MATLAB机器学习系列-5 RBF、GRNN和PNN神经网络原理及其例子代码

ゝ一纸荒年。 2022-12-18 06:56 228阅读 0赞

## RBF(径向基神经网络） ##

![20201026093253732.png][] ![20201026093337812.png][] ![2020102609340663.png][] ![20201026093450767.png][]

## GRNN广义神经网络 ##

![20201026135751160.png][] ![20201026135843567.png][]

## PNN概率神经网络 ##

![20201026140002422.png][] ![20201026140039817.png][]

## **RBF算例实现（回归）** ##

数据集

% 1. 导入数据  
load spectra\_data.mat  
NIR输入，octane输出  
![20201026140933534.png][]

%% I. 清空环境变量
    clear all
    clc
    
    %% II. 训练集/测试集产生
    %%
    % 1. 导入数据
    load spectra_data.mat
    
    %%
    % 2. 随机产生训练集和测试集
    temp = randperm(size(NIR,1));
    % 训练集——50个样本
    P_train = NIR(temp(1:50),:)';
    T_train = octane(temp(1:50),:)';
    % 测试集——10个样本
    P_test = NIR(temp(51:end),:)';
    T_test = octane(temp(51:end),:)';
    N = size(P_test,2);
    
    %% III. RBF神经网络创建及仿真测试
    %%
    % 1. 创建网络
    net = newrbe(P_train,T_train,30);%30为speend
    
    %%
    % 2. 仿真测试
    T_sim = sim(net,P_test);
    
    %% IV. 性能评价
    %%
    % 1. 相对误差error
    error = abs(T_sim - T_test)./T_test;
    
    %%
    % 2. 决定系数R^2
    R2 = (N * sum(T_sim .* T_test) - sum(T_sim) * sum(T_test))^2 / ((N * sum((T_sim).^2) - (sum(T_sim))^2) * (N * sum((T_test).^2) - (sum(T_test))^2)); 
    
    %%
    % 3. 结果对比
    result = [T_test' T_sim' error']
    
    %% V. 绘图
    figure
    plot(1:N,T_test,'b:*',1:N,T_sim,'r-o')
    legend('真实值','预测值')
    xlabel('预测样本')
    ylabel('辛烷值')
    string = { '测试集辛烷值含量预测结果对比';['R^2=' num2str(R2)]};
    title(string)

![20201026141108846.png][] ![20201026141138579.png][]

## **GRNN和PNN神经网络(分类）** ##

数据集：经典案例鸢尾花分类  
![20201026142809549.png][]

feature有4维数据：花萼长度，花萼宽度，花瓣长度，花瓣宽度

classes花的种类  
‘setosa’, ‘versicolor’, ‘virginica’

%% I. 清空环境变量
    clear all
    clc
    
    %% II. 训练集/测试集产生
    %%
    % 1. 导入数据
    load iris_data.mat
    
    %%
    % 2 随机产生训练集和测试集
    P_train = [];
    T_train = [];
    P_test = [];
    T_test = [];
    for i = 1:3
        temp_input = features((i-1)*50+1:i*50,:);
        temp_output = classes((i-1)*50+1:i*50,:);
        n = randperm(50);
        % 训练集——120个样本
        P_train = [P_train temp_input(n(1:40),:)'];
        T_train = [T_train temp_output(n(1:40),:)'];
        % 测试集——30个样本
        P_test = [P_test temp_input(n(41:50),:)'];
        T_test = [T_test temp_output(n(41:50),:)'];
    end
    
    %% III. 模型建立 
    result_grnn = [];
    result_pnn = [];
    time_grnn = [];
    time_pnn = [];
    for i = 1:4
        for j = i:4
            p_train = P_train(i:j,:);
            p_test = P_test(i:j,:);
           %% 
            % 1. GRNN创建及仿真测试
            t = cputime;
            % 创建网络
            net_grnn = newgrnn(p_train,T_train);
            % 仿真测试
            t_sim_grnn = sim(net_grnn,p_test);
            T_sim_grnn = round(t_sim_grnn);%取整操作，因为是分类，目标是整数
            t = cputime - t;
            time_grnn = [time_grnn t];
            result_grnn = [result_grnn T_sim_grnn'];
           %%
            % 2. PNN创建及仿真测试
            t = cputime;
            Tc_train = ind2vec(T_train);
            % 创建网络
            net_pnn = newpnn(p_train,Tc_train);
            % 仿真测试
            Tc_test = ind2vec(T_test);
            t_sim_pnn = sim(net_pnn,p_test);
            T_sim_pnn = vec2ind(t_sim_pnn);
            t = cputime - t;
            time_pnn = [time_pnn t];
            result_pnn = [result_pnn T_sim_pnn'];
        end
    end
    
    %% IV. 性能评价
    %%
    % 1. 正确率accuracy
    accuracy_grnn = [];
    accuracy_pnn = [];
    time = [];
    for i = 1:10
        accuracy_1 = length(find(result_grnn(:,i) == T_test'))/length(T_test);
        accuracy_2 = length(find(result_pnn(:,i) == T_test'))/length(T_test);
        accuracy_grnn = [accuracy_grnn accuracy_1];
        accuracy_pnn = [accuracy_pnn accuracy_2];
    end
    
    %%
    % 2. 结果对比
    result = [T_test' result_grnn result_pnn]
    accuracy = [accuracy_grnn;accuracy_pnn]
    time = [time_grnn;time_pnn]
    
    %% V. 绘图
    figure(1)
    plot(1:30,T_test,'bo',1:30,result_grnn(:,4),'r-*',1:30,result_pnn(:,4),'k:^')
    grid on
    xlabel('测试集样本编号')
    ylabel('测试集样本类别')
    string = { '测试集预测结果对比(GRNN vs PNN)';['正确率:' num2str(accuracy_grnn(4)*100) '%(GRNN) vs ' num2str(accuracy_pnn(4)*100) '%(PNN)']};
    title(string)
    legend('真实值','GRNN预测值','PNN预测值')
    figure(2)
    plot(1:10,accuracy(1,:),'r-*',1:10,accuracy(2,:),'b:o')
    grid on
    xlabel('模型编号')
    ylabel('测试集正确率')
    title('10个模型的测试集正确率对比(GRNN vs PNN)')
    legend('GRNN','PNN')
    figure(3)
    plot(1:10,time(1,:),'r-*',1:10,time(2,:),'b:o')
    grid on
    xlabel('模型编号')
    ylabel('运行时间(s)')
    title('10个模型的运行时间对比(GRNN vs PNN)')
    legend('GRNN','PNN')

![2020102614361413.png][] ![20201026143654293.png][] ![20201026143726124.png][]

代码解析：  
因为花有三种，所以需要分段划分

for i = 1:3
        temp_input = features((i-1)*50+1:i*50,:);
        temp_output = classes((i-1)*50+1:i*50,:);
        n = randperm(50);
        % 训练集——120个样本
        P_train = [P_train temp_input(n(1:40),:)'];
        T_train = [T_train temp_output(n(1:40),:)'];
        % 测试集——30个样本
        P_test = [P_test temp_input(n(41:50),:)'];
        T_test = [T_test temp_output(n(41:50),:)'];
    end

因为花有四个特征，我们将两两特征组合

for i = 1:4
        for j = i:4
         p_train = P_train(i:j,:);
         p_test = P_test(i:j,:);

代码和数据百度云

链接：https://pan.baidu.com/s/1Z1txLCFJ_Iif_skcb57PiQ 
    提取码：yn6c 
    复制这段内容后打开百度网盘手机App，操作更方便哦

![在这里插入图片描述][20201026150732339.jpg_pic_center]  
作者：电气工程计算机萌新：余登武  
![在这里插入图片描述][20201026150823939.gif_pic_center]

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