1.3 用Google Colab进行猫的分类

用神经网络来实现精准撸猫第一步

其实就是猫的分类，☺

打开Google Colab后，首先第一步挂载Google Drive

1. 授权和验证

!apt-get install -y -qq software-properties-common python-software-properties module-init-tools
!add-apt-repository -y ppa:alessandro-strada/ppa 2>&1 > /dev/null
!apt-get update -qq 2>&1 > /dev/null
!apt-get -y install -qq google-drive-ocamlfuse fuse
from google.colab import auth
auth.authenticate_user()
from oauth2client.client import GoogleCredentials
creds = GoogleCredentials.get_application_default()
import getpass
!google-drive-ocamlfuse -headless -id={creds.client_id} -secret={creds.client_secret} < /dev/null 2>&1 | grep URL
vcode = getpass.getpass()
!echo {vcode} | google-drive-ocamlfuse -headless -id={creds.client_id} -secret={creds.client_secret}

2. 挂载

!mkdir -p drive
!google-drive-ocamlfuse drive

3. 工作目录切换

import os

path = "/content/drive/assignment2(C1W2)"
os.chdir(path)
os.listdir(path)

通过以上操作，完成了Google Drive的挂载，现在可以继续进行后面的工作了

---

在接下来的工作里，需要用的包有：

1. numpy : 科学计算
2. matplotlib : 绘图
3. h5py ：与H5文件中的数据进行交互
4. scipy ：验证训练结果
5. PIL ：验证训练结果

• 数据集
  • 已经标记了猫和非猫的m_train图片
  • 已经标记了猫和非猫的m_test图片
  • 每个图片是一个（行像素值，列像素值，3）（3是RGB三个颜色）

---

• train_set_x_orig
  • 处理它，得到train_set_x（每一行都是一个表示图片的矩阵）
• train_set_y
  • 保持不变
• test_set_x_orig
  • 处理它，得到train_set_y（每一行都是一个表示图片的矩阵）
• test_set_y
  • 保持不变
• classes
  • 是猫么？

(209, 64, 64, 3)
# （样本量，像素值，像素值，RGB）
Number of training examples: m_train = 209
Number of testing examples: m_test = 50
Height/Width of each image: num_px = 64
Each image is of size: (64, 64, 3)
train_set_x shape: (209, 64, 64, 3)
train_set_y shape: (1, 209)
test_set_x shape: (50, 64, 64, 3)
test_set_y shape: (1, 50)

---

矩阵转换

将一个图像的复杂的矩阵(64,64,4)转换为一个numpy array(12288)，

train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],64*64*3).T
test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],64*64*3).T

---

标准化数据集
mark ：why？

train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.

如何建立一个神经网络？

1. 定义我们的模型结构（输入几个参数？假设函数？损失函数？代价函数？）
2. 初始化模型的参数
3. 循环进行前向传播，反向传播，更新参数

Sigmoid实现 ：

# GRADED FUNCTION: sigmoid

def sigmoid(z):
    """
    Compute the sigmoid of z

    Arguments:
    z -- A scalar or numpy array of any size.

    Return:
    s -- sigmoid(z)
    """

    ### START CODE HERE ### (≈ 1 line of code)
    s = np.true_divide(1,1+np.true_divide(1,np.exp(z)))
    ### END CODE HERE ###
    
    return s

---

初始化w和b

# GRADED FUNCTION: initialize_with_zeros

def initialize_with_zeros(dim):
    """
    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.
    
    Argument:
    dim -- size of the w vector we want (or number of parameters in this case)
    
    Returns:
    w -- initialized vector of shape (dim, 1)
    b -- initialized scalar (corresponds to the bias)
    """
    
    ### START CODE HERE ### (≈ 1 line of code)
    w = np.zeros((dim,1))
    b = 0
    ### END CODE HERE ###

    assert(w.shape == (dim, 1))
    assert(isinstance(b, float) or isinstance(b, int))
    
    return w, b

---

前向传播和反向传播

• 前向传播:
  • You get X
  • You compute $A=\sigma (w^{T}X+b)=(a^{(0)},a^{(1)},...,a^{(m-1)},a^{(m)})$
  • You calculate the cost function: $J=-\frac{1}{m}{\sum }_{i=1}^m{y}^{(i)}\log (a^{(i)})+(1-y^{(i)})\log (1-a^{(i)})$

Here are the two formulas you will be using:

$$\frac{\partial J}{\partial w}=\frac{1}{m}X(A-Y{)}^T\text{\hspace{1em}(7)}$$
$$\frac{\partial J}{\partial b}=\frac{1}{m}\sum _{i=1}^m(a^{(i)}-y^{(i)})\text{\hspace{1em}(8)}$$

# GRADED FUNCTION: propagate

def propagate(w, b, X, Y):
    """
    Implement the cost function and its gradient for the propagation explained above

    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat) of size (1, number of examples)

    Return:
    cost -- negative log-likelihood cost for logistic regression
    dw -- gradient of the loss with respect to w, thus same shape as w
    db -- gradient of the loss with respect to b, thus same shape as b
    
    Tips:
    - Write your code step by step for the propagation. np.log(), np.dot()
    """
    
    m = X.shape[1]
    
    # FORWARD PROPAGATION (FROM X TO COST)
    ### START CODE HERE ### (≈ 2 lines of code)
    A = sigmoid(np.dot(w.T,X)+b)          
    cost = -(np.dot(Y,np.log(A).T)+np.dot(1-Y,np.log(1-A).T))/m
    ### END CODE HERE ###
    
    # BACKWARD PROPAGATION (TO FIND GRAD)
    ### START CODE HERE ### (≈ 2 lines of code)
    dw = np.dot(X,(A-Y).T)/m
    db = np.sum(A-Y)/m
    ### END CODE HERE ###
    assert(dw.shape == w.shape)
    assert(db.dtype == float)
    cost = np.squeeze(cost)
    assert(cost.shape == ())
    
    grads = {"dw": dw,
             "db": db}
    
    return grads, cost

---

更新参数

# GRADED FUNCTION: optimize

def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):
    """
    This function optimizes w and b by running a gradient descent algorithm
    
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of shape (num_px * num_px * 3, number of examples)
    Y -- true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
    num_iterations -- number of iterations of the optimization loop
    learning_rate -- learning rate of the gradient descent update rule
    print_cost -- True to print the loss every 100 steps
    
    Returns:
    params -- dictionary containing the weights w and bias b
    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function
    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.
    
    Tips:
    You basically need to write down two steps and iterate through them:
        1) Calculate the cost and the gradient for the current parameters. Use propagate().
        2) Update the parameters using gradient descent rule for w and b.
    """
    
    costs = []
    
    for i in range(num_iterations):
        
        
        # Cost and gradient calculation (≈ 1-4 lines of code)
        ### START CODE HERE ### 
        grads, cost = propagate(w,b,X,Y)
        ### END CODE HERE ###
        
        # Retrieve derivatives from grads
        dw = grads["dw"]
        db = grads["db"]
        
        # update rule (≈ 2 lines of code)
        ### START CODE HERE ###
        w = w-learning_rate*dw
        b = b-learning_rate*db
        ### END CODE HERE ###
        
        # Record the costs
        if i % 100 == 0:
            costs.append(cost)
        
        # Print the cost every 100 training examples
        if print_cost and i % 100 == 0:
            print ("Cost after iteration %i: %f" %(i, cost))
    
    params = {"w": w,
              "b": b}
    
    grads = {"dw": dw,
             "db": db}
    
    return params, grads, costs

---

实现预测

# GRADED FUNCTION: predict

def predict(w, b, X):
    '''
    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)
    
    Arguments:
    w -- weights, a numpy array of size (num_px * num_px * 3, 1)
    b -- bias, a scalar
    X -- data of size (num_px * num_px * 3, number of examples)
    
    Returns:
    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X
    '''
    
    m = X.shape[1]
    Y_prediction = np.zeros((1,m))
    w = w.reshape(X.shape[0], 1)
    
    # Compute vector "A" predicting the probabilities of a cat being present in the picture
    ### START CODE HERE ### (≈ 1 line of code)
    A = sigmoid(np.dot(w.T,X)+b)
    ### END CODE HERE ###

    for i in range(A.shape[1]):
        
        # Convert probabilities A[0,i] to actual predictions p[0,i]
        ### START CODE HERE ### (≈ 4 lines of code)
        Y_prediction[0,i] = int(A[0,i]>0.5) 
        ### END CODE HERE ###
    
    assert(Y_prediction.shape == (1, m))
    
    return Y_prediction

---

模型集成

# GRADED FUNCTION: model

def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
    """
    Builds the logistic regression model by calling the function you've implemented previously
    
    Arguments:
    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)
    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)
    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)
    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)
    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters
    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()
    print_cost -- Set to true to print the cost every 100 iterations
    
    Returns:
    d -- dictionary containing information about the model.
    """
    
    ### START CODE HERE ###
    
    # initialize parameters with zeros (≈ 1 line of code)
    w, b = np.zeros((X_train.shape[0],1)),0

    # Gradient descent (≈ 1 line of code)
    parameters, grads, costs = optimize(w,b,X_train,Y_train,num_iterations,learning_rate,print_cost)
    
    # Retrieve parameters w and b from dictionary "parameters"
    w = parameters["w"]
    b = parameters["b"]
    
    # Predict test/train set examples (≈ 2 lines of code)
    Y_prediction_test = predict(w,b,X_test)
    Y_prediction_train = predict(w,b,X_train)

    ### END CODE HERE ###

    # Print train/test Errors
    print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
    print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))

    
    d = {"costs": costs,
         "Y_prediction_test": Y_prediction_test, 
         "Y_prediction_train" : Y_prediction_train, 
         "w" : w, 
         "b" : b,
         "learning_rate" : learning_rate,
         "num_iterations": num_iterations}
    
    return d

---

Summary

略微失望的是今天实现的图片分类器准确度真的是一般!!!
在实现过程当中主要碰到的问题便是维度的问题，在模型集成过程时，把w用样本个数来进行初始化了。
numpy函数记得不牢，查阅了几个函数：
np.true_divide：注意区分np.divide()和np.true_divide()的区别
广播机制：np_arr - 1，和1 - np_arr都是会进行广播的，刚开始愚蠢的给倒过来了，以为不可以

Question：

为什么要进行标准化？