吴恩达深度学习1-Week2课后作业-Logistic回归与梯度下降向量化

版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/Apple_hzc/article/details/83001387

一、deeplearning-assignment

这篇文章会帮助构建一个用来识别猫的逻辑回归分类器。通过这个作业能够知道如何进行神经网络学习方面的工作,指导你如何用神经网络的思维方式做到这些，同样也会加深你对深度学习的认识。

尽量不要在代码中出现for循环，可以用numpy函数代替的尽量通过向量化方法实现。

学习算法的总体架构，包括：

• 初始化参数
• 计算成本函数及其梯度
• 使用优化算法（梯度下降） 将上述三个函数按照正确的顺序收集到主模型函数中。

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二、相关算法代码

import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage


def load_dataset():
    train_dataset = h5py.File('e:/code/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('e:/code/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


train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
# index = 3
# plt.imshow(train_set_x_orig[index])
# plt.show()
# print("y = " + str(train_set_y[:, index]) + ", it's a '" +
#       classes[np.squeeze(train_set_y[:, index])].decode("utf-8") + "' picture.")

m_train = train_set_x_orig.shape[0]  # 表示训练集数
m_test = test_set_x_orig.shape[0]  # 表示测试集数
num_px = train_set_x_orig.shape[1]  # 每个image的height/width
# 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))


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
# 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.

def sigmoid(x):
    s = 1 / (1 + np.exp(-x))
    return s


def initialize_with_zeros(dim):
    w = np.zeros((dim, 1))
    b = 0
    assert (w.shape == (dim, 1))
    assert (isinstance(b, float) or isinstance(b, int))
    return w, b


# print(sigmoid(np.array([1, 2])))
# dim = 2
# w, b = initialize_with_zeros(dim)
# print("w = " + str(w))
# print("b = " + str(b))


def propagate(w, b, X, Y):
    # FORWARD PROPAGATION (FROM X TO COST)
    m = X.shape[1]
    Z = np.dot(w.T, X) + b
    A = sigmoid(Z)
    cost = - 1 / m * np.sum(np.log(A) * Y + (1 - Y) * np.log(1 - A))

    # BACKWARD PROPAGATION (TO FIND GRAD)
    dw = 1 / m * np.dot(X, (A - Y).T)
    db = 1 / m * np.sum(A - Y)
    assert (dw.shape == w.shape)
    assert (db.dtype == float)
    cost = np.squeeze(cost)
    assert (cost.shape == ())

    grads = {"dw": dw,
             "db": db}
    return grads, cost


# a test for the function above

# w, b, X, Y = np.array([[1], [2]]), 2, np.array([[1, 2], [3, 4]]), np.array([[1, 0]])
# grads, cost, A, Z = propagate(w, b, X, Y)
# print("dw = " + str(grads["dw"]))
# print("db = " + str(grads["db"]))
# print("cost = " + str(cost))


def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost=False):
    """
    :param w:weights, a numpy array of size (num_px * num_px * 3, 1)
    :param b:bias, a scalar
    :param X:data of shape (num_px * num_px * 3, number of examples)
    :param Y:true "label" vector (containing 0 if non-cat, 1 if cat), of shape (1, number of examples)
    :param num_iterations:number of iterations of the optimization loop
    :param learning_rate:learning rate of the gradient descent update rule
    :param print_cost:True to print the loss every 100 steps

    :return:
    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.
    """

    costs = []
    for i in range(num_iterations):
        grads, cost = propagate(w, b, X, Y)

        dw = grads["dw"]
        db = grads["db"]

        w = w - learning_rate * dw
        b = b - learning_rate * db

        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


# params, grads, costs = optimize(w, b, X, Y, num_iterations=100,
#                                 learning_rate=0.009, print_cost=True)
# print("w = " + str(params["w"]))
# print("b = " + str(params["b"]))
# print("dw = " + str(grads["dw"]))
# print("db = " + str(grads["db"]))
# print(costs)

def predict(w, b, X):
    m = X.shape[1]
    Y_prediction = np.zeros((1, m))
    w = w.reshape(X.shape[0], 1)
    A = sigmoid(np.dot(w.T, X) + b)
    for i in range(A.shape[1]):
        if A[0, i] <= 0.5:
            Y_prediction[0, i] = 0
        else:
            Y_prediction[0, i] = 1

    assert (Y_prediction.shape == (1, m))
    return Y_prediction


# print("predictions = " + str(predict(w, b, X)))


# Merge all functions into a model

def model(X_train, Y_train, X_test, Y_test, num_iterations=2000, learning_rate=0.5, print_cost=False):

    w, b = initialize_with_zeros(X_train.shape[0])

    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
    w = parameters["w"]
    b = parameters["b"]

    Y_prediction_test = predict(w, b, X_test)
    Y_prediction_train = predict(w, b, X_train)

    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


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()


# learning_rates = [0.01, 0.001, 0.0001]
# 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()


my_image = "la_defense.jpg"
fname = "e:/code/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.")

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三、总结

以上代码均亲自实现过，对一张图片是否是猫进行判断，其中包括sigmoid函数、初始化函数、预测函数、优化函数，最后将前面所有函数放在一个model中，对训练集进行学习，利用梯度下降算法进行优化，最后对图片进行合理预测。