机器学习——极限学习(ELM)matlab代码分析

Hello，大家好，我是小鹏同学。今天在一个网站(https://www.ntu.edu.sg/home/egbhuang/elm_random_hidden_nodes.html)上下载了基本的ELM的代码和训练集以及测试集，并阅读了一下代码，发现还是比较简单的，只要花点时间认真耐心阅读、在matlab上跑一跑应该都能很容易读懂。
好了，长话短说，我直接给出我在代码中加的注释吧，希望对大家理解ELM的Matlab代码有小小帮助。如果我在代码中的解释存在错误也欢迎大家指出。

1.对于分类的main.m(适合于二元及多元分类)

clear all;
close all;
clc;
[TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] =  ELM('diabetes_train', 'diabetes_test', 1, 20, 'sig')

2.对于回归的main.m

clear all;
close all;
clc;
[TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] =  ELM('sinc_train', 'sinc_test', 0, 20, 'sig')

3.核心代码ELM.m

function [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = ELM(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)

% Usage: elm(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)
% OR:    [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = elm(TrainingData_File, TestingData_File, Elm_Type, NumberofHiddenNeurons, ActivationFunction)
%
% Input:
% TrainingData_File     - Filename of training data set
% TestingData_File      - Filename of testing data set
% Elm_Type              - 0 for regression; 1 for (both binary and multi-classes) classification
% NumberofHiddenNeurons - Number of hidden neurons assigned to the ELM
% ActivationFunction    - Type of activation function:
%                           'sig' for Sigmoidal function
%                           'sin' for Sine function
%                           'hardlim' for Hardlim function
%                           'tribas' for Triangular basis function
%                           'radbas' for Radial basis function (for additive type of SLFNs instead of RBF type of SLFNs)
%
% Output: 
% TrainingTime          - Time (seconds) spent on training ELM
% TestingTime           - Time (seconds) spent on predicting ALL testing data
% TrainingAccuracy      - Training accuracy: 
%                           RMSE for regression or correct classification rate for classification
% TestingAccuracy       - Testing accuracy: 
%                           RMSE for regression or correct classification rate for classification
%
% MULTI-CLASSE CLASSIFICATION: NUMBER OF OUTPUT NEURONS WILL BE AUTOMATICALLY SET EQUAL TO NUMBER OF CLASSES
% FOR EXAMPLE, if there are 7 classes in all, there will have 7 output
% neurons; neuron 5 has the highest output means input belongs to 5-th class
%
% Sample1 regression: [TrainingTime, TestingTime, TrainingAccuracy, TestingAccuracy] = elm('sinc_train', 'sinc_test', 0, 20, 'sig')
% Sample2 classification: elm('diabetes_train', 'diabetes_test', 1, 20, 'sig')
%
    %%%%    Authors:    MR QIN-YU ZHU AND DR GUANG-BIN HUANG
    %%%%    NANYANG TECHNOLOGICAL UNIVERSITY, SINGAPORE
    %%%%    EMAIL:      EGBHUANG@NTU.EDU.SG; GBHUANG@IEEE.ORG
    %%%%    WEBSITE:    http://www.ntu.edu.sg/eee/icis/cv/egbhuang.htm
    %%%%    DATE:       APRIL 2004

%%%%%%%%%%% Macro definition 宏定义

REGRESSION=0;
CLASSIFIER=1;

%%%%%%%%%%% Load training dataset
train_data=load(TrainingData_File);
T=train_data(:,1)';                          %   First column are the expected output (target) for regression and classification applications  加了转置,大小为：1行*样本数量
P=train_data(:,2:size(train_data,2))';   %  获取属性列 加了转置
clear train_data;                                   %   Release raw training data array

%%%%%%%%%%% Load testing dataset
test_data=load(TestingData_File);
TV.T=test_data(:,1)';
TV.P=test_data(:,2:size(test_data,2))';
clear test_data;                                    %   Release raw testing data array

NumberofTrainingData=size(P,2);    %   训练集大小
NumberofTestingData=size(TV.P,2);  %   测试集大小
NumberofInputNeurons=size(P,1);   %   输入神经元数量，即属性个数

% 如果不是逻辑回归，即分类问题
if Elm_Type~=REGRESSION
    %%%%%%%%%%%% Preprocessing the data of classification
    sorted_target=sort(cat(2,T,TV.T),2);  %训练集和测试的标签连起来并按从小到大顺序排列，组成一个行向量
    label=zeros(1,1);                               %   Find and save in 'label' class label from training and testing data sets
    label(1,1)=sorted_target(1,1);
    j=1;
    for i = 2:(NumberofTrainingData+NumberofTestingData)  % 利用循环把第一类标签统一到（1，1）第二类统一到（1，2）, sorted_target已经从小到大排列
        if sorted_target(1,i) ~= label(1,j)
            j=j+1;
            label(1,j) = sorted_target(1,i);
        end
    end
    number_class=j;  % 类的数量
    NumberofOutputNeurons=number_class;  % 类的数量赋值给输出神经元的数量
    %%%%%%%%%% Processing the targets of training
    temp_T=zeros(NumberofOutputNeurons, NumberofTrainingData);  % 输出神经元组成矩阵的一列，用于暂时存储训练集的输出
    for i = 1:NumberofTrainingData  % 将每个训练样本的标签弄到temp_T里。如总共有5个类，第一个训练样本属于第二个类，则temp_T第一列为[0;1;0;0;0]
        for j = 1:number_class
            if label(1,j) == T(1,i)
                break; 
            end
        end
        temp_T(j,i)=1;
    end
    T=temp_T*2-1;  % temp_T矩阵的每个元素的数变化一下，如对于二分类，值为-1 或者1;T的大小变为标签数量*训练样本数量
    
    %%%%%%%%%% Processing the targets of testing  方法跟处理训练集标签一样
    temp_TV_T=zeros(NumberofOutputNeurons, NumberofTestingData);
    for i = 1:NumberofTestingData
        for j = 1:number_class
            if label(1,j) == TV.T(1,i)
                break; 
            end
        end
        temp_TV_T(j,i)=1;
    end
    TV.T=temp_TV_T*2-1;

end                                                 %   end if of Elm_Type

%%%%%%%%%%% Calculate weights & biases
start_time_train=cputime;  % 计算开始训练时刻，训练开始

%%%%%%%%%%% Random generate input weights InputWeight (w_i) and biases BiasofHiddenNeurons (b_i) of hidden neurons
%%%%%%%%%%% 随机产生隐层神经元的输入权 InputWeight (w_i)、偏置BiasofHiddenNeurons (b_i)
InputWeight=rand(NumberofHiddenNeurons,NumberofInputNeurons)*2-1;      % 输入权重是一个  隐层神经元数量*输入神经元数量  的矩阵，元素InputWeight(l,n)就表示输入n与隐层l之间的权重
                                                                                                                                                % NumberofHiddenNeurons由主函数指定，NumberofInputNeurons输入神经元的数量(即属性数量)由上面代码得到
BiasofHiddenNeurons=rand(NumberofHiddenNeurons,1);  % NumberofHiddenNeurons由主函数指定，BiasofHiddenNeurons是一个列向量，行数等于隐层神经元数量
tempH=InputWeight*P;  % tempH是一个隐层数*训练样本数的矩阵
clear P;                                            %   Release input of training data 
ind=ones(1,NumberofTrainingData);  % 元素为1的行向量
BiasMatrix=BiasofHiddenNeurons(:,ind);              %   Extend the bias matrix BiasofHiddenNeurons to match the demention of H. 
                                                                                       %  扩展偏置矩阵BiasofHiddenNeurons以匹配H的维数,有行数等于隐层列数等于1扩展成行数等于隐层列数等于训练样本数(与tempH一样)，没一行扩展的数据等于每行的第一个
tempH=tempH+BiasMatrix;  % tempH作用于一个函数即为隐层输出

%%%%%%%%%%% Calculate hidden neuron output matrix H (计算输出矩阵H)
switch lower(ActivationFunction)  % ActivationFunction由用户在主函数指定
    case {'sig','sigmoid'}
        %%%%%%%% Sigmoid 
        H = 1 ./ (1 + exp(-tempH));  % H即为隐层输出，是一个隐层数*训练样本数的矩阵
    case {'sin','sine'}
        %%%%%%%% Sine
        H = sin(tempH);    
    case {'hardlim'}
        %%%%%%%% Hard Limit
        H = double(hardlim(tempH));
    case {'tribas'}
        %%%%%%%% Triangular basis function
        H = tribas(tempH);
    case {'radbas'}
        %%%%%%%% Radial basis function
        H = radbas(tempH);
        %%%%%%%% More activation functions can be added here                
end
clear tempH;                                        %   Release the temparary array for calculation of hidden neuron output matrix H

%%%%%%%%%%% Calculate output weights OutputWeight (beta_i)
%%%%%%%%%%% 计算输出权重β(大小为：隐层数*标签数量),β(l,m)为隐层l与输出层m的权重
OutputWeight=pinv(H') * T';                        % implementation without regularization factor //refer to 2006 Neurocomputing paper
                                                                           % H是一个隐层数*训练样本数的矩阵；pinv(H')是求H的广义逆矩阵,大小也为隐层数*训练样本数
                                                                           % 标签矩阵T的大小在标签处理步骤中的85行变为：标签数量*训练样本数量，故OutputWeight(即笔记中的beta)大小为：隐层数*标签数量
%OutputWeight=inv(eye(size(H,1))/C+H * H') * H * T';   % faster method 1 //refer to 2012 IEEE TSMC-B paper
%implementation; one can set regularizaiton factor C properly in classification applications 
%OutputWeight=(eye(size(H,1))/C+H * H') \ H * T';      % faster method 2 //refer to 2012 IEEE TSMC-B paper
%implementation; one can set regularizaiton factor C properly in classification applications

%If you use faster methods or kernel method, PLEASE CITE in your paper properly: 

%Guang-Bin Huang, Hongming Zhou, Xiaojian Ding, and Rui Zhang, "Extreme Learning Machine for Regression and Multi-Class Classification," submitted to IEEE Transactions on Pattern Analysis and Machine Intelligence, October 2010. 

end_time_train=cputime;  % 训练完成，计算结束时刻
TrainingTime=end_time_train-start_time_train;         %   Calculate CPU time (seconds) spent for training ELM  计算训练耗时

%%%%%%%%%%% Calculate the training accuracy
Y=(H' * OutputWeight)';                                %   Y: the actual output of the training data. H是一个隐层数*训练样本数的矩阵；
                                                                            %  OutputWeight隐层数*标签数量,故Y的大小为:标签数量*训练样本数量，与真实标签矩阵大小一样
if Elm_Type == REGRESSION
    TrainingAccuracy=sqrt(mse(T - Y));               %   Calculate training accuracy (RMSE) for regression case
end
clear H;

%%%%%%%%%%% Calculate the output of testing input
start_time_test=cputime;  %  计算开始测试时刻
tempH_test=InputWeight*TV.P;
clear TV.P;             %   Release input of testing data             
ind=ones(1,NumberofTestingData);
BiasMatrix=BiasofHiddenNeurons(:,ind);              %   Extend the bias matrix BiasofHiddenNeurons to match the demention of H
tempH_test=tempH_test + BiasMatrix;
switch lower(ActivationFunction)
    case {'sig','sigmoid'}
        %%%%%%%% Sigmoid 
        H_test = 1 ./ (1 + exp(-tempH_test));
    case {'sin','sine'}
        %%%%%%%% Sine
        H_test = sin(tempH_test);        
    case {'hardlim'}
        %%%%%%%% Hard Limit
        H_test = hardlim(tempH_test);        
    case {'tribas'}
        %%%%%%%% Triangular basis function
        H_test = tribas(tempH_test);        
    case {'radbas'}
        %%%%%%%% Radial basis function
        H_test = radbas(tempH_test);        
        %%%%%%%% More activation functions can be added here        
end
TY=(H_test' * OutputWeight)';                       %   TY: the actual output of the testing data.  OutputWeight是用训练集训练出来的
end_time_test=cputime;  % 结束测试时刻
TestingTime=end_time_test-start_time_test;           %   Calculate CPU time (seconds) spent by ELM predicting the whole testing data

if Elm_Type == REGRESSION
    TestingAccuracy=sqrt(mse(TV.T - TY));            %   Calculate testing accuracy (RMSE) for regression case
end

if Elm_Type == CLASSIFIER  % 如果是classification问题
%%%%%%%%%% Calculate training & testing classification accuracy
    MissClassificationRate_Training=0;      %  在训练集中预测错误的样本数量
    MissClassificationRate_Testing=0;       %  在测试集中预测错误的样本数量

    % 计算TrainingAccuracy
    for i = 1 : size(T, 2)   % 真实标签矩阵T的大小在标签处理步骤中的85行变为：标签数量*训练样本数量，故for循环从1到样本数量，即遍历每个样本
        [x, label_index_expected]=max(T(:,i));  % T是真实标签矩阵。x存储最大值，label_index_expected存储所在位置号(即样本的类别) ; 如果总共有7个类别，将有7个输出神经元。神经元5的输出最高，意味着输入属于5类
        [x, label_index_actual]=max(Y(:,i));  % Y是对训练集预测的标签，TY是对测试机预测的标签
        if label_index_actual~=label_index_expected
            MissClassificationRate_Training=MissClassificationRate_Training+1;   % 如果预测错误，则MissClassificationRate_Training加1
        end
    end
    TrainingAccuracy=1-(MissClassificationRate_Training/size(T,2));  % 计算classification问题的训练精度；size(T,2)即为训练样本数量
    
    % 计算TestingAccuracy
    for i = 1 : size(TV.T, 2)
        [x, label_index_expected]=max(TV.T(:,i));
        [x, label_index_actual]=max(TY(:,i));
        if label_index_actual~=label_index_expected
            MissClassificationRate_Testing=MissClassificationRate_Testing+1;
        end
    end
    TestingAccuracy=1-MissClassificationRate_Testing/size(TV.T,2);  
end
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