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PCA_GP_RDA.m
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PCA_GP_RDA.m
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function [RMSEtrain,RMSEtest,CB,SigmaB,WB,fB]=PCA_GP_RDA(XTrain,yTrain,XTest,yTest,alpha,rr,P,nMFs,nIt,Nbs,C0,Sigma0,W0)
% This function implements the MBGD-RDA algorithm in the following paper:
%
% Dongrui Wu, Ye Yuan, Jian Huang and Yihua Tan, "Optimize TSK Fuzzy Systems for Regression Problems:
% Mini-Batch Gradient Descent with Regularization, DropRule and AdaBound (MBGD-RDA)," IEEE Trans.
% on Fuzzy Systems, 2020, accepted.
%
% It specifies the number of Gaussian MFs in each input domain by nMFs.
% Assume x1 has two MFs X1_1 and X1_2; then, all rules involving the first FS of x1 use the same X1_1,
% and all rules involving the second FS of x1 use the same X1_2
%
% By Dongrui Wu, drwu@hust.edu.cn
%
% %% Inputs:
% XTrain: N*M matrix of the training inputs. N is the number of samples, and M the feature dimensionality.
% yTrain: N*1 vector of the labels for XTrain
% XTest: {NValidation*M, NTest*M} matrix cell of the validation and test inputs
% yTest: {NValidation*1, NTest*1} vector cell of the labels for XTest
% alpha: scalar, initial learning rate
% rr: scalar, L2 regularization coefficient
% P: scalar, DropRule preservation rate
% nMFs: scalar, number of MFs in each input domain
% nIt: scalar, maximum number of iterations
% Nbs: batch size. typically 32 or 64
% C0: nRules*M initialization matrix of the centers of the Gaussian MFs
% Sigma0: nRules*M initialization matrix of the standard deviations of the Gaussian MFs
% W0: nRules*(M+1) initialization matrix of the consequent parameters for the nRules rules
%
% %% Outputs:
% RMSEtrain: 1*nIt vector of the training RMSE at different iterations
% RMSEtest: {1*nIt, 1*nIt} vector cell of the validation and test RMSE at different iterations
% CB: nRules*M matrix of the centers of the Gaussian MFs
% SigmaB: nRules*M matrix of the standard deviations of the Gaussian MFs
% WB: nRules*(M+1) matrix of the consequent parameters for the nRules rules
% fB: 1*nRules vector of the firing levels for validation inputs
beta1=0.9; beta2=0.999; thre=inf;
if ~iscell(XTest)
XTest={XTest};
yTest={yTest};
end
[N,M]=size(XTrain);
if Nbs>N; Nbs=N; end
nRules=nMFs^M; % number of rules
if nargin<11
C0=zeros(M,nMFs); Sigma0=C0; W0=zeros(nRules,M+1);
for m=1:M % Initialization
C0(m,:)=linspace(min(XTrain(:,m)),max(XTrain(:,m)),nMFs);
Sigma0(m,:)=std(XTrain(:,m));
end
end
C=C0; Sigma=Sigma0; W=W0;
minSigma=min(Sigma(:));
[CB,SigmaB,WB,fB]=deal(C,Sigma,W,zeros(1,nRules));
%% Iterative update
RMSEtrain=zeros(1,nIt); RMSEtest=cellfun(@(u)RMSEtrain,XTest,'UniformOutput',false);
mC=0; vC=0; mW=0; mSigma=0; vSigma=0; vW=0; yPred=nan(Nbs,1);
for it=1:nIt
deltaC=zeros(M,nMFs); deltaSigma=deltaC; deltaW=rr*W; deltaW(:,1)=0; % consequent
f=zeros(Nbs,nRules); % firing level of rules
idsTrain=datasample(1:N,Nbs,'replace',false);
idsGoodTrain=true(Nbs,1);
for n=1:Nbs
mu=exp(-(XTrain(idsTrain(n),:)'-C).^2./(2*Sigma.^2));
deltamuC=(XTrain(idsTrain(n),:)'-C)./(Sigma.^2);
deltamuSigma=(XTrain(idsTrain(n),:)'-C).^2./(Sigma.^3);
for m=1:M % membership grades of MFs
if m==1
pmu=mu(m,:);
[deltapmuC,deltapmuSigma]=deal(zeros(1,nMFs,nMFs));
deltapmuC(1,:,:)=diag(deltamuC(m,:));
deltapmuSigma(1,:,:)=diag(deltamuSigma(m,:));
else
pmu=[repmat(pmu,1,nMFs); reshape(repmat(mu(m,:),size(pmu,2),1),1,[])];
%deltapmuC=[repmat(deltapmuC,1,nMFs); reshape(repmat(diag(deltamuC(m,:)),size(deltapmuC,2),1),1,[],nMFs)];
%deltapmuSigma=[repmat(deltapmuSigma,1,nMFs); reshape(repmat(diag(deltamuSigma(m,:)),size(deltapmuSigma,2),1),1,[],nMFs)];
deltapmuC=[repmat(deltapmuC,1,nMFs); permute(reshape(repmat(diag(deltamuC(m,:)),size(deltapmuC,2),1),nMFs,[]),[3,2,1])];
deltapmuSigma=[repmat(deltapmuSigma,1,nMFs); permute(reshape(repmat(diag(deltamuSigma(m,:)),size(deltapmuSigma,2),1),nMFs,[]),[3,2,1])];
end
end
idsKeep=rand(1,nRules)<=P;
f(n,idsKeep)=prod(pmu(:,idsKeep),1);
if sum(~isfinite(f(n,idsKeep)))
continue;
end
if ~sum(f(n,idsKeep)) % special case: all f(n,:)=0; no dropRule
idsKeep=~idsKeep;
f(n,idsKeep)=prod(pmu(:,idsKeep),1);
idsKeep=true(1,nRules);
end
deltapmuC=deltapmuC(:,idsKeep,:);
deltapmuSigma=deltapmuSigma(:,idsKeep,:);
fBar=f(n,idsKeep)/sum(f(n,idsKeep));
yR=[1 XTrain(idsTrain(n),:)]*W(idsKeep,:)';
yPred(n)=fBar*yR'; % prediction
if isnan(yPred(n))
%save2base(); return;
idsGoodTrain(n)=false;
continue;
end
% Compute delta
deltaYmu=(yPred(n)-yTrain(idsTrain(n)))*(yR*sum(f(n,idsKeep))-f(n,idsKeep)*yR')/sum(f(n,idsKeep))^2.*f(n,idsKeep);
if ~sum(~isfinite(deltaYmu(:)))
%deltaC=deltaC+squeeze(sum(deltaYmu.*deltapmuC,2));
%deltaSigma=deltaSigma+squeeze(sum(deltaYmu.*deltapmuSigma,2));
deltaC=deltaC+permute(sum(deltaYmu.*deltapmuC,2),[1,3,2]);
deltaSigma=deltaSigma+permute(sum(deltaYmu.*deltapmuSigma,2),[1,3,2]);
deltaW(idsKeep,:)=deltaW(idsKeep,:)+(yPred(n)-yTrain(idsTrain(n)))*fBar'*[1 XTrain(idsTrain(n),:)];
end
end
% AdaBound
lb=alpha*(1-1/((1-beta2)*it+1));
ub=alpha*(1+1/((1-beta2)*it));
mC=beta1*mC+(1-beta1)*deltaC;
vC=beta2*vC+(1-beta2)*deltaC.^2;
mCHat=mC/(1-beta1^it);
vCHat=vC/(1-beta2^it);
lrC=min(ub,max(lb,alpha./(sqrt(vCHat)+10^(-8))));
C=C-lrC.*mCHat;
mSigma=beta1*mSigma+(1-beta1)*deltaSigma;
vSigma=beta2*vSigma+(1-beta2)*deltaSigma.^2;
mSigmaHat=mSigma/(1-beta1^it);
vSigmaHat=vSigma/(1-beta2^it);
lrSigma=min(ub,max(lb,alpha./(sqrt(vSigmaHat)+10^(-8))));
Sigma=max(minSigma,Sigma-lrSigma.*mSigmaHat);
mW=beta1*mW+(1-beta1)*deltaW;
vW=beta2*vW+(1-beta2)*deltaW.^2;
mWHat=mW/(1-beta1^it);
vWHat=vW/(1-beta2^it);
lrW=min(ub,max(lb,alpha./(sqrt(vWHat)+10^(-8))));
W=W-lrW.*mWHat;
% Training RMSE
RMSEtrain(it)=sqrt(sum((yTrain(idsTrain(idsGoodTrain))-yPred(idsGoodTrain)).^2)/sum(idsGoodTrain));
% Test RMSE
for i=1:length(XTest)
NTest=size(XTest{i},1);
f=zeros(NTest,nRules); % firing level of rules
for n=1:NTest
mu=exp(-(XTest{i}(n,:)'-C).^2./(2*Sigma.^2));
for m=1:M % membership grades of MFs
if m==1
pmu=mu(m,:);
else
pmu=[repmat(pmu,1,nMFs); reshape(repmat(mu(m,:),size(pmu,2),1),1,[])];
end
end
f(n,:)=prod(pmu,1);
end
f(:,P==0)=0;
yR=[ones(NTest,1) XTest{i}]*W';
yPredTest=sum(f.*yR,2)./sum(f,2); % prediction
yPredTest(isnan(yPredTest))=nanmean(yPredTest);
RMSEtest{i}(it)=sqrt((yTest{i}-yPredTest)'*(yTest{i}-yPredTest)/NTest);
if isnan(RMSEtest{i}(it)) && it>1
RMSEtest{i}(it)=RMSEtest{i}(it-1);
end
if nargout>2&&i==1&&RMSEtest{i}(it)<thre
thre=RMSEtest{i}(it);
[CB,SigmaB,WB,fB]=deal(C,Sigma,W,mean(f));
end
end
end
if length(XTest)==1
RMSEtest=RMSEtest{1};
end
end