01神经网络和深度学习-Logistic-Regression-with-a-Neural-Network-mindset-第二周编程作业2

清疚 2022-05-15 01:19 167阅读 0赞

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算法大概流程：

1、输入w，b并初始化；

2、反向传播，递归下降，计算dw，db；，

3、利用超参数学习率，迭代计算w，b的值；

4、预测。

import numpy as np
    import matplotlib.pyplot as plt
    import h5py
    import scipy
    from PIL import Image
    from scipy import ndimage
    from lr_utils import load_dataset
       
    # Loading the data (cat/non-cat)
    train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
    
    # Example of a picture
    index = 25
    plt.imshow(train_set_x_orig[index])
    print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") +  "' picture.")
    
    ### START CODE HERE ### (≈ 3 lines of code)
    m_train = train_set_x_orig.shape[0]
    m_test = test_set_x_orig.shape[0]
    num_px = train_set_x_orig.shape[1]
    ### END CODE HERE ###
     
    print ("Number of training examples: m_train = " + str(m_train))
    print ("Number of testing examples: m_test = " + str(m_test))
    print ("Height/Width of each image: num_px = " + str(num_px))
    print ("Each image is of size: (" + str(num_px) + ", " + str(num_px) + ", 3)")
    print ("train_set_x shape: " + str(train_set_x_orig.shape))
    print ("train_set_y shape: " + str(train_set_y.shape))
    print ("test_set_x shape: " + str(test_set_x_orig.shape))
    print ("test_set_y shape: " + str(test_set_y.shape))
    
    # Reshape the training and test examples
     
    ### START CODE HERE ### (≈ 2 lines of code)
    train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0],-1).T
    test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0],-1).T
    ### END CODE HERE ###
     
    print ("train_set_x_flatten shape: " + str(train_set_x_flatten.shape))
    print ("train_set_y shape: " + str(train_set_y.shape))
    print ("test_set_x_flatten shape: " + str(test_set_x_flatten.shape))
    print ("test_set_y shape: " + str(test_set_y.shape))
    print ("sanity check after reshaping: " + str(train_set_x_flatten[0:5,0]))
    
    
    train_set_x = train_set_x_flatten/255.
    test_set_x = test_set_x_flatten/255.
    
    # GRADED FUNCTION: sigmoid
    def sigmoid(z):#激活函数
        """
        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 = 1 / (1+np.exp(-z))
        ### END CODE HERE ### 
        return s
    # GRADED FUNCTION: initialize_with_zeros
    
    def initialize_with_zeros(dim):#初始化全为0
        """
        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).reshape(dim, 1)
        b = 0
    
        ### END CODE HERE ###
        assert(w.shape == (dim, 1))
        assert(isinstance(b, float) or isinstance(b, int))
        return w, b
    
    # GRADED FUNCTION: propagate
    def propagate(w, b, X, Y):#传播
        """
        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((w.T).dot(X)+b)                                     # compute activation
        cost = (-1.0/m) * np.sum(Y*np.log(A) + (1-Y)*np.log(1-A))       # compute cost
        ### END CODE HERE ###
        
        # BACKWARD PROPAGATION (TO FIND GRAD)
        ### START CODE HERE ### (≈ 2 lines of code)
        dw = (1.0/m) * X.dot(((A-Y).T))
        db = (1.0/m) * np.sum(A-Y)
        ### END CODE HERE ###
        assert(dw.shape == w.shape)#2,1
        assert(db.dtype == float)
        cost = np.squeeze(cost)
        assert(cost.shape == ())
        grads = {"dw": dw,
                 "db": db}
        return grads, cost
       
    # GRADED FUNCTION: optimize
    def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):#优化
        """
        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
    
    # GRADED FUNCTION: predict
    
    def predict(w, b, X):#预测
        '''
        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((w.T).dot(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)
            if A[0,i] <= 0.5:
               Y_prediction[0,i]=0
            elif A[0,i] > 0.5:
               Y_prediction[0,i]=1
            ### END CODE HERE ###
        assert(Y_prediction.shape == (1, m))
        return Y_prediction
      
    # 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 = initialize_with_zeros(X_train.shape[0])
    
        # Gradient descent (≈ 1 line of code)
        parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost = False)
    
        # 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
     
    if __name__=='__main__':   
        print ("sigmoid([0, 2]) = " + str(sigmoid(np.array([0,2]))))
    
        dim = 2
        w, b = initialize_with_zeros(dim)
        print ("w = " + str(w))
        print ("b = " + str(b))
    
        w, b, X, Y = np.array([[1],[2]]), 2, np.array([[1,2],[3,4]]), np.array([[1,0]])
        grads, cost = propagate(w, b, X, Y)
        print ("dw = " + str(grads["dw"]))
        print ("db = " + str(grads["db"]))
        print ("cost = " + str(cost))
    
        params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)
        print ("w = " + str(params["w"]))
        print ("b = " + str(params["b"]))
        print ("dw = " + str(grads["dw"]))
        print ("db = " + str(grads["db"]))
    
        print ("predictions = " + str(predict(w, b, X)))
    
        d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)
    
        # Example of a picture that was wrongly classified.
        index = 1
        plt.imshow(test_set_x[:,index].reshape((num_px, num_px, 3)))
        print ("y = " + str(test_set_y[0,index]) + ", you predicted that it is a \"" + classes[int(d["Y_prediction_test"][0,index])].decode("utf-8") +  "\" picture.")
        # Plot learning curve (with costs)
        costs = np.squeeze(d['costs'])
        plt.plot(costs)
        plt.ylabel('cost')
        plt.xlabel('iterations (per hundreds)')
        plt.title("Learning rate =" + str(d["learning_rate"]))
        plt.show()

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