运用Python实现机器学习算法：神经网络

def create_dataset():
    np.random.seed(1)
    m = 400 # 数据量
    N = int(m/2) # 每个标签的实例数
    D = 2 # 数据维度
    X = np.zeros((m,D)) # 数据矩阵
    Y = np.zeros((m,1), dtype='uint8') # 标签维度
    a = 4 
    
    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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.

def layer_sizes(X, Y):
    n_x = X.shape[0] # 输入层大小
    n_h = 4 # 隐藏层大小
    n_y = Y.shape[0] # 输出层大小
    return (n_x, n_h, n_y)
1.
2.
3.
4.
5.

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))
    W2 = np.random.randn(n_y, n_h)*0.01
    b2 = np.zeros((n_y, 1)) 
   
    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
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.

def forward_propagation(X, parameters):
    # 获取各参数初始值
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']    
    # 执行前向计算
    Z1 = np.dot(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2, A1) + b2
    A2 = sigmoid(Z2)    
    assert(A2.shape == (1, X.shape[1]))


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


    return A2, cache
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.

def compute_cost(A2, Y, parameters):
    # 训练样本量
    m = Y.shape[1] 
    # 计算交叉熵损失
    logprobs = np.multiply(np.log(A2),Y) + np.multiply(np.log(1-A2), 1-Y)
    cost = -1/m * np.sum(logprobs)
    # 维度压缩
    cost = np.squeeze(cost)     


    assert(isinstance(cost, float))    
    return cost
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

def backward_propagation(parameters, cache, X, Y):
    m = X.shape[1]    
    # 获取W1和W2
    W1 = parameters['W1']
    W2 = parameters['W2']    
    # 获取A1和A2
    A1 = cache['A1']
    A2 = cache['A2']    
    # 执行反向传播
    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)


    grads = {"dW1": dW1,
             "db1": db1,                      
             "dW2": dW2,             
             "db2": db2}   
    return grads
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.

def update_parameters(parameters, grads, learning_rate=1.2):
    # 获取参数
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']    
    # 获取梯度
    dW1 = grads['dW1']
    db1 = grads['db1']
    dW2 = grads['dW2']
    db2 = grads['db2']    
    # 参数更新
    W1 -= dW1 * learning_rate
    b1 -= db1 * learning_rate
    W2 -= dW2 * learning_rate
    b2 -= db2 * learning_rate


    parameters = {"W1": W1, 
                  "b1": b1,            
                  "W2": W2,   
                  "b2": b2}    
    return parameters
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.

def nn_model(X, Y, n_h, num_iterations=10000, print_cost=False):
    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]    
    # 初始化模型参数
    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']    
    # 梯度下降和参数更新循环
    for i in range(0, num_iterations):        
    # 前向传播计算
        A2, cache = forward_propagation(X, parameters)        
        # 计算当前损失
        cost = compute_cost(A2, Y, parameters)        
        # 反向传播
        grads = backward_propagation(parameters, cache, X, Y)        
        # 参数更新
        parameters = update_parameters(parameters, grads, learning_rate=1.2)        
        # 打印损失
        if print_cost and i % 1000 == 0:            
            print ("Cost after iteration %i: %f" %(i, cost))    
            
    return parameters
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.

def predict(parameters, X): 
    A2, cache = forward_propagation(X, parameters)
    predictions = (A2>0.5)
    return predictions
1.
2.
3.
4.

parameters = nn_model(X, Y, n_h = 4, 
                      num_iterations=10000, 
                      print_cost=True)
1.
2.
3.

# 预测准确率
predictions = predict(parameters, X)
print ('Accuracy: %d' % float((np.dot(Y,predictions.T) + 
      np.dot(1-Y,1-predictions.T))/float(Y.size)*100) + '%')
1.
2.
3.
4.