神经网络字符识别matlab程序,用matlab实现神经网络识别数字|学步园

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。