参考链接：https://blog.csdn.net/u013733326/article/details/79767169
搭建多层神经网络步骤：
1、初始化
2、前向传播
(1)线性部分
(2)激活部分
3、计算代价（判断有没有学习）
4、反向传播
（1）线性部分
（2）激活部分
5、更新参数
6、预测
# coding=utf-8
# This is a sample Python script.
# Press ⌃R to execute it or replace it with your code.
# Press Double ⇧ to search everywhere for classes, files, tool windows, actions, and settings.
import numpy as np
import h5py
import matplotlib.pyplot as plt
import testCases
from dnn_utils import sigmoid, sigmoid_backward, relu, relu_backward
import lr_utils
def init(layers_dims):
parameters = {}
L = len(layers_dims)
for l in range(1, L):
# print("l:", l)
parameters["W" + str(l)] = np.random.randn(layers_dims[l], layers_dims[l - 1]) / np.sqrt(layers_dims[l - 1])
parameters["b" + str(l)] = np.zeros((layers_dims[l], 1))
assert parameters["W" + str(l)].shape == (layers_dims[l], layers_dims[l - 1])
assert parameters["b" + str(l)].shape == (layers_dims[l], 1)
return parameters
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
def liner_activation_forward(A_pre, W, b, activation):
if activation == "sigmoid":
Z, linear_cache = linear_forward(A_pre, W, b)
A, activation_cache = sigmoid(Z)
elif activation == "relu":
Z, linear_cache = linear_forward(A_pre, W, b)
A, activation_cache = relu(Z)
assert A.shape == (W.shape[0], A_pre.shape[1])
cache = (linear_cache, activation_cache)
return A, cache
def l_model_forward(X, parameters):
caches = []
A = X
L = len(parameters) // 2
for l in range(1, L):
A_prev = A
A, cache = liner_activation_forward(A_prev, parameters["W" + str(l)], parameters["b" + str(l)],
activation="relu")
caches.append(cache)
AL, cache = liner_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
def cal_cost(AL, Y):
m = Y.shape[1]
cost = -np.sum(np.multiply(Y, np.log(AL)) + np.multiply(1 - Y, np.log(1 - AL))) / m
cost = np.squeeze(cost)
assert cost.shape == ()
return cost
# Press the green button in the gutter to run the script.
def liner_backward(dZ, cache):
A_prev, W, b = cache
m = A_prev.shape[1]
dW = np.dot(dZ, A_prev.T) / m
dB = np.sum(dZ, axis=1, keepdims=True) / m
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
def liner_activation_backward(dA, cache, activation):
liner_cache, activation_cache = cache
if activation == "relu":
dZ = relu_backward(dA, activation_cache)
dA_prev, dW, db = liner_backward(dZ, liner_cache)
elif activation == "sigmoid":
dZ = sigmoid_backward(dA, activation_cache)
dA_prev, dW, db = liner_backward(dZ, liner_cache)
return dA_prev, dW, db
def L_model_backward(AL, Y, caches):
grads = {}
L = len(caches)
m = AL.shape[1]
Y = Y.reshape(AL.shape)
dAL = -(np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
current_cache = caches[L - 1]
grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = liner_activation_backward(dAL, current_cache,
"sigmoid")
for l in reversed((range(L - 1))):
current_cache = caches[l]
dA_prev_tmp, dW_tmp, db_tmp = liner_activation_backward(grads["dA" + str(l + 2)], current_cache, "relu")
grads["dA" + str(l + 1)] = dA_prev_tmp
grads["dW" + str(l + 1)] = dW_tmp
grads["db" + str(l + 1)] = db_tmp
return grads
def update(parameters, grads, learning_rate):
L = len(parameters) // 2
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
def predict(X, y, parameters):
m = X.shape[1]
n = len(parameters) // 2 # 神经网络的层数
p = np.zeros((1, m))
# 根据参数前向传播
probas, caches = l_model_forward(X, parameters)
for i in range(0, probas.shape[1]):
if probas[0, i] > 0.5:
p[0, i] = 1
else:
p[0, i] = 0
print("准确度为: " + str(float(np.sum((p == y)) / m)))
return p
def solve(X, Y, layer_dims, learning_rate, num_iterations):
costs = []
parameters = init(layer_dims)
for i in range(0, num_iterations):
AL, caches = l_model_forward(X, parameters)
cost = cal_cost(AL, Y)
grads = L_model_backward(AL, Y, caches)
parameters = update(parameters, grads, learning_rate)
if i % 100 == 0:
costs.append(cost)
# 是否打印成本值
print("第", i, "次迭代，成本值为：", np.squeeze(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
if __name__ == '__main__':
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = lr_utils.load_dataset()
train_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
test_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
train_x = train_x_flatten / 255
train_y = train_set_y
test_x = test_x_flatten / 255
test_y = test_set_y
# layers_dims = [12288, 20, 7, 5, 1] # 5-layer model
layers_dims = [12288, 20, 7, 5, 1]
parameters = solve(train_x, train_y, layers_dims, 0.0075, num_iterations=2500)
predictions_train = predict(train_x, train_y, parameters) # 训练集
predictions_test = predict(test_x, test_y, parameters) # 测试集
# See PyCharm help at https://www.jetbrains.com/help/pycharm/
import numpy as np
def sigmoid(Z):
"""
Implements the sigmoid activation in numpy
Arguments:
Z -- numpy array of any shape
Returns:
A -- output of sigmoid(z), same shape as Z
cache -- returns Z as well, useful during backpropagation
"""
A = 1/(1+np.exp(-Z))
cache = Z
return A, cache
def sigmoid_backward(dA, cache):
"""
Implement the backward propagation for a single SIGMOID unit.
Arguments:
dA -- post-activation gradient, of any shape
cache -- 'Z' where we store for computing backward propagation efficiently
Returns:
dZ -- Gradient of the cost with respect to Z
"""
Z = cache
s = 1/(1+np.exp(-Z))
dZ = dA * s * (1-s)
assert (dZ.shape == Z.shape)
return dZ
def relu(Z):
"""
Implement the RELU function.
Arguments:
Z -- Output of the linear layer, of any shape
Returns:
A -- Post-activation parameter, of the same shape as Z
cache -- a python dictionary containing "A" ; stored for computing the backward pass efficiently
"""
A = np.maximum(0,Z)
assert(A.shape == Z.shape)
cache = Z
return A, cache
def relu_backward(dA, cache):
"""
Implement the backward propagation for a single RELU unit.
Arguments:
dA -- post-activation gradient, of any shape
cache -- 'Z' where we store for computing backward propagation efficiently
Returns:
dZ -- Gradient of the cost with respect to Z
"""
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] = 0
assert (dZ.shape == Z.shape)
return dZ