用matlab实现神经网络识别数字

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，有待识别的数字全集如下：

其中每一个数字都是一个大小为20*20像素的图像，如果把每个像素作为一个输入单元，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，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，隐藏层也存在表示偏差的额外输入，所以一共有26个输入。

最终的输出结果是一个10维的向量，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，这里题目中把0标记为10，其余1-9还是对应1-9），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：

从上图可以看到，神经网络中除了输入参数外，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，为25*401的向量。Theta2是隐含层到输出层每条边的权重，为10*26的向量。

为了把数据标准化减少误差，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，首先是用训练数据进行训练，得出Theta1和Theta2的权重信息，然后就可以预测了。

主要的matlab代码如下：

%% 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.%%% Initializationclear ; close all; clc%% Setup the parameters you will use for this exerciseinput_layer_size  = 400;  % 20x20 Input Images of Digitshidden_layer_size = 25;   % 25 hidden unitsnum_labels = 10;          % 10 labels, from 1 to 10                             % (note that we have mapped "0" to label 10)%% =========== Part 1: Loading and Visualizing Data =============%  We start the exercise by first loading and visualizing the dataset. %  You will be working with a dataset that contains handwritten digits.%% Load Training Datafprintf('Loading and Visualizing Data ...\n')load('ex3data1.mat');m = size(X, 1);% Randomly select 100 data points to displaysel = randperm(size(X, 1));sel = sel(1:100);displayData(X(sel, :));fprintf('Program paused. Press enter to continue.\n');pause;%% ================ Part 2: Loading Pameters ================% In this part of the exercise, we load some pre-initialized % neural network parameters.fprintf('\nLoading Saved Neural Network Parameters ...\n')% Load the weights into variables Theta1 and Theta2load('ex3weights.mat');%% ================= Part 3: Implement Predict =================%  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 = predict(Theta1, Theta2, X);fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);fprintf('Program paused. Press enter to continue.\n');pause;%  To give you an idea of the network's output, you can also run%  through the examples one at the a time to see what it is predicting.%  Randomly permute examplesrp = randperm(m);for i = 1:m    % Display     fprintf('\nDisplaying Example Image\n');    displayData(X(rp(i), :));    pred = predict(Theta1, Theta2, X(rp(i),:));    fprintf('\nNeural Network Prediction: %d (digit %d)\n', pred, mod(pred, 10));        % Pause    fprintf('Program paused. Press enter to continue.\n');    pause;end

预测函数如下：

function p = predict(Theta1, Theta2, X)%PREDICT Predict the label of an input given a trained neural network%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the%   trained weights of a neural network (Theta1, Theta2)% Useful valuesm = size(X, 1);num_labels = size(Theta2, 1);% You need to return the following variables correctly p = zeros(size(X, 1), 1);% ====================== YOUR CODE HERE ======================% 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 'help max'. If your examples are in rows, then, you%       can use max(A, [], 2) to obtain the max for each row.%X = [ones(m, 1) X];predictZ=X*Theta1';predictZ=sigmoid(predictZ);predictZ=[ones(m,1) predictZ];predictZZ=predictZ*Theta2';predictY=sigmoid(predictZZ);[mp,imp]=max(predictY,[],2);p=imp;% =========================================================================end

最终运算截图如下：

最后与回归分析做个对比：

回归分析需要对每个数字训练一个分类器，这里需要训练10个，每一个分类器迭代50次，结果为：

显然神经网络准确率要比回归分析高，同时也要显得简洁很多，代码行数也明显减少，这也正是神经网络的优势所在。