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trainRNN.m
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function [trained_net, Xlast] = trainRNN(net, param)
INP = param.input_N;
OUP = param.output_N;
NOL = param.num_layers;
NOD = param.num_nodes;
% Set Global variables
global EPOCHS
global SUB_LEN
global SEQ
num_Epoch = EPOCHS; % Number of epochs
num_sub = SUB_LEN; % Length of subset
sig_seq = SEQ; % Length of training sequence
% Get weights from struct
Win = net.win;
W = net.w;
Wn = net.wn;
Wout = net.wout;
% Generate cross evaluation data
[cv_INP, cv_TRG] = datagen_rank3e(sig_seq, sig_seq, 1);
cv_OUT = zeros(sig_seq,1);
% Initialize some variables for training
% Starting point of subset in data sequence
start = ceil((sig_seq-num_sub-(INP+OUP)+2)*rand(1,num_Epoch));
% Anneal R from 100 to 5
R = annealing(100,5,num_Epoch);
% Anneal Q from 1E-2 to 1E-6
Q = annealing(1E-2,1E-6,num_Epoch);
% Learning rate
learning_rate = annealing(1,1E-4,num_Epoch);
now = 1;
min_mse = 1;
updated=0;
% Training
for t = (1:num_Epoch)
% Get training data
[DInput, Dtarget] = datagen_rank3e(sig_seq, num_sub, start(t));
[INPsize, INPnum] = size(DInput');
[OUTsize, OUTnum] = size(Dtarget');
% Initalize output and X matrix
% X0, X1, X2, X3 - output of each layer at different time steps
out = zeros(INPnum,1);
X0 = zeros(NOL,NOD);
%2 first runs of RNN (initialization)
[X, out(1)] = runRNN(net, param, DInput(1,:), X0);
X1 = X;
[X, out(2)] = runRNN(net, param, DInput(2,:), X1);
X2 = X;
% Ricatti equation initialization
for m = (1:NOL*NOD+OUP)
if (m<NOD+1)
K(m).value = 0.01^(-1)*eye(NOD+INP);
elseif (m<2*NOD+1)
if (NOL<3)
K(m).value = 0.01^(-1)*eye(NOD);
else
K(m).value = 0.01^(-1)*eye(2*NOD);
end
elseif (m<(NOL-1)*NOD+1)
K(m).value = 0.01^(-1)*eye(2*NOD);
elseif (m<NOL*NOD+1)
K(m).value = 0.01^(-1)*eye(NOD);
else
K(m).value = 0.01^(-1)*eye(NOD);
end
end
W0 = zeros(NOD,NOD+INP);
% Remaining runs of RNN
for k = (3:INPnum)
temp = 0;
% Forward running of network
[X, out(k)] = runRNN(net, param, DInput(k,:), X2);
X3 = X;
% Get updated weights from struct
Win = net.win;
W = net.w;
Wn = net.wn;
Wout = net.wout;
%Backpropagation of error and jacobian matrix 'C' calculation
%
% -> @ output neuron
for j = (NOL*NOD+1:NOL*NOD+OUP)
C(j).value = X3(NOL,:);
end
% -> @ non recurrent layer
D = Wout*diag(d_tanh1(Wn*X3(NOL-1,:)'));
D1 = D'*X3(NOL-1,:);
for j = (1:NOD)
C((NOL-1)*NOD+j).value = D1(j,:);
end
if NOL>2
if NOL>3
% -> @ last recurrent layer
D = D*Wn*diag(d_tanh1(W((NOL-3)*NOD+1:(NOL-2)*NOD,:)*[X2(NOL-1,:) X3(NOL-1,:)]'));
D1 = D'*[X2(NOL-1,:) X3(NOL-1,:)];
D2 = D1 + (D*W((NOL-3)*NOD+1:(NOL-2)*NOD,1:NOD)*diag(d_tanh1(W((NOL-4)*NOD+1:(NOL-3)*NOD,:)* ...
[X1(NOL-1,:) X2(NOL-1,:)]')))' * [X1(NOL-1,:) X2(NOL-1,:)];
for j = (1:NOD)
C((NOL-2)*NOD+j).value = D2(j,:);
end
% -> @ previous recurrent layers
for i = (NOL-3:-1:2)
D = D*W(i*NOD+1:(i+1)*NOD,1:NOD)*diag(d_tanh1(W((i-1)*NOD+1:i*NOD,:)*[X2(i,:) X3(i,:)]'));
D1 = D'*[X2(i,:) X3(i,:)];
D2 = D1 + (D*W((i-1)*NOD+1:i*NOD,1:NOD)*diag(d_tanh1(W((i-2)*NOD+1:(i-1)*NOD,:)* ...
[X1(i,:) X2(i,:)]')))' * [X1(i,:) X2(i,:)];
for j = (1:NOD)
C((NOL-1-i)*NOD+j).value = D2(j,:);
end
end
end
% -> @ 2nd recurrent layer
if (NOL>3)
D = D*W(NOD+1:2*NOD,1:NOD)*diag(d_tanh1(W(1:NOD,:)*[X2(2,:) X3(2,:)]'));
else
D = D*Wn*diag(d_tanh1(W(1:NOD,:)*[X2(2,:) X3(2,:)]'));
end
D1 = D'*[X2(2,:) X3(2,:)];
if INP>NOD
D2 = D1 + (D*W(1:NOD,1:NOD)*diag(d_tanh1(Win(:,1:2*NOD)*[X1(2,:) X2(2,:)]')))' * [X1(2,:) X2(2,:)];
else
Wtemp = zeros(NOD,2*NOD);
Wtemp(:,1:NOD+INP) = Win;
D2 = D1 + (D*W(1:NOD,1:NOD)*diag(d_tanh1(Wtemp(:,1:2*NOD)*[X1(2,:) X2(2,:)]')))' * [X1(2,:) X2(2,:)];
end
for j = (1:NOD)
C(NOD+j).value = D2(j,:);
end
end
% ---
% -> @ 1st recurrent layer
if (NOL<3)
D = D*Wn(1:NOD,1:NOD)*diag(d_tanh1(Win*[X2(1,:) DInput(k,:)]'));
else
D = D*W(1:NOD,1:NOD)*diag(d_tanh1(Win*[X2(1,:) DInput(k,:)]'));
end
D1 = D'*[X2(1,:) DInput(k,:)];
D2 = D1 + (D*Win(:,1:NOD)*diag(d_tanh1(W0*[X1(1,:) DInput(k-1,:)]')))' * [X1(1,:) DInput(k-1,:)];
for j = (1:NOD)
C(j).value = D2(j,:);
end
Winput = Win;
%Decoupled EKF
alpha = Dtarget(k) - out(k); % Innovation of output
for m = (1:NOL*NOD+OUP)
temp = C(m).value*K(m).value*C(m).value' + temp;
end
%Inverse of temp+R(t)
temp2 = temp+R(t);
[U, S, V]= svd(temp2);
s= diag(S); p= sum(s> 1e-9);
Gamma = (U(:, 1: p)* diag(1./ s(1: p))* V(:, 1: p)')';
for m = (1:NOL*NOD+OUP)
G(m).value = K(m).value*C(m).value'*Gamma;
%update weights if innovation > threshold
if abs(alpha) > 1E-3 %|| wrong<0
updated = updated+1;
if (m<NOD+1)
Win(m,:) = Win(m,:) + learning_rate(t)*(G(m).value*alpha)';
%Win(m,:) = Win(m,:) + 0.2*(G(m).value*alpha)';
end
if (m>NOD && m<(NOL-1)*NOD+1)
W(m-NOD,:) = W(m-NOD,:) + learning_rate(t)*(G(m).value*alpha)';
%W(m-NOD,:) = W(m-NOD,:) + 0.2*(G(m).value*alpha)';
end
if (m>(NOL-1)*NOD && m<NOL*NOD+1)
Wn(m-(NOL-1)*NOD,:) = Wn(m-(NOL-1)*NOD,:) + learning_rate(t)*(G(m).value*alpha)';
%Wn(m-(NOL-1)*NOD,:) = Wn(m-(NOL-1)*NOD,:) + 0.2*(G(m).value*alpha)';
end
if (m>NOL*NOD)
Wout(m-NOL*NOD,:) = Wout(m-NOL*NOD,:) + learning_rate(t)*(G(m).value*alpha)';
%Wout(m-NOL*NOD,:) = Wout(m-NOL*NOD,:) + 0.2*(G(m).value*alpha)';
end
end
% Re-calculte ricatti equation
K(m).value = K(m).value - G(m).value*C(m).value*K(m).value + Q(t);
net.win = Win;
net.w = W;
net.wn = Wn;
net.wout = Wout;
%for i=1:sig_seq
% [X, tmp_out] = runRNN(net, param, cv_INP(i,:), X3);
% cv_OUT(i) = tmp_out(1);
%end
%cv_mse = sqrt(mean((tmp_out(1:end) - cv_TRG(1:end)).^2));
%if cv_mse<0.0001, break; end;
end
%End of Decoupled EKF
% Update recurrent states for next run
X1 = X2;
X2 = X3;
% Replace 1st layer weights
W0 = Winput;
end
% Calculate MSE
mse(t) = sqrt(mean((out(1:end) - Dtarget(1:end)).^2));
dis(t)= sum(abs(out(1:end) - Dtarget(1:end)));
% Calculate cross evaluation MSE
for i=1:sig_seq
[X, tmp_out] = runRNN(net, param, cv_INP(i,:), X3);
cv_OUT(i) = tmp_out(1);
end
cv_mse = mean((cv_OUT(1:end) - cv_TRG(1:end)).^2);
if cv_mse<min_mse
now = t;
min_mse = cv_mse;
X_min = X3;
min_Win = Win;
min_W = W;
min_Wn = Wn;
min_Wout = Wout;
end
fprintf('Epoch: %d, Bunch MSE: %f, Total Distance: %f, Cross MSE: %f\n', t, mse(t), dis(t), cv_mse);
%if mse(t)<0.001 break; end;
if cv_mse<0.00001, break; end;
end
fprintf('\nWeights Updated %d Times\n',updated/(NOL*NOD+OUP));
fprintf('Best net at epoch %d with cross mse of %f\n\n\n',now, min_mse);
% Return variables
Xlast = X_min;
trained_net.win = min_Win;
trained_net.w = min_W;
trained_net.wn = min_Wn;
trained_net.wout = min_Wout;
end