基于MATLAB的MNIST手写体数字识别

### 使用MATLAB实现MNIST手写体数字识别

#### 加载并预处理MNIST数据集
在开始之前，需要加载和准备MNIST数据集。该数据集被称为手写数字的MNIST数据库[^3]。

% 下载并解压MNIST数据集
url = 'http://yann.lecun.com/exdb/mnist/';
files = {'train-images-idx3-ubyte.gz', 'train-labels-idx1-ubyte.gz',...
         't10k-images-ubyte.gz', 't10k-labels-ubyte.gz'};
for i = 1:length(files)
    if ~exist(files{i}(1:end-3), 'file')
        websave(files{i}, [url files{i}]);
        gunzip(files{i});
    end
end

% 定义读取函数来解析二进制文件
function [images, labels] = load_mnist_data(image_file, label_file)
    fid = fopen(label_file,'r','b');
    magic_num = fread(fid,1,'int32',0,'ieee-be'); %#ok<UNRCH>
    size_labels = fread(fid,1,'int32',0,'ieee-be');
    labels = fread(fid,[size_labels,1],'unsigned char')';
    
    fid = fopen(image_file,'r','b');
    magic_num = fread(fid,1,'int32',0,'ieee-be'); %#ok<UNRCH>
    size_images = fread(fid,1,'int32',0,'ieee-be');
    rows = fread(fid,1,'int32',0,'ieee-be');
    cols = fread(fid,1,'int32',0,'ieee-be');
    images = reshape(fread(fid,size_images*rows*cols,'unsigned char'),...
                     cols,rows,size_images);
    fclose('all');
end

[trainImages, trainLabels] = load_mnist_data('train-images-ubyte', ...
                                             'train-ubyte');

disp(['Training set dimensions:', num2str(size(trainImages))])
disp(['Test set dimensions:' ,num2str(size(testImages))])

% 显示一些样本图像
figure;
montage(mat2cell(double(trainImages(:,:,1:8)),28,28,ones(1,8)));
title('Sample Training Images from MNIST Dataset')

#### 构建神经网络模型
接下来构建一个多层感知器（MLP），用于对手写数字进行分类。

hiddenLayerSize = 100;

net = patternnet(hiddenLayerSize);

% 设置训练参数
net.trainParam.showWindow = false;
net.trainParam.epochs = 50;
net.trainParam.goal = 1e-6;

% 准备输入向量形式的数据
trainData = double(reshape(trainImages,[],size(trainImages,3)))'/255;
testData = double(reshape(testImages,[],size(testImages,3)))'/255;

% 训练网络
[trainedNet,tr] = train(net,trainData,trainLabels);

% 测试性能
predictedLabels = vec2ind(trainedNet(testData));
accuracy = sum(predictedLabels == testLabels)/length(testLabels)*100;
fprintf('Accuracy on the testing dataset is %.2f%%.\n', accuracy);

#### 创建图形界面(GUI)供用户绘制自己的数字
为了使应用程序更加友好，可以创建一个简单的GUI让用户能够画出自定义的手写字母，并通过已训练好的模型预测其类别[^1]。

function create_gui()
    f = uifigure('Position',[300 300 400 400],...
                 'Name','Handwritten Digit Recognition GUI');
                 
    ax = uiaxes(f,...
                'Units','normalized',...
                'Position',[0.1 0.1 0.7 0.7]);

    btnClear = uibutton(f,'Text','Clear',...
                       'Position',[290 200 80 22],...
                       'ButtonPushedFcn',{@clear_canvas,f});

    btnSave = uibutton(f,'Text','Predict',...
                      'Position',[290 150 80 22],...
                      'ButtonPushedFcn',{@predict_digit,f,ax});

    % 初始化绘图区域状态变量
    guidata(f,struct('drawingMode',false));

    % 绘制事件监听器
    addlistener(ax,'ButtonDownFcn',@(src,event)start_drawing(src,event,f));
    addlistener(ax,'WindowButtonMotionFcn',@(src,event)motion_handler(src,event,f));
    addlistener(ax,'WindowButtonUpFcn', @(src,event)stop_drawing(src,event,f));
end

function start_drawing(~,eventdata,hObject)
    handles = guidata(hObject);
    handles.drawingMode = true;
    guidata(hObject,handles);
end

function motion_handler(~, eventdata, hObject)
    handles = guidata(hObject);
    if handles.drawingMode
        pos = get(gca,'CurrentPoint');
        line([pos(1,1);pos(2,1)], [pos(1,2);pos(2,2)],'Color','w',...
             'LineWidth',10,'Parent',gca);
    end
end

function stop_drawing(~, eventdata, hObject)
    handles = guidata(hObject);
    handles.drawingMode = false;
    guidata(hObject,handles);
end

function clear_canvas(~,~,hObject)
    cla(hObject.Children{1},'reset');
end

function predict_digit(~,~,hObject,axesHandle)
    img = flipud(getframe(axesHandle).cdata);
    grayImg = rgb2gray(img);
    bwImg = imbinarize(grayImg);
    resizedImg = imresize(bwImg,[28 28]);
    inputVector = double(resizedImg(:))/255;
    
    prediction = trainedNet(inputVector)';
    predictedLabel = find(prediction==max(prediction))-1;
    msgbox(sprintf('The recognized digit is:%d',predictedLabel),'Prediction Result');
end