Andrew Ng机器学习第四周的编程练习是用matlab实现一个神经网络对一幅图中的数字进行识别&＃xff0c;有待识别的数字全集如下&＃xff1a;
其中每一个数字都是一个大小为20*20像素的图像&＃xff0c;如果把每个像素作为一个输入单元&＃xff0c;那有400个输入。考虑到神经网络还需要增加一个额外输入单元表示偏差&＃xff0c;一共有401个输入单元。题目中给的训练数据X是一个5000*400的向量。
题目中要求包含一个25个节点的隐藏层&＃xff0c;隐藏层也存在表示偏差的额外输入&＃xff0c;所以一共有26个输入。
最终的输出结果是一个10维的向量&＃xff0c;分别表示该数字在0-9上面的概率值(由于没有0这个下标位&＃xff0c;这里题目中把0标记为10&＃xff0c;其余1-9还是对应1-9)&＃xff0c;找到其中概率最大的就是要识别的结果。
神经网络的结构如下&＃xff1a;
从上图可以看到&＃xff0c;神经网络中除了输入参数外&＃xff0c;还包含Theta1和Theta2两个参数。
其中的Theta1就表示输入层到隐含层中每条边的权重&＃xff0c;为25*401的向量。Theta2是隐含层到输出层每条边的权重&＃xff0c;为10*26的向量。
为了把数据标准化减少误差&＃xff0c;这里要对每一步的输出用sigmoid函数进行处理。
构造好神经网络后&＃xff0c;首先是用训练数据进行训练&＃xff0c;得出Theta1和Theta2的权重信息&＃xff0c;然后就可以预测了。
主要的matlab代码如下&＃xff1a;
%% Machine Learning Online Class - Exercise 3 | Part 2: Neural Networks
% Instructions
% ------------
%
% This file contains code that helps you get started on the
% linear exercise. You will need to complete the following functions
% in this exericse:
%
% lrCostFunction.m (logistic regression cost function)
% oneVsAll.m
% predictOneVsAll.m
% predict.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%
%% Initialization
clear ; close all; clc
%% Setup the parameters you will use for this exercise
input_layer_size &＃61; 400; % 20x20 Input Images of Digits
hidden_layer_size &＃61; 25; % 25 hidden units
num_labels &＃61; 10; % 10 labels, from 1 to 10
% (note that we have mapped "0" to label 10)
%% &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61; Part 1: Loading and Visualizing Data &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;
% We start the exercise by first loading and visualizing the dataset.
% You will be working with a dataset that contains handwritten digits.
%
% Load Training Data
fprintf(&＃39;Loading and Visualizing Data ...\n&＃39;)
load(&＃39;ex3data1.mat&＃39;);
m &＃61; size(X, 1);
% Randomly select 100 data points to display
sel &＃61; randperm(size(X, 1));
sel &＃61; sel(1:100);
displayData(X(sel, :));
fprintf(&＃39;Program paused. Press enter to continue.\n&＃39;);
pause;
%% &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61; Part 2: Loading Pameters &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;
% In this part of the exercise, we load some pre-initialized
% neural network parameters.
fprintf(&＃39;\nLoading Saved Neural Network Parameters ...\n&＃39;)
% Load the weights into variables Theta1 and Theta2
load(&＃39;ex3weights.mat&＃39;);
%% &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61; Part 3: Implement Predict &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;
% After training the neural network, we would like to use it to predict
% the labels. You will now implement the "predict" function to use the
% neural network to predict the labels of the training set. This lets
% you compute the training set accuracy.
pred &＃61; predict(Theta1, Theta2, X);
fprintf(&＃39;\nTraining Set Accuracy: %f\n&＃39;, mean(double(pred &＃61;&＃61; y)) * 100);
fprintf(&＃39;Program paused. Press enter to continue.\n&＃39;);
pause;
% To give you an idea of the network&＃39;s output, you can also run
% through the examples one at the a time to see what it is predicting.
% Randomly permute examples
rp &＃61; randperm(m);
for i &＃61; 1:m
% Display
fprintf(&＃39;\nDisplaying Example Image\n&＃39;);
displayData(X(rp(i), :));
pred &＃61; predict(Theta1, Theta2, X(rp(i),:));
fprintf(&＃39;\nNeural Network Prediction: %d (digit %d)\n&＃39;, pred, mod(pred, 10));
% Pause
fprintf(&＃39;Program paused. Press enter to continue.\n&＃39;);
pause;
end
预测函数如下&＃xff1a;
function p &＃61; predict(Theta1, Theta2, X)
%PREDICT Predict the label of an input given a trained neural network
% p &＃61; PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
% trained weights of a neural network (Theta1, Theta2)
% Useful values
m &＃61; size(X, 1);
num_labels &＃61; size(Theta2, 1);
% You need to return the following variables correctly
p &＃61; zeros(size(X, 1), 1);
% &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61; YOUR CODE HERE &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;
% Instructions: Complete the following code to make predictions using
% your learned neural network. You should set p to a
% vector containing labels between 1 to num_labels.
%
% Hint: The max function might come in useful. In particular, the max
% function can also return the index of the max element, for more
% information see &＃39;help max&＃39;. If your examples are in rows, then, you
% can use max(A, [], 2) to obtain the max for each row.
%
X &＃61; [ones(m, 1) X];
predictZ&＃61;X*Theta1&＃39;;
predictZ&＃61;sigmoid(predictZ);
predictZ&＃61;[ones(m,1) predictZ];
predictZZ&＃61;predictZ*Theta2&＃39;;
predictY&＃61;sigmoid(predictZZ);
[mp,imp]&＃61;max(predictY,[],2);
p&＃61;imp;
% &＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;&＃61;
end
最终运算截图如下&＃xff1a;
最后与回归分析做个对比&＃xff1a;
回归分析需要对每个数字训练一个分类器&＃xff0c;这里需要训练10个&＃xff0c;每一个分类器迭代50次&＃xff0c;结果为&＃xff1a;
显然神经网络准确率要比回归分析高&＃xff0c;同时也要显得简洁很多&＃xff0c;代码行数也明显减少&＃xff0c;这也正是神经网络的优势所在。
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