【UWB】ELM，Extreme Learning Machine
2021-10-20 10:40:41

% 任務(wù)2: ELM 網(wǎng)絡(luò)
% Date: 2021-10-15
% Author: Zhao-Jichao
clear
clc

%% 訓(xùn)練
% 導(dǎo)入數(shù)據(jù)集
data = [760,4550,4550,6300];    % 輸入數(shù)據(jù)
label = [500, 500, 880];    % 示教數(shù)據(jù)輸出

[N,n] = size(data);         % 返回輸入數(shù)據(jù)的維度

L = 7;        % 隱層節(jié)點(diǎn)個(gè)數(shù)
m = 3;          % 要分的類別數(shù)

% 初始化權(quán)重和偏置矩陣
W = rand(n,L)*2-1;                  % rand 隨機(jī)生成范圍是 (0,1)，*2-1運(yùn)算后為 (-1,1)
b_1 = rand(1,L);                    % 隨機(jī)生成 b 偏置矩陣
ind = ones(N,1); b = b_1(ind,:);    % 將生成的 b 矩陣擴(kuò)充成 N*L 維度的矩陣，為了計(jì)算
H = G(data*W+b);                    % 得到 H

beta = pinv(H)*label;       % 求解出來輸出權(quán)重 beta 的最小二乘解

output = H * beta;          % 計(jì)算實(shí)際輸出

%% 驗(yàn)證
validataData = [4580 6000 1290 3960];
G(validataData*W+b) * beta

%% 激活函數(shù)的定義
function out = G(in)
    out = 1./(1 + exp(-in));
%     out = x;
end

%% I. 清空環(huán)境變量
clear
clc

%% II. 訓(xùn)練集/測(cè)試集產(chǎn)生
% 1. 導(dǎo)入數(shù)據(jù)
load spectra_data.mat

% 2. 隨機(jī)產(chǎn)生訓(xùn)練集和測(cè)試集
temp = randperm(size(NIR,1));       % randperm 整數(shù)的隨機(jī)排列

% 訓(xùn)練集――50個(gè)樣本
P_train = NIR(temp(1:50),:)';       % 401x50
T_train = octane(temp(1:50),:)';    % 1x50

% 測(cè)試集――10個(gè)樣本
P_test = NIR(temp(51:end),:)';
T_test = octane(temp(51:end),:)';

% 有了隨機(jī)，效果更好

%% III. 數(shù)據(jù)歸一化
% 1. 訓(xùn)練集
[Pn_train,inputps] = mapminmax(P_train);
Pn_test = mapminmax('apply',P_test,inputps);

% 2. 測(cè)試集
[Tn_train,outputps] = mapminmax(T_train);
Tn_test = mapminmax('apply',T_test,outputps);

%% IV. ELM創(chuàng)建/訓(xùn)練
[IW,B,LW,TF,TYPE] = elmtrain(Pn_train,Tn_train,300,'sig',0);

%% V. ELM仿真測(cè)試
tn_sim = elmpredict(Pn_test,IW,B,LW,TF,TYPE);
% 1. 反歸一化
T_sim = mapminmax('reverse',tn_sim,outputps);

%% VI. 結(jié)果對(duì)比
result = [T_test' T_sim'];

% 1. 均方誤差
E = mse(T_sim - T_test);

% 2. 決定系數(shù)
N = length(T_test);
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)); 

%% VII. 繪圖
figure(1)
plot(1:N,T_test,'r-*',1:N,T_sim,'b:o')
grid on
legend('真實(shí)值','預(yù)測(cè)值')
xlabel('樣本編號(hào)')
ylabel('辛烷值')
string = {'測(cè)試集辛烷值含量預(yù)測(cè)結(jié)果對(duì)比(ELM)';['(mse = ' num2str(E) ' R^2 = ' num2str(R2) ')']};
title(string)


%%
function [IW,B,LW,TF,TYPE] = elmtrain(P,T,N,TF,TYPE)
% ELMTRAIN Create and Train a Extreme Learning Machine
% Syntax
% [IW,B,LW,TF,TYPE] = elmtrain(P,T,N,TF,TYPE)
% Description
% Input
% P   - Input Matrix of Training Set  (R*Q)
% T   - Output Matrix of Training Set (S*Q)
% N   - Number of Hidden Neurons (default = Q)
% TF  - Transfer Function:
%       'sig' for Sigmoidal function (default)
%       'sin' for Sine function
%       'hardlim' for Hardlim function
% TYPE - Regression (0,default) or Classification (1)
% Output
% IW  - Input Weight Matrix (N*R)
% B   - Bias Matrix  (N*1)
% LW  - Layer Weight Matrix (N*S)
% Example
% Regression:
% [IW,B,LW,TF,TYPE] = elmtrain(P,T,20,'sig',0)
% Y = elmtrain(P,IW,B,LW,TF,TYPE)
% Classification:
% [IW,B,LW,TF,TYPE] = elmtrain(P,T,20,'sig',1)
% Y = elmtrain(P,IW,B,LW,TF,TYPE)
% See also ELMPREDICT
% Yu Lei,11-7-2010
% Copyright www.matlabsky.com
% $Revision:1.0 $
if nargin < 2
    error('ELM:Arguments','Not enough input arguments.');
end
if nargin < 3
    N = size(P,2);
end
if nargin < 4
    TF = 'sig';
end
if nargin < 5
    TYPE = 0;
end
if size(P,2) ~= size(T,2)
    error('ELM:Arguments','The columns of P and T must be same.');
end
[R,Q] = size(P);
if TYPE  == 1
    T  = ind2vec(T);
end
[S,Q] = size(T);
% Randomly Generate the Input Weight Matrix
IW = rand(N,R) * 2 - 1;
% Randomly Generate the Bias Matrix
B = rand(N,1);
BiasMatrix = repmat(B,1,Q);
% Calculate the Layer Output Matrix H
tempH = IW * P + BiasMatrix;
switch TF
    case 'sig'
        H = 1 ./ (1 + exp(-tempH));
    case 'sin'
        H = sin(tempH);
    case 'hardlim'
        H = hardlim(tempH);
end
% Calculate the Output Weight Matrix
LW = pinv(H') * T';
end