deeplearning_LogisticRegressionwithaNeuralNetworkmindset

此文为deeplearning课程第二周的编程作业实现一个逻辑回归分类器（识别一个图片中有没有猫）

需要用到的库

import numpy as npimport matplotlib.pyplot as pltimport h5pyimport scipyfrom PIL import Imagefrom scipy import ndimagefrom lr_utils import load_dataset

其中lr_utils中load_dataset是一个用于取得数据的方法，代码实现如下

import numpy as npimport h5py   def load_dataset():    train_dataset = h5py.File('datasets/train_catvnoncat.h5', "r")    train_set_x_orig = np.array(train_dataset["train_set_x"][:]) # your train set features    train_set_y_orig = np.array(train_dataset["train_set_y"][:]) # your train set labels    test_dataset = h5py.File('datasets/test_catvnoncat.h5', "r")    test_set_x_orig = np.array(test_dataset["test_set_x"][:]) # your test set features    test_set_y_orig = np.array(test_dataset["test_set_y"][:]) # your test set labels    classes = np.array(test_dataset["list_classes"][:]) # the list of classes    train_set_y_orig = train_set_y_orig.reshape((1, train_set_y_orig.shape[0]))    test_set_y_orig = test_set_y_orig.reshape((1, test_set_y_orig.shape[0]))    return train_set_x_orig, train_set_y_orig, test_set_x_orig, test_set_y_orig, classes

加载数据

train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()

建立神经网络的基本步骤

1. Define the model structure (such as number of input features)
2. Initialize the model’s parameters
3. Loop:
   
   • Calculate current loss (forward propagation)
   • Calculate current gradient (backward propagation)
   • Update parameters (gradient descent)

需要用到的方法

逻辑回归中的sigmod方法

公式：

# GRADED FUNCTION: sigmoiddef 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 = 1/(1+np.exp(-z))    ### END CODE HERE ###    return s

初始化参数w,b

assert方法用于检查我们初始化的shape是否是正确的

# GRADED FUNCTION: initialize_with_zerosdef 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

前向传播与反向传播

返回梯度和代价函数
公式：

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)  # compute activation    cost = (-1/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/m)*(np.dot(X,(A-Y).T))    db =(1/m)*np.sum(A-Y)    ### 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

梯度下降使得代价函数最小

返回代价函数最小时的参数w,b ; 梯度；代价函数
公式：

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

预测predict

根据已经算好的参数w,b；对输入的X进行预测，判断这张图片是不是猫

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)        if A[0,i]<=0.5:            Y_prediction[0,i] = 0        else:            Y_prediction[0,i] = 1        ### END CODE HERE ###    assert(Y_prediction.shape == (1, m))return Y_prediction

将这些方法组合的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)；对训练集进行训练，得到最优的参数    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)；使用w,b这两个最优的参数对训练集合测试集进行判断    Y_prediction_test = predict(w,b,X_test)    Y_prediction_train = predict(w,b,X_train)    ### END CODE HERE ###    # Print train/test Errors 分别输出训练集合测试集的误差    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 dd = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)

最终结果是

Expected Output:

**Train Accuracy** 99.04306220095694 % **Test Accuracy** 70.0 %

由此可见，此模型存在过拟合的现象

自己输入图片判断

## START CODE HERE ## (PUT YOUR IMAGE NAME) my_image = "my_image.jpg"   # change this to the name of your image file ## END CODE HERE ### We preprocess the image to fit your algorithm.fname = "images/" + my_imageimage = np.array(ndimage.imread(fname, flatten=False))#调整图片至需要的矩阵大小及shapemy_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T#使用已有参数w,b进行预测(d由之前的model得到)my_predicted_image = predict(d["w"], d["b"], my_image)plt.imshow(image)print("y = " + str(np.squeeze(my_predicted_image)) + ", your algorithm predicts a \"" + classes[int(np.squeeze(my_predicted_image)),].decode("utf-8") +  "\" picture.")