【深度学习_1.3】搭建浅层神经网络模型

目的：搭建一层隐藏层的浅层神经网络

【准备】

1.导入相关包

import xxxx

2.加载数据集

X, Y = load_planar_dataset()

3.查看数据

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

[image]

4.查看数据集dim

shape_X = X.shape
shape_Y = Y.shape
m = X.shape[1]  # training set size

【构建算法模型】

1.定义基本模型

def layer_sizes(X, Y):

    n_x = X.shape[0] # 定义输入层size
    n_h = 4 #定义隐藏层size
    n_y = Y.shape[0] # 定义输出层size

2.初始化参数

def initialize_parameters(n_x, n_h, n_y):

    W1 = np.random.randn(n_h, n_x)*0.01
    b1 = np.zeros((n_h, 1))*0.01
    W2 = np.random.randn(n_y, n_h)*0.01
    b2 = np.zeros((n_y, 1))

3.正向传播

def forward_propagation(X, parameters):

    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    Z1 = np.dot(W1,X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2,A1) + b2
    A2 = 1/(1+np.exp(-Z2))

4.计算损失函数

def compute_cost(A2, Y, parameters):

    logprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1-A2),1-Y)
    cost = - np.sum(logprobs)

5.反向传播

def backward_propagation(parameters, cache, X, Y):

    W1 = parameters["W1"]
    W2 = parameters["W2"]

    A1 = cache['A1']
    A2 = cache['A2']

    dZ2 = A2 - Y
    dW2 = np.dot(dZ2,A1.T)/m
    db2 = (1/m)*np.sum(dZ2,axis=1,keepdims=True)
    dZ1 = np.multiply(np.dot(W2.T,dZ2),(1 - np.power(A1, 2)))
    dW1 = np.dot(dZ1,X.T)/m
    db1 = (1/m)*np.sum(dZ1,axis=1,keepdims=True)

6.优化参数

def update_parameters(parameters, grads, learning_rate = 1.2):

    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    dW1 = grads["dW1"]
    db1 = grads["db1"]
    dW2 = grads["dW2"]
    db2 = grads["db2"]

    W1 = W1 - learning_rate*dW1
    b1 = b1 - learning_rate*db1
    W2 = W2 - learning_rate*dW2

    b2 = b2 - learning_rate*db2

7.整合各个方法

def nn_model(X, Y, n_h, num_iterations = 10000, print_cost=False):

    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = np.random.randn(n_h, n_x)*0.01
    b1 = np.zeros((n_h, 1))*0.01
    W2 = np.random.randn(n_y, n_h)*0.01
    b2 = np.zeros((n_y, 1))

    for i in range(0, num_iterations):
       
        # 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, learning_rate = 1.2)

8.执行预测

def predict(parameters, X):

    A2, cache = forward_propagation(X, parameters)
    predictions = (A2 > 0.5)

【测试】

# 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))