吴恩达老师深度学习跟随作业（二）---------带有一个隐藏层的平面数据分类（IMUDGES）

参考博客：https://blog.youkuaiyun.com/u013733326/article/details/79702148

---

在本次学习过程中，我们的目的是：

1. 构建具有单隐藏层的2类分类神经网络。
2. 使用具有非线性激活功能激活函数，例如tanh。
3. 计算交叉熵损失（损失函数）。
4. 实现向前和向后传播。

---

提前导入软件包

import numpy as np
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

在这里，testCases.py和planar_utils.py需要自己编写，代码如下：

#testCases.py

import numpy as np

def layer_sizes_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(5, 3)
    Y_assess = np.random.randn(2, 3)
    return X_assess, Y_assess

def initialize_parameters_test_case():
    n_x, n_h, n_y = 2, 4, 1
    return n_x, n_h, n_y

def forward_propagation_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)

    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    return X_assess, parameters

def compute_cost_test_case():
    np.random.seed(1)
    Y_assess = np.random.randn(1, 3)
    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    a2 = (np.array([[ 0.5002307 ,  0.49985831,  0.50023963]]))

    return a2, Y_assess, parameters

def backward_propagation_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    Y_assess = np.random.randn(1, 3)
    parameters = {'W1': np.array([[-0.00416758, -0.00056267],
        [-0.02136196,  0.01640271],
        [-0.01793436, -0.00841747],
        [ 0.00502881, -0.01245288]]),
     'W2': np.array([[-0.01057952, -0.00909008,  0.00551454,  0.02292208]]),
     'b1': np.array([[ 0.],
        [ 0.],
        [ 0.],
        [ 0.]]),
     'b2': np.array([[ 0.]])}

    cache = {'A1': np.array([[-0.00616578,  0.0020626 ,  0.00349619],
         [-0.05225116,  0.02725659, -0.02646251],
         [-0.02009721,  0.0036869 ,  0.02883756],
         [ 0.02152675, -0.01385234,  0.02599885]]),
  'A2': np.array([[ 0.5002307 ,  0.49985831,  0.50023963]]),
  'Z1': np.array([[-0.00616586,  0.0020626 ,  0.0034962 ],
         [-0.05229879,  0.02726335, -0.02646869],
         [-0.02009991,  0.00368692,  0.02884556],
         [ 0.02153007, -0.01385322,  0.02600471]]),
  'Z2': np.array([[ 0.00092281, -0.00056678,  0.00095853]])}
    return parameters, cache, X_assess, Y_assess

def update_parameters_test_case():
    parameters = {'W1': np.array([[-0.00615039,  0.0169021 ],
        [-0.02311792,  0.03137121],
        [-0.0169217 , -0.01752545],
        [ 0.00935436, -0.05018221]]),
 'W2': np.array([[-0.0104319 , -0.04019007,  0.01607211,  0.04440255]]),
 'b1': np.array([[ -8.97523455e-07],
        [  8.15562092e-06],
        [  6.04810633e-07],
        [ -2.54560700e-06]]),
 'b2': np.array([[  9.14954378e-05]])}

    grads = {'dW1': np.array([[ 0.00023322, -0.00205423],
        [ 0.00082222, -0.00700776],
        [-0.00031831,  0.0028636 ],
        [-0.00092857,  0.00809933]]),
 'dW2': np.array([[ -1.75740039e-05,   3.70231337e-03,  -1.25683095e-03,
          -2.55715317e-03]]),
 'db1': np.array([[  1.05570087e-07],
        [ -3.81814487e-06],
        [ -1.90155145e-07],
        [  5.46467802e-07]]),
 'db2': np.array([[ -1.08923140e-05]])}
    return parameters, grads

def nn_model_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    Y_assess = np.random.randn(1, 3)
    return X_assess, Y_assess

def predict_test_case():
    np.random.seed(1)
    X_assess = np.random.randn(2, 3)
    parameters = {'W1': np.array([[-0.00615039,  0.0169021 ],
        [-0.02311792,  0.03137121],
        [-0.0169217 , -0.01752545],
        [ 0.00935436, -0.05018221]]),
     'W2': np.array([[-0.0104319 , -0.04019007,  0.01607211,  0.04440255]]),
     'b1': np.array([[ -8.97523455e-07],
        [  8.15562092e-06],
        [  6.04810633e-07],
        [ -2.54560700e-06]]),
     'b2': np.array([[  9.14954378e-05]])}
    return parameters, X_assess

#planar_utils.py

import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model

def plot_decision_boundary(model, X, y):
    # 设置最大值和最小值
    x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
    y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
    h = 0.01
    # 生成一个点之间距离为h的网格
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    # 预测整个网格的函数值
    Z = model(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    # 绘制轮廓图和训练实例
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.ylabel('x2')
    plt.xlabel('x1')
    plt.scatter(X[0, :], X[1, :], c=np.squeeze(y), cmap=plt.cm.Spectral)


def sigmoid(x):
    s = 1/(1+np.exp(-x))
    return s

def load_planar_dataset():
    np.random.seed(1)
    m = 400 # 样本数量
    N = int(m/2) # 每个类别的样本量
    D = 2 # 维数
    X = np.zeros((m,D)) # 数据矩阵，其中每一行都是一个例子
    Y = np.zeros((m,1), dtype='uint8') # 标签向量(0代表红色，1代表蓝色)
    a = 4 # 花的最大长度

    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——Θ
        r = a*np.sin(4*t) + np.random.randn(N)*0.2 # 半径
        X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
        Y[ix] = j

    X = X.T
    Y = Y.T

    return X, Y

def load_extra_datasets():
    N = 200
    noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)
    noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)
    blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)
    gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)
    no_structure = np.random.rand(N, 2), np.random.rand(N, 2)

    return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure

其中一些关键内容都标有注释，你可以直接粘贴

---

接下来，就是正主的部分了，，，

每一个块注释都是对上一部分代码的测试

import numpy as np
import matplotlib.pyplot as plt
from testCases import *
import sklearn
import sklearn.datasets
import sklearn.linear_model
from planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets

np.random.seed(1) #设置一个固定的随机种子，以保证接下来的步骤中我们的结果是一致的。

#加载数据
X, Y = load_planar_dataset()

"""
#查看数据集
plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral)#绘制散点图
plt.show()
"""

#X 一个numpy的矩阵，包含上面图中的数据点数值
#Y 一个numpy向量，对应X的标签

shape_X = X.shape
shape_Y = Y.shape
m = Y.shape[1]  #训练集里的数量
"""
#查看细节
print ("X的维度为: " + str(shape_X))
print ("Y的维度为: " + str(shape_Y))
print ("数据集里面的数据有：" + str(m) + " 个")
"""

#搭建神经网络
#预先定义神经网络的结构 n_x:输入层数量  n_h:隐藏层数量(在这里设置为4)  n_y:输出层数量

def layer_sizes(X, Y):
    """

    :param X: 输入数据集
    :param Y: 标签
    :return:
    n_x:输入层数量
    n_h:隐藏层数量
    n_y:输出层数量
    """
    n_x = X.shape[0]
    n_h = 4
    n_y = Y.shape[0]
    return (n_x, n_h, n_y)

"""
#测试layer_sizes
X_asses, Y_asses = layer_sizes_test_case()
(n_x, n_h, n_y) = layer_sizes(X_asses, Y_asses)
print("输入层的节点数量为: n_x = " + str(n_x))
print("隐藏层的节点数量为: n_h = " + str(n_h))
print("输出层的节点数量为: n_y = " + str(n_y))
"""

#初始化模型的参数
#随机初始化权重矩阵  np.random.randn(a，b)* 0.01来随机初始化一个维度为(a，b)的矩阵
#将偏向量初始化为零  np.zeros((a，b))用零初始化矩阵（a，b）

def initialize_parameters(n_x, n_h, n_y):
    """
    :param n_x:输入层节点的数量
    :param n_h:输入层节点的数量
    :param n_y:输入层节点的数量
    :return:
            parameter：包含参数的字典
            W1:权重矩阵，维度（n_h,n_x）
            b1:偏向量，维度（n_h， 1）
            W2:权重矩阵，维度（n_y ，n_h）
            b2:偏向量，维度（n_y， 1）
    """
    np.random.seed(2)
    W1 = np.random.randn(n_h, n_x) * 0.01
    b1 = np.zeros(shape=(n_h, 1))
    W2 = np.random.randn(n_y, n_h) * 0.01
    b2 = np.zeros(shape=(n_y, 1))

    #使用断言确保数据格式是正确的
    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

"""
#测试initialize_parameters
n_x, n_h, n_y = initialize_parameters_test_case()
parameters = initialize_parameters(n_x, n_h, n_y)
print("W1 = " + str(parameters["W1"]))
print("b1 = " + str(parameters["b1"]))
print("W2 = " + str(parameters["W2"]))
print("b2 = " + str(parameters["b2"]))
"""

##循环

#前向传播
def forward_propagation(X, parameters):
    """

    :param X: 维度为（n_x, m）的输入数据
    :param parameters: 初始化函数（initialize_parameters）的输出
    :return: A2：使用sigmoid（）函数计算的第二次激活后的数值
    :return: cache：包含“Z1”，“A1”，“Z2”和“A2”的数字类型变量
    """
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]
    #前向传播计算A2
    Z1 = np.dot(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2, A1) + b2
    A2 = sigmoid(Z2)
    #使用断言确保数据格式是正确的
    assert (A2.shape == (1, X.shape[1]))
    cache = {
        "Z1":Z1,
        "A1":A1,
        "Z2":Z2,
        "A2":A2
    }

    return A2, cache

"""
#测试forward_propagation
X_assess, parameters = forward_propagation_test_case()
A2, cache = forward_propagation(X_assess, parameters)
print(np.mean(cache["Z1"]), np.mean(cache["A1"]), np.mean(cache["Z2"]), np.mean(cache["A2"]))
"""

#计算损失
def compute_cost(A2, Y, parameters):
    """
    计算交叉熵成本
    :param A2:使用sigmoid函数计算的第二次激活后的数值
    :param Y:"Ture"标签向量，维度为（1，数量）
    :param parameters:字典
    :return:成本
    """
    m = Y.shape[1]
    W1 = parameters["W1"]
    W2 = parameters["W2"]

    #计算成本
    logprobs = np.multiply(np.log(A2), Y) + np.multiply((1 - Y), np.log(1 - A2))
    cost = -np.sum(logprobs) / m
    cost = float(np.squeeze(cost))

    return cost

"""
#测试compute_cost
A2 , Y_assess , parameters = compute_cost_test_case()
print("cost = " + str(compute_cost(A2,Y_assess,parameters)))
"""

#后向传播
def backward_propagation(parameter, cache, X, Y):
    """

    :param parameter: 参数字典
    :param cache: 包含“Z1”，“A1”，“Z2”和“A2”的字典类型的变量
    :param X: 输入数据，维度为（2，数量）
    :param Y: “True”标签，维度为（1，数量）
    :return: 包含W和b的导数的字典类型的变量
    """
    m = X.shape[1]

    W1 = parameter["W1"]
    W2 = parameter["W2"]

    A1 = cache["A1"]
    A2 = cache["A2"]

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

"""
#测试backward_propagation
parameters, cache, X_assess, Y_assess = backward_propagation_test_case()
grads = backward_propagation(parameters, cache, X_assess, Y_assess)
print ("dW1 = "+ str(grads["dW1"]))
print ("db1 = "+ str(grads["db1"]))
print ("dW2 = "+ str(grads["dW2"]))
print ("db2 = "+ str(grads["db2"]))
"""

#更新参数
def update_parameters(parameters, grads, learning_rate=1.2):
    """

    :param parameters: 包含参数的字典类型的变量
    :param grads: 包含导数值的字典类型的变量
    :param learning_rate:学习速率
    :return: parameters - 包含更新参数的数字类型的变量
    """
    W1, W2 = parameters["W1"], parameters["W2"]
    b1, b2 = parameters["b1"], parameters["b2"]

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

    W1 = W1 - learning_rate * dW1
    b1 = b1 - learning_rate * db1
    W2 = W2 - learning_rate * dW2
    b2 = b2 - learning_rate * db2

    parameters = {
        "W1":W1,
        "b1":b1,
        "W2":W2,
        "b2":b2
    }
    return parameters

"""
#测试update_parameters
parameters, grads = update_parameters_test_case()
parameters = update_parameters(parameters, grads)

print("W1 = " + str(parameters["W1"]))
print("b1 = " + str(parameters["b1"]))
print("W2 = " + str(parameters["W2"]))
print("b2 = " + str(parameters["b2"]))
"""

#整合
def nn_model(X, Y, n_h, num_iterations, print_cost=False):
    """

    :param X:数据集,维度为（2，示例数）
    :param Y:标签，维度为（1，示例数）
    :param n_h:隐藏层的数量
    :param num_iterations:梯度下降循环中的迭代次数
    :param print_cost:如果为True，则每1000次迭代打印一次成本数值
    :return:parameters - 模型学习的参数，它们可以用来进行预测
    """

    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]

    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    for i in range(num_iterations):
        A2, cache = forward_propagation(X, parameters)
        cost = compute_cost(A2, Y, parameters)
        grads = backward_propagation(parameters, cache, X, Y)
        parameters = update_parameters(parameters, grads, learning_rate=0.5)

        if print_cost:
            if i%1000 == 0:
                print("第 ",i," 次循环，成本为："+str(cost))

    return parameters

"""
#测试nn_mode()
X_assess, Y_assess = nn_model_test_case()
parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10000, print_cost=False)
print("W1 = " + str(parameters["W1"]))
print("b1 = " + str(parameters["b1"]))
print("W2 = " + str(parameters["W2"]))
print("b2 = " + str(parameters["b2"]))
"""

#预测
def predict(parameters, X):
    """

    :param parameters: 包含参数的字典类型的变量
    :param X: 输入数据（n_x，m）
    :return: predictions - 我们模型预测的向量（红色：0 /蓝色：1）
    """
    A2 ,cache = forward_propagation(X, parameters)
    predictions = np.round(A2)
    return predictions

"""
#测试predict
parameters, X_assess = predict_test_case()
predictions = predict(parameters, X_assess)
print("预测的平均值 = " + str(np.mean(predictions)))
"""

#正式运行
parameters = nn_model(X, Y, n_h = 4, num_iterations=10000, print_cost=True)
#绘制边界
plot_decision_boundary(lambda x:predict(parameters, x.T), X, Y)
predictions = predict(parameters, X)
print('准确率: %d' % float((np.dot(Y, predictions.T) + np.dot(1 - Y, 1 - predictions.T)) / float(Y.size) * 100) + '%')
plt.show()