[置顶] Coursera-Deep Learning Specialization 课程之（一）：Neural Networks and Deep Learning-weak3编程作业

Planar data classification with a hidden layer

1 - Packages

# Package imports
import numpy as np
import matplotlib.pyplot as plt
from testCases_v2 import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets
%matplotlib inline
np.random.seed(1) # set a seed so that the results are consistent

2 - Dataset

def load_planar_dataset():
np.random.seed(1)
m = 400 # 样本数量
N = int(m/2) # 每个类别的样本量
D = 2 # 维度数
X = np.zeros((m,D)) # 初始化X
Y = np.zeros((m,1), dtype='uint8') # 初始化Y
a = 4 # 花儿的最大长度

for j in range(2):
ix = range(N*j,N*(j+1))
t = np.linspace(j*3.12,(j+1)*3.12,N) + np.random.randn(N)*0.2 # theta
r = a*np.sin(4*t) + np.random.randn(N)*0.2 # radius
X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
Y[ix] = j
X = X.T
Y = Y.T
return X, Y
X, Y = load_planar_dataset()

# Visualize the data:
plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);

### START CODE HERE ### (≈ 3 lines of code)
shape_X = X.shape
shape_Y = Y.shape
m = 400  # training set size
### END CODE HERE ###

print ('The shape of X is: ' + str(shape_X))
print ('The shape of Y is: ' + str(shape_Y))
print ('I have m = %d training examples!' % (m))

3 - Simple Logistic Regression

# Train the logistic regression classifier
clf = sklearn.linear_model.LogisticRegressionCV();
clf.fit(X.T, Y.T);

# Plot the decision boundary for logistic regression
plot_decision_boundary(lambda x: clf.predict(x), X, Y)
plt.title("Logistic Regression")

# Print accuracy
LR_predictions = clf.predict(X.T)
print ('Accuracy of logistic regression: %d ' % float((np.dot(Y,LR_predictions) + np.dot(1-Y,1-LR_predictions))/float(Y.size)*100) +
'% ' + "(percentage of correctly labelled datapoints)")

4 - Neural Network model

4.1 - Defining the neural network structure

# GRADED FUNCTION: layer_sizes
def layer_sizes(X, Y):
"""
Arguments:
X -- input dataset of shape (input size, number of examples)
Y -- labels of shape (output size, number of examples)
Returns:
n_x -- the size of the input layer
n_h -- the size of the hidden layer
n_y -- the size of the output layer
"""
### START CODE HERE ### (≈ 3 lines of code)
n_x = X.shape[0] # size of input layer
n_h = 4
n_y = Y.shape[0] # size of output layer
### END CODE HERE ###
return (n_x, n_h, n_y)

X_assess, Y_assess = layer_sizes_test_case()
(n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)
print("The size of the input layer is: n_x = " + str(n_x))
print("The size of the hidden layer is: n_h = " + str(n_h))
print("The size of the output layer is: n_y = " + str(n_y))

4.2 - Initialize the model’s parameters

# GRADED FUNCTION: initialize_parameters
def initialize_parameters(n_x, n_h, n_y):
"""
Argument:
n_x -- size of the input layer
n_h -- size of the hidden layer
n_y -- size of the output layer

Returns:
params -- python dictionary containing your parameters:
W1 -- weight matrix of shape (n_h, n_x)
b1 -- bias vector of shape (n_h, 1)
W2 -- weight matrix of shape (n_y, n_h)
b2 -- bias vector of shape (n_y, 1)
"""
np.random.seed(2) # we set up a seed so that your output matches ours although the initialization is random.

### START CODE HERE ### (≈ 4 lines of code)
W1 = np.random.randn(n_h, n_x)*0.01
b1 = np.zeros((n_h, 1))
W2 = np.random.randn(n_y, n_h)*0.01
b2 = np.zeros((n_y, 1))
### END CODE HERE ###

assert (W1.shape == (n_h, n_x))
assert (b1.shape == (n_h, 1))
assert (W2.shape == (n_y, n_h))
assert (b2.shape == (n_y, 1))

parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}

return parameters

4.3 - The Loop

# GRADED FUNCTION: forward_propagation
def forward_propagation(X, parameters):
"""
Argument:
X -- input data of size (n_x, m)
parameters -- python dictionary containing your parameters (output of initialization function)
Returns:
A2 -- The sigmoid output of the second activation
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2"
"""
# Retrieve each parameter from the dictionary "parameters"
### START CODE HERE ### (≈ 4 lines of code)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
### END CODE HERE ###

# Implement Forward Propagation to calculate A2 (probabilities)
### START CODE HERE ### (≈ 4 lines of code)
Z1 = np.dot(W1,X)+b1
A1 = np.tanh(Z1)
Z2 = np.dot(W2,A1)+b2
A2 = sigmoid(Z2)
### END CODE HERE ###

assert(A2.shape == (1, X.shape[1]))

cache = {"Z1": Z1,
"A1": A1,
"Z2": Z2,
"A2": A2}

return A2, cache

# GRADED FUNCTION: compute_cost
def compute_cost(A2, Y, parameters):
"""
Computes the cross-entropy cost given in equation (13)
Arguments:
A2 -- The sigmoid output of the second activation, of shape (1, number of examples)
Y -- "true" labels vector of shape (1, number of examples)
parameters -- python dictionary containing your parameters W1, b1, W2 and b2
Returns:
cost -- cross-entropy cost given equation (13)
"""

m = Y.shape[1] # number of example

# Compute the cross-entropy cost
### START CODE HERE ### (≈ 2 lines of code)
logprobs =  np.multiply(np.log(A2),Y)+np.multiply(np.log(1-A2),1-Y)
cost = -1/m*np.sum(logprobs)
### END CODE HERE ###
cost = np.squeeze(cost)     # makes sure cost is the dimension we expect.
# E.g., turns [[17]] into 17
assert(isinstance(cost, float))
return cost

# GRADED FUNCTION: backward_propagation
def backward_propagation(parameters, cache, X, Y):
"""
Implement the backward propagation using the instructions above.

Arguments:
parameters -- python dictionary containing our parameters
cache -- a dictionary containing "Z1", "A1", "Z2" and "A2".
X -- input data of shape (2, number of examples)
Y -- "true" labels vector of shape (1, number of examples)

Returns:
grads -- python dictionary containing your gradients with respect to different parameters
"""
m = X.shape[1]

# First, retrieve W1 and W2 from the dictionary "parameters".
### START CODE HERE ### (≈ 2 lines of code)
W1 = parameters["W1"]
W2 = parameters["W2"]
### END CODE HERE ###

# Retrieve also A1 and A2 from dictionary "cache".
### START CODE HERE ### (≈ 2 lines of code)
A1 = cache['A1']
A2 = cache['A2']
### END CODE HERE ###

# Backward propagation: calculate dW1, db1, dW2, db2.
### START CODE HERE ### (≈ 6 lines of code, corresponding to 6 equations on slide above)
dZ2 = A2-Y
dW2 = 1/m*np.dot(dZ2,A1.T)
db2 = 1/m*np.sum(dZ2,axis=1,keepdims=True)
dZ1 = np.dot(W2.T,dZ2)*(1 - np.power(A1, 2))
dW1 = 1/m*np.dot(dZ1,X.T)
db1 = 1/m*np.sum(dZ1,axis=1,keepdims=True)
### END CODE HERE ###

grads = {"dW1": dW1,
"db1": db1,
"dW2": dW2,
"db2": db2}
return grads

# GRADED FUNCTION: update_parameters

def update_parameters(parameters, grads, learning_rate = 1.2):
"""
Updates parameters using the gradient descent update rule given above

Arguments:
parameters -- python dictionary containing your parameters
grads -- python dictionary containing your gradients

Returns:
parameters -- python dictionary containing your updated parameters
"""
# Retrieve each parameter from the dictionary "parameters"
### START CODE HERE ### (≈ 4 lines of code)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
### END CODE HERE ###

# Retrieve each gradient from the dictionary "grads"
### START CODE HERE ### (≈ 4 lines of code)
dW1 = grads["dW1"]
db1 = grads["db1"]
dW2 = grads["dW2"]
db2 = grads["db2"]
## END CODE HERE ###

# Update rule for each parameter
### START CODE HERE ### (≈ 4 lines of code)
W1 = W1-learning_rate*dW1
b1 = b1-learning_rate*db1
W2 = W2-learning_rate*dW2
b2 = b2-learning_rate*db2
### END CODE HERE ###

parameters = {"W1": W1,
"b1": b1,
"W2": W2,
"b2": b2}

return parameters

4.4 - Integrate parts 4.1, 4.2 and 4.3 in nn_model()

# GRADED FUNCTION: nn_model
def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):
"""
Arguments:
X -- dataset of shape (2, number of examples)
Y -- labels of shape (1, number of examples)
n_h -- size of the hidden layer
num_iterations -- Number of iterations in gradient descent loop
print_cost -- if True, print the cost every 1000 iterations

Returns:
parameters -- parameters learnt by the model. They can then be used to predict.
"""

np.random.seed(3)
n_x = layer_sizes(X, Y)[0]
n_y = layer_sizes(X, Y)[2]

# Initialize parameters, then retrieve W1, b1, W2, b2. Inputs: "n_x, n_h, n_y". Outputs = "W1, b1, W2, b2, parameters".
### START CODE HERE ### (≈ 5 lines of code)
parameters =initialize_parameters(n_x, n_h, n_y)
W1 = parameters["W1"]
b1 = parameters["b1"]
W2 = parameters["W2"]
b2 = parameters["b2"]
### END CODE HERE ###

# Loop (gradient descent)

for i in range(0, num_iterations):

### START CODE HERE ### (≈ 4 lines of code)
# Forward propagation. Inputs: "X, parameters". Outputs: "A2, cache".
A2, cache = forward_propagation(X, parameters)

# Cost function. Inputs: "A2, Y, parameters". Outputs: "cost".
cost = compute_cost(A2, Y, parameters)

# Backpropagation. Inputs: "parameters, cache, X, Y". Outputs: "grads".
grads = backward_propagation(parameters, cache, X, Y)

# Gradient descent parameter update. Inputs: "parameters, grads". Outputs: "parameters".
parameters = update_parameters(parameters, grads)

### END CODE HERE ###

# Print the cost every 1000 iterations
if print_cost and i % 1000 == 0:
print ("Cost after iteration %i: %f" %(i, cost))

return parameters

4.5 Predictions

# GRADED FUNCTION: predict
def predict(parameters, X):
"""
Using the learned parameters, predicts a class for each example in X
Arguments:
parameters -- python dictionary containing your parameters
X -- input data of size (n_x, m)

Returns
predictions -- vector of predictions of our model (red: 0 / blue: 1)
"""

# Computes probabilities using forward propagation, and classifies to 0/1 using 0.5 as the threshold.
### START CODE HERE ### (≈ 2 lines of code)
A2, cache = forward_propagation(X, parameters)
predictions = (A2>0.5)
### END CODE HERE ###

return predictions

# Build a model with a n_h-dimensional hidden layer
parameters = nn_model(X, Y, n_h = 4, num_iterations = 10000, print_cost=True)

# Plot the decision boundary
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title("Decision Boundary for hidden layer size " + str(4))

Cost after iteration 0: 0.693048

Cost after iteration 1000: 0.288083

Cost after iteration 2000: 0.254385

Cost after iteration 3000: 0.233864

Cost after iteration 4000: 0.226792

Cost after iteration 5000: 0.222644

Cost after iteration 6000: 0.219731

Cost after iteration 7000: 0.217504

Cost after iteration 8000: 0.219454

Cost after iteration 9000: 0.218607

# Print accuracy
predictions = predict(parameters, X)
print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')

Accuracy 90%

4.6 - Tuning hidden layer size (optional/ungraded exercise)

plt.figure(figsize=(16, 32))
hidden_layer_sizes = [1, 2, 3, 4, 5, 20, 50]
for i, n_h in enumerate(hidden_layer_sizes):
plt.subplot(5, 2, i+1)
plt.title('Hidden Layer of size %d' % n_h)
parameters = nn_model(X, Y, n_h, num_iterations = 5000)
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
predictions = predict(parameters, X)
accuracy = float((np.dot(Y,predictions.T) + np.dot(1-Y,1-predictions.T))/float(Y.size)*100)
print ("Accuracy for {} hidden units: {} %".format(n_h, accuracy))

Accuracy for 1 hidden units: 67.5 %

Accuracy for 2 hidden units: 67.25 %

Accuracy for 3 hidden units: 90.75 %

Accuracy for 4 hidden units: 90.5 %

Accuracy for 5 hidden units: 91.25 %

Accuracy for 20 hidden units: 90.0 %

Accuracy for 50 hidden units: 90.25 %

5) Performance on other datasets

# Datasets
noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure = load_extra_datasets()
datasets = {"noisy_circles": noisy_circles,
"noisy_moons": noisy_moons,
"blobs": blobs,
"gaussian_quantiles": gaussian_quantiles}

### START CODE HERE ### (choose your dataset)
dataset = "noisy_circles"
### END CODE HERE ###

X, Y = datasets[dataset]
X, Y = X.T, Y.reshape(1, Y.shape[0])

# make blobs binary
if dataset == "blobs":
Y = Y%2

# Visualize the data
plt.scatter(X[0, :], X[1, :], c=Y, s=40, cmap=plt.cm.Spectral);

参考Deep Learning Specialization