一、 激活函数
def sigmoid(Z):
A = 1/(1+np.exp(-Z))
cache = Z
return A, cache
def relu(Z):
A = np.maximum(0,Z)
cache = Z
return A, cache
二、 激活函数backward
"""
Implement the backward propagation for a single RELU unit.
"""
def relu_backward(dA, cache):
Z = cache
dZ = np.array(dA, copy=True) # just converting dz to a correct object.
# When z <= 0, you should set dz to 0 as well.
dZ[Z <= 0] = 0return dZ
"""
Implement the backward propagation for a single SIGMOID unit.
"""
def sigmoid_backward(dA, cache):
Z = cache
s = 1/(1+np.exp(-Z))
dZ = dA * s * (1-s)
return dZ
三、 网络层前馈和激活函数前馈
"""
Implement the linear part of a layer's forward propagation.
"""
def linear_forward(A, W, b):
Z = np.dot(W, A) + b
assert(Z.shape == (W.shape[0], A.shape[1]))
cache = (A, W, b)
return Z, cache
"""
Implement the forward propagation for the LINEAR->ACTIVATION layer
"""
def linear_activation_forward(A_prev, W, b, activation):
if activation == "sigmoid":
# Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
# Inputs: "A_prev, W, b". Outputs: "A, activation_cache".
Z, linear_cache = linear_forward(A_prev, W, b)
A, activation_cache = relu(Z)
assert (A.shape == (W.shape[0], A_prev.shape[1]))
cache = (linear_cache, activation_cache)
return A, cache
四、 构建L层前馈
"""
Implement forward propagation for the [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID computation
"""
def L_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2 # number of layers in the neural network
# Implement [LINEAR -> RELU]*(L-1). Add "cache" to the "caches" list.
for l in range(1, L):
A_prev = A
A, cache = linear_activation_forward(A_prev, parameters['W' + str(l)],parameters['b' + str(l)], activation = "relu")
caches.append(cache)
# Implement LINEAR -> SIGMOID. Add "cache" to the "caches" list.
AL, cache = linear_activation_forward(A, parameters['W' + str(L)], \
parameters['b' + str(L)], activation = "sigmoid")
caches.append(cache)
assert(AL.shape == (1,X.shape[1]))
return AL, caches
五、 计算cost
def compute_cost(AL, Y):
"""
Implement the cost function defined by equation (7).
Arguments:
AL -- probability vector corresponding to your label predictions, shape (1, number of examples)
Y -- true "label" vector (for example: containing 0 if non-cat, 1 if cat), shape (1, number of examples)
Returns:
cost -- cross-entropy cost
"""
m = Y.shape[1]
# Compute loss from aL and y.
### START CODE HERE ### (≈ 1 lines of code)
cost = np.average(np.power(AL-Y,2))
### END CODE HERE ###
return cost
六、 网络层反馈及激活函数反馈
"""
Implement the linear portion of backward propagation for a single layer (layer l)
"""
def linear_backward(dZ, cache):
A_prev, W, b = cache # b没用上
m = A_prev.shape[1]
dW = (1 / m) * np.dot(dZ, A_prev.T)
db = (1 / m) * np.sum(dZ, axis=1, keepdims=True)
dA_prev = np.dot(W.T, dZ)
assert (dA_prev.shape == A_prev.shape)
assert (dW.shape == W.shape)
assert (db.shape == b.shape)
return dA_prev, dW, db
"""
Implement the backward propagation for the LINEAR->ACTIVATION layer.
"""
def linear_activation_backward(dA, cache, activation):
linear_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
elif activation == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = linear_backward(dZ, linear_cache)
return dA_prev, dW, db
七、 L层网络反馈
"""
Implement the backward propagation for the [LINEAR->RELU] * (L-1) -> LINEAR -> SIGMOID group
"""
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches) # the number of layers
# m = AL.shape[1]
Y = Y.reshape(AL.shape) # after this line, Y is the same shape as AL
# Initializing the backpropagation
dAL = AL - Y # derivative of cost with respect to AL
# Lth layer (SIGMOID -> LINEAR) gradients. Inputs: "AL, Y, caches". Outputs: "grads["dAL"], grads["dWL"], grads["dbL"]
current_cache = caches[L-1] #((A W b), (Z))
grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = \
linear_activation_backward(dAL, current_cache, activation = "sigmoid")
for l in reversed(range(L - 1)):
# lth layer: (RELU -> LINEAR) gradients.
# Inputs: "grads["dA" + str(l + 2)], caches". Outputs: "grads["dA" + str(l + 1)] , grads["dW" + str(l + 1)] , grads["db" + str(l + 1)]
current_cache = caches[l]
dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(l+2)], current_cache, activation = "relu")
grads["dA" + str(l + 1)] = dA_prev_temp
grads["dW" + str(l + 1)] = dW_temp
grads["db" + str(l + 1)] = db_temp
return grads
八、 梯度下降
"""
Update parameters using gradient descent
"""
def update_parameters(parameters, grads, learning_rate):
L = len(parameters) // 2 # number of layers in the neural network
# Update rule for each parameter. Use a for loop.
for l in range(L):
parameters["W" + str(l+1)] = parameters["W" + str(l+1)] - learning_rate * grads["dW" + str(l + 1)]
parameters["b" + str(l+1)] = parameters["b" + str(l+1)] - learning_rate * grads["db" + str(l + 1)]
return parameters
九、 整合成一个模型
"""
Implements a L-layer neural network: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
"""
def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):#lr was 0.009
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)
return parameters
