深度學習第二週
# 學習目標，實現一個二分類具有一個隱藏層的神經網路，使用一個例如tanh的非線性啟用函式
# 計算交叉熵損失函式，實現前向和反向傳播
# 首先我們匯入需要的包
import numpyas np
import operator
from functoolsimport reduce
import matplotlib.pyplotas plt
from testCases_v2import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utilsimport plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets
# matplotlib inline
np.random.seed(1)#如果設定相同的seed值，則每次隨機數結果是一致的
# Dataset首先，我們獲取所需要的資料，變數是Ｘ, Y
X, Y = load_planar_dataset()
print(X.shape, Y.shape)
# Visualize the data, 因為plt scatter函式進行了微小的改版我們也需要修改下
#plt.scatter(X[0, :], X[1, :],c=reduce(operator.add, Y),s=40,cmap=plt.cm.Spectral)
#plt.show()
# 練習How many training examples do you have? in addition,what is the shape of the variables X and Y
def ex1():
### START CODE HERE ### (≈ 3 lines of code)
shape_X = np.shape(X)
shape_Y = np.shape(Y)
m = np.shape(X)[1]# 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))
# 簡單的logistic regression嘗試一下效果
def simple_logistic():
clf = sklearn.linear_model.LogisticRegressionCV()
clf.fit(X.T, Y.T)
#畫出他的決策邊界
plot_decision_boundary(lambda x: clf.predict(x), X, Y)
plt.title('Logistic regression')
plt.show()
# 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)")
# 下面實現一個簡單的神經網路實現二分類，隱藏層設計為4個神經元組成,理論上來說越寬的神經元可以模擬任何函式
# 對於本例子有z1i = w1.dot xi+ b1
# a1i = tanh(z1i)
# z2i = w2.dot a1i+b2
# yi = a2i=sigmoid(z2i)
# yi = 1 if a2i > 0.5 else 0
# 交叉熵損失用於分類通常比MSE要好：j = ∑(yi*log(a2i)+(1-yi)*log(1-a2i))/-m
# 具體步驟：
# 1. Define the neural network structure ( # of input units, # of hidden units, etc).
# 2. Initialize the model's parameters
# 3. Loop:
# - Implement forward propagation
# - Compute loss
# - Implement backward propagation to get the gradients
# - Update parameters (gradient descent)
# 定義神經網路的結構
def layer_size(X,Y):
'''
:paramX: input dataset of shape(input size , number of examples)
:paramY: labels of shape(output size, number if examples)
:return:
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 = np.shape(X)[0]# size of input layer
n_h =4
n_y = np.shape(Y)[0]# size of output layer
### END CODE HERE ###
return (n_x, n_h, n_y)
# 初始化引數，首先可以使我們初始化的引數足夠小
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
# 進行前向傳播計算A1,A2,Z1,Z2......
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
# 計算我們的損失函式
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 = -np.sum(logprobs) / m
### 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
# 進行反向傳播，計算dw,db
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 = np.dot(dZ2, A1.T) / m
db2 = np.sum(dZ2,axis=1,keepdims=True) / m
dZ1 = np.multiply(np.dot(W2.T, dZ2), (1 - np.power(A1,2)))
dW1 = np.dot(dZ1, X.T) / m
db1 = np.sum(dZ1,axis=1,keepdims=True) *1. / m
### END CODE HERE ###
grads = {"dW1": dW1,
"db1": db1,
"dW2": dW2,
"db2": db2}
return grads
# 此處我們的alha學習速率需要適中，過小則太慢，過大則無法達到區域性最優點
#更新我們的引數w,b
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
# 這時候需要建立一個模型，方便呼叫
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 iin 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_costand i %1000 ==0:
print("Cost after iteration %i: %f" % (i, cost))
return parameters
X_assess, Y_assess = layer_sizes_test_case()
(n_x, n_h, n_y) = layer_size(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))
#simple_logistic()
# 小結,關於隱藏層的神經元選擇較為重要，學習速率，以及啟用函式的選擇也是比較重要的，通常我們只在二分類上使用sigmoid函式，否則一般會
# 使用relu, leaky relu, tanh函式作為我們的啟用函式．