zoukankan      html  css  js  c++  java
  • 【MATLAB深度学习】卷积神经网络

     卷积神经网络

      深度神经网络的重要性在于,它开启了通向复杂非线性模型和对知识进行分层处理的系统方法的大门。人们开发了很多提取图像特征的技术:SIFT、HoG、Textons、图像旋转、RIFT、GLOH等。卷积神经网络的特点和优势在于自动提取特征。

      卷积层生成特征映射图(feature map)的新图像,其突出了原始图像的独特特征。卷积滤波器矩阵的值时通过训练过程确定的。

      池化是一种在其他许多图像处理处理方法中采用的典型技术。池化层在一定程度上补偿了目标的偏心和倾斜。由于池化缩减了图像大小,它对减轻计算负载和防止过拟合是非常有益的。

    MNIST示例

      60000幅图像用于训练,10000幅图像用于测试,每幅都是28*28黑白图像。本例使用10000幅图像,训练测试比为8:2。网络结果如下表所示:

    备注 激活函数
    输入层 28*28个节点  
    卷积层 20个9*9卷积滤波器 ReLU
    池化层 一个平均池化(2*2)  
    隐含层 100个节点 ReLU
    输出层 10个节点 Softmax

      网络结构定义如下:

    function [W1, W5, Wo] = MnistConv(W1, W5, Wo, X, D)
    % W1,W5,W0分别是卷积滤波器矩阵、池化-隐含层权重矩阵和隐含-输出层权重矩阵
    % 使用反向传播算法、minibatch方法训练网络
    % 使用动量来调整权重
    
    alpha = 0.01;
    beta  = 0.95;
    
    momentum1 = zeros(size(W1));
    momentum5 = zeros(size(W5));
    momentumo = zeros(size(Wo));
    
    N = length(D);
    
    % minibatch
    bsize = 100;  
    blist = 1:bsize:(N-bsize+1);
    
    % One epoch loop
    %
    for batch = 1:length(blist)
      dW1 = zeros(size(W1));
      dW5 = zeros(size(W5));
      dWo = zeros(size(Wo));
      
      % Mini-batch loop
      % 对100个权重更新值求和并取平均值
      begin = blist(batch);
      for k = begin:begin+bsize-1
        % Forward pass = inference
        %
        x  = X(:, :, k);               % Input,           28x28
        y1 = Conv(x, W1);              % Convolution,  20x20x20
        y2 = ReLU(y1);                 %
        y3 = Pool(y2);                 % Pooling,      10x10x20
        y4 = reshape(y3, [], 1);       %
        v5 = W5*y4;                    % ReLU,             2000
        y5 = ReLU(v5);                 %
        v  = Wo*y5;                    % Softmax,          10x1
        y  = Softmax(v);               %
    
        % One-hot encoding
        %
        d = zeros(10, 1);
        d(sub2ind(size(d), D(k), 1)) = 1;
    
        % Backpropagation
        %
        e      = d - y;                   % Output layer  
        delta  = e;
    
        e5     = Wo' * delta;             % Hidden(ReLU) layer
        delta5 = (y5 > 0) .* e5;
    
        e4     = W5' * delta5;            % Pooling layer
        
        e3     = reshape(e4, size(y3));
    
        e2 = zeros(size(y2));           
        W3 = ones(size(y2)) / (2*2);
        for c = 1:20
          e2(:, :, c) = kron(e3(:, :, c), ones([2 2])) .* W3(:, :, c);
        end
        
        delta2 = (y2 > 0) .* e2;          % ReLU layer
      
        delta1_x = zeros(size(W1));       % Convolutional layer
        for c = 1:20
          delta1_x(:, :, c) = conv2(x(:, :), rot90(delta2(:, :, c), 2), 'valid');
        end
        
        dW1 = dW1 + delta1_x; 
        dW5 = dW5 + delta5*y4';    
        dWo = dWo + delta *y5';
      end 
      
      % Update weights
      %
      dW1 = dW1 / bsize;
      dW5 = dW5 / bsize;
      dWo = dWo / bsize;
      
      % 动量
      momentum1 = alpha*dW1 + beta*momentum1;
      W1        = W1 + momentum1;
      
      momentum5 = alpha*dW5 + beta*momentum5;
      W5        = W5 + momentum5;
       
      momentumo = alpha*dWo + beta*momentumo;
      Wo        = Wo + momentumo;  
    end
    
    end
    

      其中卷积定义为:

    function y = Conv(x, W)
    % 接受输入图像和卷积和卷积滤波器矩阵,返回特征映射图
    %
    
    [wrow, wcol, numFilters] = size(W);
    [xrow, xcol, ~         ] = size(x);
    
    yrow = xrow - wrow + 1;
    ycol = xcol - wcol + 1;
    
    y = zeros(yrow, ycol, numFilters);
    
    for k = 1:numFilters
      filter = W(:, :, k); 
      filter = rot90(squeeze(filter), 2);
      y(:, :, k) = conv2(x, filter, 'valid');
    end
    
    end
    

      池化定义为:

    function y = Pool(x)
    %     
    % 2x2 mean pooling
    %
    %
    [xrow, xcol, numFilters] = size(x);
    
    y = zeros(xrow/2, xcol/2, numFilters);
    for k = 1:numFilters
      filter = ones(2) / (2*2);    % for mean    
      image  = conv2(x(:, :, k), filter, 'valid');
      
      y(:, :, k) = image(1:2:end, 1:2:end);
    end
    
    end
     
    

      测试代码如下:

    clear all
    
    Images = loadMNISTImages('./MNIST/t10k-images.idx3-ubyte');
    Images = reshape(Images, 28, 28, []);
    Labels = loadMNISTLabels('./MNIST/t10k-labels.idx1-ubyte');
    Labels(Labels == 0) = 10;    % 0 --> 10
    
    rng(1);
    
    % Learning
    %
    W1 = 1e-2*randn([9 9 20]);
    W5 = (2*rand(100, 2000) - 1) * sqrt(6) / sqrt(360 + 2000);
    Wo = (2*rand( 10,  100) - 1) * sqrt(6) / sqrt( 10 +  100);
    
    X = Images(:, :, 1:8000);
    D = Labels(1:8000);
    
    for epoch = 1:3
      epoch
      [W1, W5, Wo] = MnistConv(W1, W5, Wo, X, D);
    end
    
    save('MnistConv.mat');
    
    
    % Test
    %
    X = Images(:, :, 8001:10000);
    D = Labels(8001:10000);
    
    acc = 0;
    N   = length(D);
    for k = 1:N
      x = X(:, :, k);                   % Input,           28x28
    
      y1 = Conv(x, W1);                 % Convolution,  20x20x20
      y2 = ReLU(y1);                    %
      y3 = Pool(y2);                    % Pool,         10x10x20
      y4 = reshape(y3, [], 1);          %                   2000  
      v5 = W5*y4;                       % ReLU,              360
      y5 = ReLU(v5);                    %
      v  = Wo*y5;                       % Softmax,            10
      y  = Softmax(v);                  %
    
      [~, i] = max(y);
      if i == D(k)
        acc = acc + 1;
      end
    end
    
    acc = acc / N;
    fprintf('Accuracy is %f
    ', acc);
    

      三轮运算后,结果为Accuracy is 0.946500。同时生成MnistConv.mat文件。下面分析图像在卷积神经网络每一层中的实际演变过程。代码如下:

    clear all
    
    load('MnistConv.mat')
    
    k  = 2;
    x  = X(:, :, k);
    y1 = Conv(x, W1);                 % Convolution,  20x20x20
    y2 = ReLU(y1);                    %
    y3 = Pool(y2);                    % Pool,         10x10x20
    y4 = reshape(y3, [], 1);          %                   2000  
    v5 = W5*y4;                       % ReLU,              360
    y5 = ReLU(v5);                    %
    v  = Wo*y5;                       % Softmax,            10
    y  = Softmax(v);                  %
      
    
    figure;
    display_network(x(:));
    title('Input Image')
    
    convFilters = zeros(9*9, 20);
    for i = 1:20
      filter            = W1(:, :, i);
      convFilters(:, i) = filter(:);
    end
    figure
    display_network(convFilters);
    title('Convolution Filters')
    
    fList = zeros(20*20, 20);
    for i = 1:20
      feature     = y1(:, :, i);
      fList(:, i) = feature(:);
    end
    figure
    display_network(fList);
    title('Features [Convolution]')
    
    fList = zeros(20*20, 20);
    for i = 1:20
      feature     = y2(:, :, i);
      fList(:, i) = feature(:);
    end
    figure
    display_network(fList);
    title('Features [Convolution + ReLU]')
    
    fList = zeros(10*10, 20);
    for i = 1:20
      feature     = y3(:, :, i);
      fList(:, i) = feature(:);
    end
    figure
    display_network(fList);
    title('Features [Convolution + ReLU + MeanPool]')
    

      输出的结果为:

    图1

    图2

      图2是20个经过训练的卷积滤波器组成。值越大,阴影越亮。

    图3

      图3呈现的是卷积层图像处理的结果。

    图4

      图4是卷积层采用ReLU处理特征映射图所得的结果。去除之前图像中的暗色像素,当前图像的字符主要是白色像素。但其中有一个格子变暗了,这不是一个好现象,因为它未能捕捉到输入图像“2”的任何特征。

    图5

      图5显示的是特征提取神经网络的最终结果。这些图像被转换为一个一维向量,并存储在分类神经网络中。

      上述代码中用到的辅助函数如下:

    function images = loadMNISTImages(filename)
    %loadMNISTImages returns a 28x28x[number of MNIST images] matrix containing
    %the raw MNIST images
    
    fp = fopen(filename, 'rb');
    assert(fp ~= -1, ['Could not open ', filename, '']);
    
    magic = fread(fp, 1, 'int32', 0, 'ieee-be');
    assert(magic == 2051, ['Bad magic number in ', filename, '']);
    
    numImages = fread(fp, 1, 'int32', 0, 'ieee-be');
    numRows = fread(fp, 1, 'int32', 0, 'ieee-be');
    numCols = fread(fp, 1, 'int32', 0, 'ieee-be');
    
    images = fread(fp, inf, 'unsigned char=>unsigned char');
    images = reshape(images, numCols, numRows, numImages);
    images = permute(images,[2 1 3]);
    
    fclose(fp);
    
    % Reshape to #pixels x #examples
    images = reshape(images, size(images, 1) * size(images, 2), size(images, 3));
    % Convert to double and rescale to [0,1]
    images = double(images) / 255;
    
    end
    
    function labels = loadMNISTLabels(filename)
    %loadMNISTLabels returns a [number of MNIST images]x1 matrix containing
    %the labels for the MNIST images
    
    fp = fopen(filename, 'rb');
    assert(fp ~= -1, ['Could not open ', filename, '']);
    
    magic = fread(fp, 1, 'int32', 0, 'ieee-be');
    assert(magic == 2049, ['Bad magic number in ', filename, '']);
    
    numLabels = fread(fp, 1, 'int32', 0, 'ieee-be');
    
    labels = fread(fp, inf, 'unsigned char');
    
    assert(size(labels,1) == numLabels, 'Mismatch in label count');
    
    fclose(fp);
    
    end
    
    function [h, array] = display_network(A, opt_normalize, opt_graycolor, cols, opt_colmajor)
    % This function visualizes filters in matrix A. Each column of A is a
    % filter. We will reshape each column into a square image and visualizes
    % on each cell of the visualization panel. 
    % All other parameters are optional, usually you do not need to worry
    % about it.
    % opt_normalize: whether we need to normalize the filter so that all of
    % them can have similar contrast. Default value is true.
    % opt_graycolor: whether we use gray as the heat map. Default is true.
    % cols: how many columns are there in the display. Default value is the
    % squareroot of the number of columns in A.
    % opt_colmajor: you can switch convention to row major for A. In that
    % case, each row of A is a filter. Default value is false.
    warning off all
    
    if ~exist('opt_normalize', 'var') || isempty(opt_normalize)
        opt_normalize= true;
    end
    
    if ~exist('opt_graycolor', 'var') || isempty(opt_graycolor)
        opt_graycolor= true;
    end
    
    if ~exist('opt_colmajor', 'var') || isempty(opt_colmajor)
        opt_colmajor = false;
    end
    
    % rescale
    A = A - mean(A(:));
    
    if opt_graycolor, colormap(gray); end
    
    % compute rows, cols
    [L M]=size(A);
    sz=sqrt(L);
    buf=1;
    if ~exist('cols', 'var')
        if floor(sqrt(M))^2 ~= M
            n=ceil(sqrt(M));
            while mod(M, n)~=0 && n<1.2*sqrt(M), n=n+1; end
            m=ceil(M/n);
        else
            n=sqrt(M);
            m=n;
        end
    else
        n = cols;
        m = ceil(M/n);
    end
    
    array=-ones(buf+m*(sz+buf),buf+n*(sz+buf));
    
    if ~opt_graycolor
        array = 0.1.* array;
    end
    
    
    if ~opt_colmajor
        k=1;
        for i=1:m
            for j=1:n
                if k>M, 
                    continue; 
                end
                clim=max(abs(A(:,k)));
                if opt_normalize
                    array(buf+(i-1)*(sz+buf)+(1:sz),buf+(j-1)*(sz+buf)+(1:sz))=reshape(A(:,k),sz,sz)/clim;
                else
                    array(buf+(i-1)*(sz+buf)+(1:sz),buf+(j-1)*(sz+buf)+(1:sz))=reshape(A(:,k),sz,sz)/max(abs(A(:)));
                end
                k=k+1;
            end
        end
    else
        k=1;
        for j=1:n
            for i=1:m
                if k>M, 
                    continue; 
                end
                clim=max(abs(A(:,k)));
                if opt_normalize
                    array(buf+(i-1)*(sz+buf)+(1:sz),buf+(j-1)*(sz+buf)+(1:sz))=reshape(A(:,k),sz,sz)/clim;
                else
                    array(buf+(i-1)*(sz+buf)+(1:sz),buf+(j-1)*(sz+buf)+(1:sz))=reshape(A(:,k),sz,sz);
                end
                k=k+1;
            end
        end
    end
    
    if opt_graycolor
        h=imagesc(array,'EraseMode','none',[-1 1]);
    else
        h=imagesc(array,'EraseMode','none',[-1 1]);
    end
    axis image off
    
    drawnow;
    
    warning on all
    
    function rng(x)
      randn('seed', x)
      rand('seed', x)
    end
    
    function y = Softmax(x)
      ex = exp(x);
      y  = ex / sum(ex);
    end
    function y = ReLU(x)
      y = max(0, x);
    end
    
  • 相关阅读:
    204. Count Primes (Integer)
    203. Remove Linked List Elements (List)
    202. Happy Number (INT)
    201. Bitwise AND of Numbers Range (Bit)
    200. Number of Islands (Graph)
    199. Binary Tree Right Side View (Tree, Stack)
    198. House Robber(Array; DP)
    191. Number of 1 Bits (Int; Bit)
    190. Reverse Bits (Int; Bit)
    189. Rotate Array(Array)
  • 原文地址:https://www.cnblogs.com/Negan-ZW/p/9613896.html
Copyright © 2011-2022 走看看