_orig shape: " + str(test_x_orig.shape))
print ("test_y shape: " + str(test_y.shape))Number of training examples: 209
Number of testing examples: 50
Each image is of size: (64, 64, 3)
train_x_orig shape: (209, 64, 64, 3)
train_y shape: (1, 209)
test_x_orig shape: (50, 64, 64, 3)
test_y shape: (1, 50)
# Reshape the training and test examples
train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0], -1).T
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))train_x's shape: (12288, 209)
test_x's shape: (12288, 50)
- L-layer Neural Network
- 2-layers Neural Netwrork
- 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
Helper functions from utils.py:
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
n_y = 1
layers_dims = (n_x, n_h, n_y)
learning_rate = 0.0075## 2-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 1 if cat, 0 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
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"]
# Gradient descent
for i in range(0, num_iterations):
A1, cache1 = linear_activation_forward(X, W1, b1, "relu")
A2, cache2 = linear_activation_forward(A1, W2, b2, "sigmoid")
# Compute cost
cost = compute_cost(A2, Y)
dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
dA1, dW2, db2 = linear_activation_backward(dA2, cache2, "sigmoid")
dA0, dW1, db1 = linear_activation_backward(dA1, cache1, "relu")
grads['dW1'] = dW1
grads['db1'] = db1
grads['dW2'] = dW2
grads['db2'] = db2
# Update parameters
parameters = update_parameters(parameters, grads, learning_rate)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
# Print the cost every 100 iterations
if print_cost and i % 100 == 0 or i == num_iterations - 1:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if i % 100 == 0 or i == num_iterations:
costs.append(cost)
return parameters, costs
def plot_costs(costs, learning_rate=0.0075):
plt.plot(np.squeeze(costs))
plt.ylabel('cost')
plt.xlabel('iterations (per hundreds)')
plt.title("Learning rate =" + str(learning_rate))
plt.show()parameters, costs = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=False)
plot_costs(costs, learning_rate)Cost after iteration 2499: 0.04421498215868956
predictions_train = predict(train_x, train_y, parameters)Accuracy: 0.9999999999999998
predictions_test = predict(test_x, test_y, parameters)Accuracy: 0.72
Helper functions from utils.py:
def initialize_parameters_deep(layers_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 parametersdef L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
"""
Arguments:
X -- input data, of shape (n_x, number of examples)
Y -- true "label" vector (containing 1 if cat, 0 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 = initialize_parameters_deep(layers_dims)
for i in range(0, num_iterations):
AL, caches = L_model_forward(X, parameters)
cost = compute_cost(AL, Y)
grads = L_model_backward(AL, Y, caches)
parameters = update_parameters(parameters, grads, learning_rate)
if print_cost and i % 100 == 0 or i == num_iterations - 1:
print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
if i % 100 == 0 or i == num_iterations:
costs.append(cost)
return parameters, costsparameters, costs = L_layer_model(train_x, train_y, layers_dims, num_iterations = 1, print_cost = False)
print("Cost after first iteration: " + str(costs[0]))Cost after iteration 0: 0.6950464961800915
Cost after first iteration: 0.6950464961800915
parameters, costs = L_layer_model(train_x, train_y, layers_dims, num_iterations = 2500, print_cost = True)
plot_costs(costs, learning_rate)Cost after iteration 0: 0.6950464961800915
Cost after iteration 100: 0.5892596054583805
Cost after iteration 200: 0.5232609173622991
Cost after iteration 300: 0.4497686396221906
Cost after iteration 400: 0.4209002161883899
Cost after iteration 500: 0.37246403061745953
Cost after iteration 600: 0.34742051870201895
Cost after iteration 700: 0.31719191987370277
Cost after iteration 800: 0.2664377434774657
Cost after iteration 900: 0.21991432807842554
Cost after iteration 1000: 0.14357898893623783
Cost after iteration 1100: 0.45309212623221284
Cost after iteration 1200: 0.09499357670093515
Cost after iteration 1300: 0.08014128076781371
Cost after iteration 1400: 0.06940234005536462
Cost after iteration 1500: 0.06021664023174592
Cost after iteration 1600: 0.05327415758001877
Cost after iteration 1700: 0.04762903262098433
Cost after iteration 1800: 0.04297588879436869
Cost after iteration 1900: 0.03903607436513818
Cost after iteration 2000: 0.03568313638049027
Cost after iteration 2100: 0.03291526373054675
Cost after iteration 2200: 0.030472193059120623
Cost after iteration 2300: 0.02838785921294613
Cost after iteration 2400: 0.026615212372776073
Cost after iteration 2499: 0.02482129221835338
pred_train = predict(train_x, train_y, parameters)Accuracy: 0.9999999999999998
pred_test = predict(test_x, test_y, parameters)Accuracy: 0.74
print_mislabeled_images(classes, test_x, test_y, pred_test)