吴恩达深度学习1-Week3课后作业-浅层神经网络

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/83027944

一、deeplearning-assignment

在本次作业的开始，针对一个非线性可分的数据集通过sklearn的内置函数来训练数据集上的逻辑回归分类器，可以看到逻辑回归的表现并不理想，准确度只有47%。

因此建立一个神经网络模型，该模型有一个隐藏层，每个隐藏层有四个节点。

神经网络的正向传播：

神经网络的反向传播：

反向传播是深度学习中最难的（最具数学意义的）部分。为了帮助你，拿出了讲座中的幻灯片。您将要使用这张幻灯片右边的六个公式，因为您正在构建一个矢量化的实现。

其中，

为了计算dZ1，你需要计算 ，由于是激活函数tanh，因此如果那么.。你就可以通过numpy的函数(1 - np.power(A1, 2))来计算 的值。

---

二、相关算法代码

import numpy as np
import matplotlib.pyplot as plt
import sklearn
import sklearn.datasets
import sklearn.linear_model
from week3.testCases import *
from week3.planar_utils import plot_decision_boundary, sigmoid, load_planar_dataset, load_extra_datasets
np.random.seed(1)

X, Y = load_planar_dataset()  # 加载数据集
# plt.scatter(X[0, :], X[1, :], c=np.squeeze(Y), s=40, cmap=plt.cm.Spectral)
# plt.show()

# 通过sklearn内置函数对数据集进行逻辑回归
# logistic = sklearn.linear_model.LogisticRegressionCV()
# logistic.fit(X.T, Y.T.ravel())
# plot_decision_boundary(lambda x: logistic.predict(x), X, Y)
# plt.title("Logistic Regression")
# plt.show()
#
# LR_predictions = logistic.predict(X.T)
# print('Accuracy of logistic regression: %d ' % float((np.dot(Y, LR_predictions) +
#             np.dot(1-Y, 1-LR_predictions)) / float(Y.size) * 100) +
#        '% ' + "(percentage of correctly labelled datapoints)")


# shape_X = X.shape
# shape_Y = Y.shape
# m = shape_X[1]
# print('The shape of X is: ' + str(shape_X))
# print('The shape of Y is: ' + str(shape_Y))
# print('I have m = %d training examples!' % (m))


def layer_sizes(X, Y):  # 初始化各个维度的值
    n_x = X.shape[0]
    n_h = 4
    n_y = Y.shape[0]
    return n_x, n_h, n_y


# X_assess, Y_assess = layer_sizes_test_case()
# (n_x, n_h, n_y) = layer_sizes(X_assess, Y_assess)
# print("The size of the input layer is: n_x = " + str(n_x))
# print("The size of the hidden layer is: n_h = " + str(n_h))
# print("The size of the output layer is: n_y = " + str(n_y))


def initialize_parameters(n_x, n_h, n_y):  # 对W1, W2, b1, b2进行初始化
    """
    Returns:
    params -- python dictionary containing your parameters:
        W1 -- weight matrix of shape (n_h, n_x)
        b1 -- bias vector of shape (n_h, 1)
        W2 -- weight matrix of shape (n_y, n_h)
        b2 -- bias vector of shape (n_y, 1)
    """

    np.random.seed(2)
    W1 = np.random.rand(n_h, n_x) * 0.01
    b1 = np.zeros((n_h, 1))
    W2 = np.random.rand(n_y, n_h) * 0.01
    b2 = np.zeros((n_y, 1))

    # 深度学习常见的bug就是维度异常
    # 吴恩达的经验：编码中嵌入assert代码，检测维度
    assert (W1.shape == (n_h, n_x))
    assert (b1.shape == (n_h, 1))
    assert (W2.shape == (n_y, n_h))
    assert (b2.shape == (n_y, 1))

    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}
    return parameters


# n_x, n_h, n_y = initialize_parameters_test_case()
# parameters = initialize_parameters(n_x, n_h, n_y)
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))


def forward_propagation(X, parameters):  # 正向传播
    W1 = parameters["W1"]
    b1 = parameters["b1"]
    W2 = parameters["W2"]
    b2 = parameters["b2"]

    Z1 = np.dot(W1, X) + b1
    A1 = np.tanh(Z1)
    Z2 = np.dot(W2, A1) + b2
    A2 = sigmoid(Z2)

    assert (A2.shape == (1, X.shape[1]))

    cache = {"Z1": Z1,
             "A1": A1,
             "Z2": Z2,
             "A2": A2}

    return A2, cache


# X_assess, parameters = forward_propagation_test_case()
# print(X_assess)
# print(parameters)

# A2, cache = forward_propagation(X_assess, parameters)
# print(cache)
# print("mean:", np.mean(cache['Z1']), np.mean(cache['A1']), np.mean(cache['Z2']), np.mean(cache['A2']))


def compute_cost(A2, Y, parameters):  # 计算cost

    m = Y.shape[1]  # number of example

    logprobs = np.multiply(Y, np.log(A2)) + np.multiply(1 - Y, np.log(1 - A2))
    cost = - 1 / m * np.sum(logprobs)
    cost = np.squeeze(cost)  # sqeeze从数组的形状中删除单维条目，即把shape中为1的维度去掉
    # E.g., turns [[17]] into 17
    assert (isinstance(cost, float))

    return cost


# A2, Y_assess, parameters = compute_cost_test_case()
# print("cost = " + str(compute_cost(A2, Y_assess, parameters)))


def backward_propagation(parameters, cache, X, Y):  # 反向传播
    m = X.shape[1]

    W1 = parameters["W1"]
    W2 = parameters["W2"]

    A1 = cache["A1"]
    A2 = cache["A2"]

    dZ2 = A2 - Y
    dW2 = 1 / m * np.dot(dZ2, A1.T)
    db2 = 1 / m * np.sum(dZ2, axis=1, keepdims=True)

    dZ1 = np.dot(W2.T, dZ2) * (1 - np.power(A1, 2))
    dW1 = 1 / m * np.dot(dZ1, X.T)
    db1 = 1 / m * np.sum(dZ1, axis=1, keepdims=True)

    grads = {"dW1": dW1,
             "db1": db1,
             "dW2": dW2,
             "db2": db2}

    return grads


# parameters, cache, X_assess, Y_assess = backward_propagation_test_case()
# grads = backward_propagation(parameters, cache, X_assess, Y_assess)
# print("dW1 = " + str(grads["dW1"]))
# print("db1 = " + str(grads["db1"]))
# print("dW2 = " + str(grads["dW2"]))
# print("db2 = " + str(grads["db2"]))

def update_parameters(parameters, grads, learning_rate=1.2):  # 更新W1, W2, b1, b2
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']

    dW1 = grads["dW1"]
    db1 = grads["db1"]
    dW2 = grads["dW2"]
    db2 = grads["db2"]

    W1 -= dW1 * learning_rate
    b1 -= db1 * learning_rate
    W2 -= dW2 * learning_rate
    b2 -= db2 * learning_rate

    parameters = {"W1": W1,
                  "b1": b1,
                  "W2": W2,
                  "b2": b2}

    return parameters


# parameters, grads = update_parameters_test_case()
# parameters = update_parameters(parameters, grads)
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))


#  The neural network model has to use the previous functions in the right order.
def nn_model(X, Y, n_h, num_iterations=10000, print_cost=False):

    np.random.seed(3)
    n_x = layer_sizes(X, Y)[0]
    n_y = layer_sizes(X, Y)[2]

    n_x, n_h, n_y = layer_sizes(X, Y)
    parameters = initialize_parameters(n_x, n_h, n_y)
    W1 = parameters['W1']
    b1 = parameters['b1']
    W2 = parameters['W2']
    b2 = parameters['b2']

    for i in range(0, num_iterations):

        A2, cache = forward_propagation(X, parameters)

        cost = compute_cost(A2, Y, parameters)

        grads = backward_propagation(parameters, cache, X, Y)

        parameters = update_parameters(parameters, grads)

        if print_cost and i % 1000 == 0:
            print("Cost after iteration %i: %f" % (i, cost))

    return parameters


# X_assess, Y_assess = nn_model_test_case()
# parameters = nn_model(X_assess, Y_assess, 4, num_iterations=10, print_cost=False)
# print("W1 = " + str(parameters["W1"]))
# print("b1 = " + str(parameters["b1"]))
# print("W2 = " + str(parameters["W2"]))
# print("b2 = " + str(parameters["b2"]))


def predict(parameters, X):

    A2, cache = forward_propagation(X, parameters)
    predictions = np.array([1 if x > 0.5 else 0 for x in A2.reshape(-1, 1)]).reshape(A2.shape)

    return predictions


# parameters, X_assess = predict_test_case()
# predictions = predict(parameters, X_assess)
# print("predictions:", predictions)
# print("predictions mean = " + str(np.mean(predictions)))


# Build a model with a n_h-dimensional hidden layer
parameters = nn_model(X, Y, n_h=4, num_iterations=10000, print_cost=True)
# Plot the decision boundary
plot_decision_boundary(lambda x: predict(parameters, x.T), X, Y)
plt.title("Decision Boundary for hidden layer size " + str(4))
plt.show()

# Print accuracy
predictions = predict(parameters, X)
print('Accuracy: %d' % float((np.dot(Y, predictions.T) +
                              np.dot(1-Y, 1-predictions.T))/float(Y.size)*100) + '%')

通过神经网络的分类结果，准确率为90%：

---

三、总结

通过这次作业可以看到，对于非线性可分的数据集，前面学的逻辑回归并不能进行很好的学习，而通过神经网络，在隐藏层引入tanh这种非线性激活函数，能够很好地对数据集进行训练和拟合，期待接下来的学习！