吴恩达深度学习学习笔记——C1W3——浅层神经网络——作业——平面数据分类

这里主要梳理一下作业的主要内容和思路，完整作业文件可参考:

https://github.com/pandenghuang/Andrew-Ng-Deep-Learning-notes/tree/master/assignments/C1W3

作业完整截图，参考本文结尾：作业完整截图。

作业目录：

作业目标：

Planar data classification with one hidden layer

Welcome to your week 3 programming assignment. It's time to build your first neural network, which will have a hidden layer. You will see a big difference between this model and the one you implemented using logistic regression.

You will learn how to:

• Implement a 2-class classification neural network with a single hidden layer
• Use units with a non-linear activation function, such as tanh
• Compute the cross entropy loss
• Implement forward and backward propagation

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1 - Packages（所需包）

Let's first import all the packages that you will need during this assignment.

• numpy is the fundamental package for scientific computing with Python.
• sklearn provides simple and efficient tools for data mining and data analysis.
• matplotlib is a library for plotting graphs in Python.
• testCases provides some test examples to assess the correctness of your functions
• planar_utils provide various useful functions used in this assignment

 

 

2 - Dataset（数据集）

First, let's get the dataset you will work on. The following code will load a "flower" 2-class dataset into variables X and Y.

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3 - Simple Logistic Regression（简单Logistic回归的效果，并不理想）

Before building a full neural network, lets first see how logistic regression performs on this problem. You can use sklearn's built-in functions to do that. Run the code below to train a logistic regression classifier on the dataset.

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4 - Neural Network model（神经网络模型闪亮登场）

Logistic regression did not work well on the "flower dataset". You are going to train a Neural Network with a single hidden layer.

数学原理：

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4.2 - Initialize the model's parameters（初始化模型参数）

Exercise: Implement the function initialize_parameters().

Instructions:

• Make sure your parameters' sizes are right. Refer to the neural network figure above if needed.
• You will initialize the weights matrices with random values.
  • Use: np.random.randn(a,b) * 0.01 to randomly initialize a matrix of shape (a,b).
• You will initialize the bias vectors as zeros.
  • Use: np.zeros((a,b)) to initialize a matrix of shape (a,b) with zeros.

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4.3 - The Loop（循环体，对应神经网络单个隐层的功能）

Question: Implement forward_propagation().（前向传播）

Instructions:

• Look above at the mathematical representation of your classifier.
• You can use the function sigmoid(). It is built-in (imported) in the notebook.
• You can use the function np.tanh(). It is part of the numpy library.
• The steps you have to implement are:
  1. Retrieve each parameter from the dictionary "parameters" (which is the output of initialize_parameters()) by using parameters[".."].
  2. Implement Forward Propagation. Compute [1],[1],[2]Z[1],A[1],Z[2] and [2]A[2] (the vector of all your predictions on all the examples in the training set).
• Values needed in the backpropagation are stored in "cache". The cache will be given as an input to the backpropagation function.

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成本函数：

 

后向传播：

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选择合适的学习率并更新参数（即反向传播过程）：

Question: Implement the update rule. Use gradient descent. You have to use (dW1, db1, dW2, db2) in order to update (W1, b1, W2, b2).

General gradient descent rule: =−∂∂θ=θ−α∂J∂θ where α is the learning rate and θ represents a parameter.

Illustration: The gradient descent algorithm with a good learning rate (converging) and a bad learning rate (diverging). Images courtesy of Adam Harley.

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4.4 - Integrate parts 4.1, 4.2 and 4.3 in nn_model()（组装模型）

Question: Build your neural network model in nn_model().

Instructions: The neural network model has to use the previous functions in the right order.

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4.5 Predictions（使用模型计算预测值）

Question: Use your model to predict by building predict(). Use forward propagation to predict results.

Reminder: predictions = ={activation > 0.5}={10if >0.5otherwiseyprediction=1{activation > 0.5}={1if activation>0.50otherwise

As an example, if you would like to set the entries of a matrix X to 0 and 1 based on a threshold you would do: X_new = (X > threshold)

 

 

作业完整截屏：