机器学习___ELM，学习___elm
一.带有随机隐藏节点的单隐层前馈神经网络
1.相关条件：
- N个不同样本(
xi,ti ),xi =[xi1,xi2,xi3,........,xin]T ,ti =[ti1,ti2,ti3,........,tim]T - 第i个隐藏节点和输入节点间的权重向量：
wi=[wi1,wi2,........win]T - 第i个隐藏节点的阀值：
bi=[bi1,bi2,........bin]T - 第i个隐藏节点和输出节点间的权重向量：
βi=[βi1,βi2,........βin]T - 激活函数：g(x)
2.方程改写：
SLFNs ：
∑N‘i=1βig(wi∗xj+bi) =tj , 简写成：Hβ =T 其中
3.简易模型：
4.两个相关定理(可以自行证明)：
- 定理 1： 给定一个具有N个隐藏节点以及在任何区间都无限可导的激活函数的标准SLFN。对N个任意不同样本，，SLFN在随机产生的情况下，形成的隐藏层输出矩阵H是可逆的，且
- 定理 2. 对于任意小的，及在任何区间都无限可导的激活函数，对N个任意不同样本，，总存在个隐节点的SLFN，使得在随机产生的情况下。
二.SLFNs的最小范数的最小二乘(LS)
三.ELM算法
给定训练样本集合N个不同样本(
四.代码
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
REGRESSION=0;
CLASSIFIER=1;
%%%%%%%%%%% Load training dataset
train_data=load(TrainingData_File);
T=train_data(:,1)';
P=train_data(:,2:size(train_data,2))';
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);
NumberofTestingData=size(TV.P,2);
NumberofInputNeurons=size(P,1);
if Elm_Type~=REGRESSION
%%%%%%%%%%%% Preprocessing the data of classification
sorted_target=sort(cat(2,T,TV.T),2);
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)
if sorted_target(1,i) ~= label(1,j)
j=j+1;
label(1,j) = sorted_target(1,i);
end
end
number_class=j;
NumberofOutputNeurons=number_class;
%%%%%%%%%% Processing the targets of training
temp_T=zeros(NumberofOutputNeurons, NumberofTrainingData);
for i = 1:NumberofTrainingData
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;
%%%%%%%%%% Processing the targets of testing
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;
%%%%%%%%%%% Random generate input weights InputWeight (w_i) and biases BiasofHiddenNeurons (b_i) of hidden neurons
InputWeight=rand(NumberofHiddenNeurons,NumberofInputNeurons)*2-1;
BiasofHiddenNeurons=rand(NumberofHiddenNeurons,1);
tempH=InputWeight*P;
clear P; % Release input of training data
ind=ones(1,NumberofTrainingData);
BiasMatrix=BiasofHiddenNeurons(:,ind); % Extend the bias matrix BiasofHiddenNeurons to match the demention of H
tempH=tempH+BiasMatrix;
%%%%%%%%%%% Calculate hidden neuron output matrix H
switch lower(ActivationFunction)
case {'sig','sigmoid'}
%%%%%%%% Sigmoid
H = 1 ./ (1 + exp(-tempH));
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)
OutputWeight=pinv(H') * T'; % slower implementation
%OutputWeight=inv(eye(size(H,1))/C+H * H') * H * T'; % faster method 1
%implementation; one can set regularizaiton factor C properly in classification applications
%OutputWeight=(eye(size(H,1))/C+H * H') \ H * T'; % faster method 2
%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;
TrainingTime=end_time_train-start_time_train % Calculate CPU time (seconds) spent for training ELM
%%%%%%%%%%% Calculate the training accuracy
Y=(H' * OutputWeight)'; % Y: the actual output of the training data
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;
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
end_time_test=cputime;
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
%%%%%%%%%% Calculate training & testing classification accuracy
MissClassificationRate_Training=0;
MissClassificationRate_Testing=0;
for i = 1 : size(T, 2)
[x, label_index_expected]=max(T(:,i));
[x, label_index_actual]=max(Y(:,i));
if label_index_actual~=label_index_expected
MissClassificationRate_Training=MissClassificationRate_Training+1;
end
end
TrainingAccuracy=1-MissClassificationRate_Training/size(T,2)
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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