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2023-11-30：Deep-Neural-Network-Application

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本文字数： 12k 阅读时长 ≈ 22 分钟

1.任务

创建并且部署一个深度神经网络来进行监督学习

2.数据预处理

2.1导入依赖包

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import time
import numpy as np
import h5py
import matplotlib.pyplot as plt
import scipy
from PIL import Image
from scipy import ndimage
from dnn_app_utils_v2 import *
import datetime
%matplotlib inline
plt.rcParams['figure.figsize'] = (5.0, 4.0) # set default size of plots
plt.rcParams['image.interpolation'] = 'nearest'
plt.rcParams['image.cmap'] = 'gray'

%load_ext autoreload
%autoreload 2

np.random.seed(1)

2.2导入数据集

这里使用的是之前案例中的“Cat vs non-Cat”数据集"data.h5"

  • 数据集介绍：
  1. 标记为猫(1)或非猫(0)的m_train图像的训练集
  2. m_test图像标记为猫和非猫的测试集
  3. 每个图像的形状是(num_px, num_px, 3)，其中3是3通道(RGB)。
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train_x_orig, train_y, test_x_orig, test_y, classes = load_data()
  • 数据形状查看：
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m_train = train_x_orig.shape[0]
num_px = train_x_orig.shape[1]
m_test = test_x_orig.shape[0]

print ("Number of training examples: " + str(m_train))
print ("Number of testing examples: " + str(m_test))
print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
print ("train_x_orig shape: " + str(train_x_orig.shape))
print ("train_y shape: " + str(train_y.shape))
print ("test_x_orig shape: " + str(test_x_orig.shape))
print ("test_y shape: " + str(test_y.shape))

输出：

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Number of training examples: 209
Number of testing examples: 50
Each image is of size: (64, 64, 3)
train_x_orig shape: (209, 64, 64, 3)
train_y shape: (1, 209)
test_x_orig shape: (50, 64, 64, 3)
test_y shape: (1, 50)
  • 在把它们输入网络之前应该先归一化并reshape！
图片的向量转化 
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train_x_flatten = train_x_orig.reshape(train_x_orig.shape[0],-1).T
test_x_faltten = test_x_orig.reshape(test_x_orig.shape[0],-1).T

train_x = train_x_flatten/255
test_x = test_x_faltten/255

print ("train_x's shape: " + str(train_x.shape))
print ("test_x's shape: " + str(test_x.shape))
print ("train_x_orig: " + str(train_x_orig.shape))
print ("test_x_orig: " + str(test_x_orig.shape))

输出：

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train_x's shape: (12288, 209) #209*64*64
test_x's shape: (12288, 50)  #50*64*64
train_x_orig: (209, 64, 64, 3)
test_x_orig: (50, 64, 64, 3)

3.架构模型

架构两种模型:

  • A 2-layer neural network
  • An L-layer deep neural network

3.1 2-layer neural network

image-20231130102115721

这个模型可以总结为：

INPUT -> LINEAR -> RELU -> LINEAR -> SIGMOID -> OUTPUT

具体细节介绍：

image-20231130102249622

3.2 L-layer deep neural network

image-20231130102323498

这个模型可以归纳为：

**[LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID**

具体细节介绍：

image-20231130102504229

4. Two-layer neural network实现

4.1定义基本功能

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#初始化参数
def initialize_parameters(n_x,n_h,n_y):
    np.random.seed(1)
    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))
    #验证矩阵维度是否正确
    assert((n_h, n_x) == W1.shape)
    assert((n_h, 1) == b1.shape)
    assert((n_y, n_h) == W2.shape)
    assert((n_y, 1) == b2.shape)
    #整合参数到parameters中输出
    parameters = {
        "W1": W1,
        "b1": b1,
        "W2": W2,
        "b2": b2
    }
    
    return parameters
#前向传播
def linear_activation_forward(A_prev, W, b, activation):
   # 执行线性变换（矩阵乘法 + 偏置项）
   if activation == "sigmoid":
       # 计算 Z 和线性缓存
       Z, linear_cache = linear_forward(A_prev, W, b)
       # 应用 Sigmoid 激活函数并计算激活缓存
       A, activation_cache = sigmoid(Z)
   elif activation == "relu":
       # 计算 Z 和线性缓存
       Z, linear_cache = linear_forward(A_prev, W, b)
       # 应用 ReLU 激活函数并计算激活缓存
       A, activation_cache = relu(Z)

   # 检查输出形状是否正确
   assert(A.shape == (W.shape[0], A_prev.shape[1]))
   
   # 将线性缓存和激活缓存组合在一起
   cache = (linear_cache, activation_cache)
   
   # 返回输出和缓存
   return A, cache

#计算损失值
def compute_cost(AL,Y):
    m = Y.shape[1]
    
    cost = -(np.dot(np.log(AL), Y.T) + np.dot(np.log(1 - AL), (1 - Y).T)) / (1.0 * m)
    cost = np.squeeze(cost)
    
    assert(cost.shape==())
    
    return cost
 
 #反向传播
def linear_activation_backward(dA, cache, activation):
   # 从缓存中获取线性缓存和激活缓存
   linear_cache, activation_cache = cache

   # 根据激活函数选择相应的反向传播函数
   if activation == "relu":
       # 计算ReLU激活函数的梯度
       dZ = relu_backward(dA, activation_cache)
       # 计算线性层的梯度
       dA_prev, dW, db = linear_backward(dZ, linear_cache)
   elif activation == "sigmoid":
       # 计算Sigmoid激活函数的梯度
       dZ = sigmoid_backward(dA, activation_cache)
       # 计算线性层的梯度
       dA_prev, dW, db = linear_backward(dZ, linear_cache)

   # 返回各参数的梯度
   return dA_prev, dW, db
#参数更新
def update_parameters(parameters, grads, learning_rate):
   # 计算层数 L（不包括输入层）
   L = len(parameters) // 2

   # 遍历每一层
   for i in range(1, L + 1):
       # 更新权重矩阵 W
       parameters["W" + str(i)] -= learning_rate * grads["dW" + str(i)]
       # 更新偏置项 b
       parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]

   # 返回更新后的参数
   return parameters

4.2定义模型参数

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n_x = 12288     # num_px * num_px * 3
n_h = 7
n_y = 1
layers_dims = (n_x, n_h, n_y)

4.3Two-layer neural network定义

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def two_layer_model(X,Y,layers_dims,learning_rate = 0.0075,num_iterations=3000,print_cost=False):
    """实现一个两层神经网络：LINEAR->RELU->LINEAR->SIGMOID.
    参数：
    X -- 输入数据，形状为 (n_x, 样本数量)
    Y -- 真实标签向量（猫为 0，非猫为 1），形状为 (1, 样本数量)
    layers_dims -- 层的维度 (n_x, n_h, n_y)
    num_iterations -- 优化循环的迭代次数
    learning_rate -- 梯度下降的 learning rate
    print_cost -- 如果设为 True，将每 100 次迭代打印一次损失函数值
    返回：
    parameters -- 包含 W1, W2, b1, b2 的字典"""
    np.random.seed(1)
    grads = {}
    costs = []
    m = X.shape[1]
    (n_x,n_h,n_y) = layers_dims
    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(0,num_iterations):
        #前向传播
        A1,cache1 = linear_activation_forward(X,parameters["W1"],parameters["b1"],activation="relu")
        A2,cache2 = linear_activation_forward(A1,parameters["W2"],parameters["b2"],activation="sigmoid")
        
        #计算损失
        cost = compute_cost(A2,Y)
        
        #初始化反向传播
        dA2 = - (np.divide(Y, A2) - np.divide(1 - Y, 1 - A2))
        
        #反向传播：输入“dA2, cache2, cache1”,输出“dA1, dW2, db2; also dA0 (not used), dW1, db1”
        dA1,dW2,db2 = linear_activation_backward(dA2,cache2,activation="sigmoid")
        dA0,dW1,db1 = linear_activation_backward(dA1,cache1,activation="relu")
        
        # 设置 grads['dWl'] 为 dW1, grads['db1'] 为 db1, grads['dW2'] 为 dW2, grads['db2'] 为 db2
        grads['dW1'] = dW1
        grads['db1'] = db1
        grads['dW2'] = dW2
        grads['db2'] = db2
        
        #更新参数
        parameters = update_parameters(parameters,grads,learning_rate)
        
        #从新的参数中获取 W1, b1, W2, b2
        W1 = parameters["W1"]
        b1 = parameters["b1"]
        W2 = parameters["W2"]
        b2 = parameters["b2"]
        
        #每训练100个样本输出一次损失值
        if print_cost and i%100 == 0:
            print("Cost after iteration {}: {}".format(i, np.squeeze(cost)))
        if i % 100 == 0:
            costs.append(cost)
    if not(print_cost):
        print("The final cost = %f" %(cost))
    # 画出损失函数曲线
    plt.plot(np.squeeze(costs))
    plt.ylabel('cost')
    plt.xlabel('iterations (per hundreds)')
    plt.title("Learning rate =" + str(learning_rate))
    plt.show()
    
    return parameters

4.4运行该网络进行训练

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parameters = two_layer_model(train_x, train_y, layers_dims = (n_x, n_h, n_y), num_iterations = 2500, print_cost=True)
image-20231130110334416
  • 接着通过改变不同的学习率来寻找一个最合适的学习率来进行训练
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print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0005, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0010, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0035, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0075, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0150, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.0750, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())
two_layer_model(train_x, train_y, layers_dims=(n_x, n_h, n_y), learning_rate=0.1500, num_iterations=2500, print_cost=False)
print(datetime.datetime.now())

image-20231130113327369

4.5定义预测函数

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def predict(X, y, parameters):
    m = X.shape[1]
    n = len(parameters) // 2
    p = np.zeros((1, m))
    
    probas, caches = L_model_forward(X, parameters)
    
    for i in range(probas.shape[1]):
        if probas[0,i] > 0.5:
            p[0, i] = 1
        else:
            p[0, i] = 0
            
    print("Accuracy: " + str(np.sum(p == y) / (1.0 * m)))
    
    return p

4.6执行预测

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predictions_train = predict(train_x, train_y, parameters)
predictions_test = predict(test_x, test_y, parameters)

结果：

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1.0
0.72

​ 我们可以注意到，在更少的迭代(比如1500次)上运行模型可以在测试集上获得更好的准确性。这被称为“提前停止”。提前停止是防止过拟合的一种方法。

​ 该2层神经网络比逻辑回归实现(70%)有更好的性能(72%)。接着我们看看用\(L\)层模型是否可以做得更好。

5. L-layer Neural Network实现

5.1定义基本功能

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def initialize_parameters_deep(layer_dims):
    np.random.seed(1)  # 设置随机种子，确保每次运行结果相同
    parameters = {}
    L = len(layer_dims)  # 网络层数

    for i in range(1, L):
        # 注意，这里的标准差是 np.sqrt(layer_dims[i - 1])，而不是固定的0.01
        parameters['W' + str(i)] = np.random.randn(layer_dims[i], layer_dims[i - 1]) / np.sqrt(layer_dims[i - 1])
        parameters["b" + str(i)] = np.zeros((layer_dims[i], 1))  # 初始化偏置为0
        
        # 确保权重和偏置的维度正确
        assert((layer_dims[i], layer_dims[i - 1]) == parameters["W" + str(i)].shape)
        assert((layer_dims[i], 1) == parameters["b" + str(i)].shape)
        
    return parameters

def L_model_forward(X, parameters):
    caches = []
    A = X  # 初始激活值设置为输入X
    L = len(parameters) // 2  # 网络层数

    for i in range(1, L):
        A_prev = A  # 上一层的激活值
        # 前向传播，使用ReLU激活函数
        A, cache = linear_activation_forward(A_prev, parameters["W" + str(i)], parameters["b" + str(i)], "relu")
        caches.append(cache)  # 保存缓存
        
    # 最后一层使用sigmoid激活函数
    AL, cache = linear_activation_forward(A, parameters["W" + str(L)], parameters["b" + str(L)], "sigmoid")
    caches.append(cache)
    
    # 确保输出AL的形状正确
    assert(AL.shape == (1, X.shape[1]))
    
    return AL, caches

def compute_cost(AL, Y):
    m = Y.shape[1]  # 样本数量
    
    # 计算成本
    cost = -(np.dot(np.log(AL), Y.T) + np.dot(np.log(1 - AL), (1 - Y).T)) / (m * 1.0)
    cost = np.squeeze(cost)  # 移除单维度条目
    assert(cost.shape == ())  # 确保成本是标量
    return cost

def L_model_backward(AL, Y, caches):
    grads = {}
    L = len(caches)  # 网络层数
    m = AL.shape[1]  # 样本数量
    Y = Y.reshape(AL.shape)  # 调整Y的形状与AL相匹配
    
    # 计算梯度
    dAL = -(np.divide(Y, AL) - np.divide(1 - Y, 1 - AL))
    
    # 反向传播的最后一层
    current_cache = caches[L - 1]
    grads["dA" + str(L)], grads["dW" + str(L)], grads["db" + str(L)] = linear_activation_backward(dAL, current_cache, activation="sigmoid")
    
    # 反向传播的其他层
    for i in reversed(range(L - 1)):
        current_cache = caches[i]
        dA_prev_temp, dW_temp, db_temp = linear_activation_backward(grads["dA" + str(i + 2)], current_cache, activation="relu")
        grads["dA" + str(i + 1)] = dA_prev_temp
        grads["dW" + str(i + 1)] = dW_temp
        grads["db" + str(i + 1)] = db_temp
        
    return grads

def update_parameters(parameters, grads, learning_rate):
    L = len(parameters) // 2  # 网络层数
    for i in range(1, L + 1):
        # 使用梯度下降更新参数
        parameters["W" + str(i)] -= learning_rate * grads["dW" + str(i)]
        parameters["b" + str(i)] -= learning_rate * grads["db" + str(i)]
        
    return parameters

5.2定义模型参数

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layers_dims = [12288, 20, 7, 5, 1] #  5-layer model

5.3L_layer_model网络定义

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def L_layer_model(X, Y, layers_dims, learning_rate = 0.0075, num_iterations = 3000, print_cost=False):
    """
    实现一个L层神经网络: [LINEAR->RELU]*(L-1)->LINEAR->SIGMOID.
    
    参数:
    X -- 数据，形状为 (样本数, num_px * num_px * 3) 的numpy数组
    Y -- 真实的“标签”向量（如果是猫则为0，不是猫则为1），形状为 (1, 样本数)
    layers_dims -- 包含输入大小和每层大小的列表，长度为 (层数 + 1)
    learning_rate -- 梯度下降更新规则的学习率
    num_iterations -- 优化循环的迭代次数
    print_cost -- 如果为True，则每100步打印一次成本
    
    返回:
    parameters -- 模型学习到的参数。它们可以用于预测。
    """

    np.random.seed(1)  # 设置随机种子以保持结果的一致性
    costs = []  # 记录成本

    # 参数初始化
    parameters = initialize_parameters_deep(layers_dims)
    
    # 梯度下降循环
    for i in range(0, num_iterations):

        # 前向传播: [LINEAR -> RELU]*(L-1) -> LINEAR -> SIGMOID
        AL, caches = L_model_forward(X, parameters)
        
        # 计算成本
        cost = compute_cost(AL, Y)
    
        # 反向传播
        grads = L_model_backward(AL, Y, caches)
 
        # 更新参数
        parameters = update_parameters(parameters, grads, learning_rate)
                
        # 每100个训练样本打印成本
        if print_cost and i % 100 == 0:
            print ("迭代次数 %i 后的成本: %f" %(i, cost))
        if print_cost and i % 100 == 0:
            costs.append(cost)
            
    # 绘制成本曲线
    plt.plot(np.squeeze(costs))
    plt.ylabel('成本')
    plt.xlabel('迭代次数（每十个）')
    plt.title("学习率 = " + str(learning_rate))
    plt.show()
    
    return parameters

5.4运行该网络进行训练

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parameters = L_layer_model(train_x,train_y,layers_dims,num_iterations=2500,print_cost=True)
image-20231130112550816

5.5执行预测

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pred_train = predict(train_x, train_y, parameters)
pred_test = predict(test_x, test_y, parameters)

结果：

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Accuracy: 0.9856459330143539
Accuracy: 0.8

​ 该网络比4.3提到的网络测试集准确率提高了8%的准确率。

​ 我们也可以利用print_mislabeled_images函数来看被L_layer网络错误分类的图片。

1
print_mislabeled_images(classes, test_x, test_y, pred_test)
image-20231130113042197
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