-
Notifications
You must be signed in to change notification settings - Fork 1
/
FCM_RDpAdaBound.m
143 lines (133 loc) · 5.69 KB
/
FCM_RDpAdaBound.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
function [RMSEtrain,RMSEtest,CB,SigmaB,WB,fB]=FCM_RDpAdaBound(XTrain,yTrain,XTest,yTest,alpha,rr,P,gammaP,nRules,nIt,Nbs,C0,Sigma0,W0)
% %% 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
% gammaP: scalar, Powerball power exponent
% nRules: scalar, total number of rules
% 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);
Nbs=min(N,Nbs);
if nargin<12
W0=zeros(nRules,M+1); % Rule consequents
% FCM initialization
[C0,U] = fcm(XTrain,nRules,[2 100 0.001 0]);
Sigma0=C0;
for r=1:nRules
Sigma0(r,:)=std(XTrain,U(r,:));
W0(r,1)=U(r,:)*yTrain/sum(U(r,:));
end
Sigma0(Sigma0==0)=mean(Sigma0(:));
end
C=C0; Sigma=Sigma0; W=W0;
minSigma=.1*min(Sigma0(:));
[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(nRules,M); 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
idsKeep=rand(1,nRules)<=P;
f(n,idsKeep)=prod(exp(-(XTrain(idsTrain(n),:)-C(idsKeep,:)).^2./(2*Sigma(idsKeep,:).^2)),2);
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(exp(-(XTrain(idsTrain(n),:)-C(idsKeep,:)).^2./(2*Sigma(idsKeep,:).^2)),2);
idsKeep=true(1,nRules);
end
deltamuC=(XTrain(idsTrain(n),:)-C(idsKeep,:))./(Sigma(idsKeep,:).^2);
deltamuSigma=(XTrain(idsTrain(n),:)-C(idsKeep,:)).^2./(Sigma(idsKeep,:).^3);
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(idsKeep,:)=deltaC(idsKeep,:)+deltaYmu'.*deltamuC;
deltaSigma(idsKeep,:)=deltaSigma(idsKeep,:)+deltaYmu'.*deltamuSigma;
deltaW(idsKeep,:)=deltaW(idsKeep,:)+(yPred(n)-yTrain(idsTrain(n)))*fBar'*[1 XTrain(idsTrain(n),:)];
end
end
% powerball
deltaC=sign(deltaC).*(abs(deltaC).^gammaP);
deltaSigma=sign(deltaSigma).*(abs(deltaSigma).^gammaP);
deltaW=sign(deltaW).*(abs(deltaW).^gammaP);
% 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 on the minibatch
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
f(n,:)=prod(exp(-(XTest{i}(n,:)-C).^2./(2*Sigma.^2)),2);
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