deep_learning_week2_logistic回归

机器学习深度学习

代码已上传github:
https://github.com/PerfectDemoT/my_deeplearning_homework

这是吴恩达深度学习里的第一次作业

实现logistic回归

1. 先导入包

import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
import pylab
from scipy import ndimage
from lr_utils import load_dataset #这个是里面的一个导入数据的py文件

2. 导入数据，再显示一张图片看看效果

导入数据代码如下：

# Loading the data (cat/non-cat)
train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
#分别为训练集x 209个,训练集y 209个,测试集x 50个,测试集y 50个

这是一张图片

#这时输出上面这张图的代码
index = 19
plt.imshow(train_set_x_orig[index])
pylab.show()
print ("y = " + str(train_set_y[:, index]) + ", it's a '" + classes[np.squeeze(train_set_y[:, index])].decode("utf-8") +  "' picture.")

之后会让你看看导入数据的维数，代码如下：

### 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))

结果显示是这样：

3. 现在可以开始写函数了

首先把训练数据的64*64*3的矩阵变化为向量，代码如下：

### 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
###现在处理好了图像，将其全部向量化了

将原来的四维（样本个数，图片横，竖，RGB）变为二维（样本个数，其他所有）

然后现在开始归一化

#现在开始归一化，将RGB里的0-255全部变为0-1（除以255）
train_set_x = train_set_x_flatten/255.
test_set_x = test_set_x_flatten/255.

现在可以开始写各种函数了：

sogmoid函数

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

随机初始化w和b的函数

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

现在来前向和反向传播

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 = np.sum(Y * np.log(A) + (1-Y) * np.log(1-A))/(-m)  # compute cost
        ### 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w和b的函数

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
        # 每100次输出一个代价函数
        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

现在这是预测函数

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 = np.dot(w.T , X)
    ### 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] = 1
        else:
            Y_prediction[0][i] = 0
        ### END CODE HERE ###
    assert (Y_prediction.shape == (1, m))
    return Y_prediction

4.现在终于可以开始真正的训练参数了（之前都是用的测试，现在开始用真正的图片数据来训练）

代码如下：

#现在开始将上面的这些函数整合起来
# GRADED FUNCTION: model
print("===============终于，开始处理图像了=========================")
def model(X_train, Y_train, X_test, Y_test, num_iterations=10000, learning_rate=0.01, 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

下面是调用这个函数来训练的例子：

d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 10000, learning_rate = 0.001, print_cost = True)

训练完毕，我们来看看准确率

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))

结果是这样的：

现在我们来看看代价函数曲线(代码长这样)：

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()

图是这样的(这里的学习速率是0.001，迭代次数10000)：

下面来看看学习速率的选择(先上代码)：

learning_rates = [0.01, 0.001, 0.0001]#定义一个有三个值的数组，这里只是给你看方法，实际上的取值是有方法的（在机器学习里）
models = {}
for i in learning_rates:
    print ("learning rate is: " + str(i))
    models[str(i)] = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 1500, learning_rate = i, print_cost = False)
    print ('\n' + "-------------------------------------------------------" + '\n')
for i in learning_rates:
    plt.plot(np.squeeze(models[str(i)]["costs"]), label= str(models[str(i)]["learning_rate"]))
plt.ylabel('cost')
plt.xlabel('iterations')
legend = plt.legend(loc='upper center', shadow=True)
frame = legend.get_frame()
frame.set_facecolor('0.90')
plt.show()
#通过图像的发现，三个学习速率中，0.001是最好的（好吧，如果不管前面蓝色的波动，0.01或许也不错，不过，你会发现训练集的误差已经很小了，但验证集误差却很大，存在过拟合情况，所以用0.01并不会减小验证集的误差）

下面是图片

然后学习率对应的准确率如下：

最后，来点有趣的，用自己的图

现在用自己的图像玩玩，1表示预测是猫，0表示不是

## START CODE HERE ## (PUT YOUR IMAGE NAME)
my_image = "my_image2.jpg"   # change this to the name of your image file
## END CODE HERE ##
# ​
# We preprocess the image to fit your algorithm.
fname = "images/" + my_image
image = np.array(ndimage.imread(fname, flatten=False))
my_image = scipy.misc.imresize(image, size=(num_px,num_px)).reshape((1, num_px*num_px*3)).T
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.")

图长这样：

然后判断是：

我还试了一张埃菲尔铁塔的，判断为不是猫，感觉还不错。。。（好吧，其实看识别率还挺低），这里还缺少了一个正规化来防止过拟合（并且个人感觉，这个一定overfitting了，因为训练样本准确率非常高，而测试样本准确率却很低），防止过拟合将在下次来实现