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MBGD_RDA2_T.m
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MBGD_RDA2_T.m
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function [RMSEtrain,RMSEtest,A,B,C,D,W,yPredTest,A0,B0,C0,D0,W0]=...
MBGD_RDA2_T(XTrain,yTrain,XTest,yTest,alpha,rr,P,nRules,nIt,Nbs,A0,B0,C0,D0,W0)
% This function implements a variant of 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 uses trapezoidal MFs, and specifies the total number of rules by nRules.
%
% 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: NTest*M matrix of the test inputs
% yTest: NTest*1 vector of the labels for XTest
% alpha: scalar, learning rate
% rr: scalar, L2 regularization coefficient
% P: scalar in [0.5, 1), dropRule rate
% nRules: scalar in [2, 100], total number of rules
% nIt: scalar, maximum number of iterations
% Nbs: batch size. typically 32 or 64
% A0,B0,C0,D0: M*nRules matrices specifying the initial a, b, c, d parameters of the trapezoidal MFs. See derivations.pdf
% W: nRules*(M+1) matrix of the initial consequent parameters for the rules.
%
% %% Outputs:
% RMSEtrain: 1*nIt vector of the training RMSE at different iterations
% RMSEtest: 1*nIt vector of the test RMSE at different iterations
% A,B,C,D: M*nRules matrices specifying the a, b, c, d parameters of the trapezoidal MFs. See derivations.pdf
% W: nRules*(M+1) matrix of the consequent parameters for the rules.
beta1=0.9; beta2=0.999;
[N,M]=size(XTrain); NTest=size(XTest,1);
Nbs=min(N,Nbs);
%% k-means initialization
if nargin<11
W0=zeros(nRules,M+1); % Rule consequents
[ids,C0] = kmeans(XTrain,nRules,'replicate',3);
Sigma=C0;
for r=1:nRules
Sigma(r,:)=std(XTrain(ids==r,:));
W0(r,1)=mean(yTrain(ids==r));
end
Sigma(Sigma==0)=mean(Sigma(:));
A0=C0-10*Sigma; D0=C0+10*Sigma; B0=C0-.5*Sigma; C0=C0+.5*Sigma;
end
A=A0; B=B0; C=C0; D=D0; W=W0;
%% Iterative update
RMSEtrain=zeros(1,nIt); RMSEtest=RMSEtrain;
mA=0; vA=0; mB=0; vB=0; mC=0; vC=0; mD=0; vD=0;
mW=0; vW=0; yPred=nan(Nbs,1);
for it=1:nIt
deltaA=zeros(nRules,M); deltaB=deltaA; deltaC=deltaA; deltaD=deltaA; deltaW=rr*W; deltaW(:,1)=0; % consequent
f=ones(Nbs,nRules); % firing level of rules
idsTrain=datasample(1:N,Nbs,'replace',false);
idsGoodTrain=true(Nbs,1);
for n=1:Nbs
idsKeep=rand(1,nRules)<=P;
f(n,~idsKeep)=0;
for r=1:nRules
if idsKeep(r)
f(n,r)=prod(MG(XTrain(idsTrain(n),:),[A(r,:); B(r,:); C(r,:); D(r,:)]));
end
end
if ~sum(f(n,:)) % special case: all f(n,:)=0; no dropRule
idsKeep=~idsKeep;
f(n,idsKeep)=1;
for r=1:nRules
if idsKeep(r)
f(n,r)=prod(MG(XTrain(idsTrain(n),:),[A(r,:); B(r,:); C(r,:); D(r,:)]));
end
end
idsKeep=true(1,nRules);
end
fBar=f(n,:)/sum(f(n,:));
yR=[1 XTrain(idsTrain(n),:)]*W';
yPred(n)=fBar*yR'; % prediction
if isnan(yPred(n))
%save2base(); return;
idsGoodTrain(n)=false;
continue;
end
% Compute delta
for r=1:nRules
if idsKeep(r)
temp=(yPred(n)-yTrain(idsTrain(n)))*(yR(r)*sum(f(n,:))-f(n,:)*yR')/sum(f(n,:))^2*f(n,r);
if ~isnan(temp) && abs(temp)<inf
% delta of c, sigma, and b
for m=1:M
if XTrain(idsTrain(n),m)>A(r,m) && XTrain(idsTrain(n),m)<B(r,m)
deltaA(r,m)=deltaA(r,m)+temp*(XTrain(idsTrain(n),m)-B(r,m))/...
(MG(XTrain(idsTrain(n),m),[A(r,m); B(r,m); C(r,m); D(r,m)])*(B(r,m)-A(r,m))^2);
deltaB(r,m)=deltaB(r,m)-temp/(B(r,m)-A(r,m));
end
if XTrain(idsTrain(n),m)>C(r,m) && XTrain(idsTrain(n),m)<D(r,m)
deltaD(r,m)=deltaD(r,m)+temp*(XTrain(idsTrain(n),m)-C(r,m))/...
(MG(XTrain(idsTrain(n),m),[A(r,m); B(r,m); C(r,m); D(r,m)])*(D(r,m)-C(r,m))^2);
deltaC(r,m)=deltaC(r,m)+temp/(D(r,m)-C(r,m));
end
deltaW(r,m+1)=deltaW(r,m+1)+(yPred(n)-yTrain(idsTrain(n)))*fBar(r)*XTrain(idsTrain(n),m);
end
% delta of b0
deltaW(r,1)=deltaW(r,1)+(yPred(n)-yTrain(idsTrain(n)))*fBar(r);
end
end
end
end
% AdaBound
lb=alpha*(1-1/((1-beta2)*it+1));
ub=alpha*(1+1/((1-beta2)*it));
mA=beta1*mA+(1-beta1)*deltaA;
vA=beta2*vA+(1-beta2)*deltaA.^2;
mAHat=mA/(1-beta1^it);
vAHat=vA/(1-beta2^it);
lrA=min(ub,max(lb,alpha./(sqrt(vAHat)+10^(-8))));
A=A-lrA.*mAHat;
mB=beta1*mB+(1-beta1)*deltaB;
vB=beta2*vB+(1-beta2)*deltaB.^2;
mBHat=mB/(1-beta1^it);
vBHat=vB/(1-beta2^it);
lrB=min(ub,max(lb,alpha./(sqrt(vBHat)+10^(-8))));
B=B-lrB.*mBHat;
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;
mD=beta1*mD+(1-beta1)*deltaD;
vD=beta2*vD+(1-beta2)*deltaD.^2;
mDHat=mD/(1-beta1^it);
vDHat=vD/(1-beta2^it);
lrD=min(ub,max(lb,alpha./(sqrt(vDHat)+10^(-8))));
D=D-lrD.*mDHat;
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;
% Adjust the rank to make sure a<=b<=c<=d
for r=1:nRules
for m=1:M
abcd=sort([A(r,m) B(r,m) C(r,m) D(r,m)]);
A(r,m)=abcd(1); B(r,m)=abcd(2);
C(r,m)=abcd(3); D(r,m)=abcd(4);
end
end
% Training RMSE
RMSEtrain(it)=sqrt(sum((yTrain(idsTrain(idsGoodTrain))-yPred(idsGoodTrain)).^2)/sum(idsGoodTrain));
% Test RMSE
f=ones(NTest,nRules); % firing level of rules
for n=1:NTest
for r=1:nRules
f(n,r)= prod(MG(XTest(n,:),[A(r,:); B(r,:); C(r,:); D(r,:)]));
end
end
yR=[ones(NTest,1) XTest]*W';
yPredTest=sum(f.*yR,2)./sum(f,2); % prediction
yPredTest(isnan(yPredTest))=nanmean(yPredTest);
RMSEtest(it)=sqrt((yTest-yPredTest)'*(yTest-yPredTest)/NTest);
if isnan(RMSEtest(it)) && it>1
RMSEtest(it)=RMSEtest(it-1);
end
end
end
function mu=MG(x,abcd)
% if abcd(1)==abcd(2); abcd(2)=abcd(1)+2*eps; end
% if abcd(4)==abcd(3); abcd(4)=abcd(3)+2*eps; end
mu=max(0,min(1,min((x-abcd(1,:))./(abcd(2,:)-abcd(1,:)),(abcd(4,:)-x)./(abcd(4,:)-abcd(3,:)))));
end