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train_NLSM.m
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train_NLSM.m
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%======================================================================
% Training Generalized Polynomial Nets by our Nonlinear Spectral Method
% Objective: Loss + regul*<1, F> where F is output layer
%
% Written by: Quynh Nguyen
% Last update: 17.05.2016
%======================================================================
function model = train_NLSM(nnet, data, algOptions)
% network settings
[DimX, N] = size(data.X);
for l = 2:nnet.nLayers
if ~isfield(nnet.layers{l}, 'mask')
nnet.layers{l}.mask = ones(nnet.layers{l}.nUnits, nnet.layers{l-1}.nUnits);
end
nnet.layers{l}.mask = logical(nnet.layers{l}.mask);
if ~isfield(nnet.layers{l}, 'alpha')
nnet.layers{l}.alpha = ones(nnet.layers{l}.nUnits, 1);
end
nnet.layers{l}.alpha = reshape(nnet.layers{l}.alpha, numel(nnet.layers{l}.alpha), 1);
end
% utilities
allPos = @(x)(all(x(:) > 0));
allNonneg = @(x)(all(x(:) >= 0));
allNeg = @(x)(all(x(:) < 0));
allNonpos = @(x)(all(x(:) <= 0));
%======================================================================
% computing params
model.A = cell(nnet.nLayers, 1);
model.Z = cell(nnet.nLayers, 1);
model.Delta = cell(nnet.nLayers, 1);
model.W = cell(nnet.nLayers, 1);
model.trainAcc = []; model.trainScore = []; model.trainLoss = [];
model.testAcc = []; model.testScore = []; model.testLoss = [];
%======================================================================
% initialization
for l = 2:nnet.nLayers
model.W{l} = rand(nnet.layers{l}.nUnits, nnet.layers{l-1}.nUnits);
model.W{l}(~nnet.layers{l}.mask) = 0;
model.W{l} = normalize(model.W{l}, nnet.layers{l}.pNorm, nnet.layers{l}.rho, nnet.layers{l}.normType);
assert(allPos(model.W{l}(nnet.layers{l}.mask)), ['W', num2str(l), ' must be initialized to be positive']);
end
model.initW = model.W;
model.A{1} = data.X; % pass input to 1st layer
%======================================================================
% training phase
success = true; iter = 0; stopCrit = 1;
% NOTE: one can use a higher precison for stopping criteria below
while success && iter < 100 && stopCrit > 1e-7
% monitor test performance
[score, loss, acc] = getScore(nnet, model, algOptions, data, 'test');
model.testScore = [model.testScore; score];
model.testLoss = [model.testLoss; loss];
model.testAcc = [model.testAcc; acc];
iter = iter + 1;
if algOptions.debug
disp('===========================================');
disp(['iter = ', num2str(iter)]);
end
oldW = model.W;
% forward
for l = 2:nnet.nLayers
model.Z{l} = model.W{l} * model.A{l-1};
model.A{l} = bsxfun(@power, model.Z{l}, nnet.layers{l}.alpha);
if ~isfield(nnet.layers{l}, 'normFact')
nnet.layers{l}.normFact = sum(model.A{l}(:));
if algOptions.debug
disp(['setting normalization factor to layer ', num2str(l), ': ', num2str(nnet.layers{l}.normFact)]);
end
end
model.A{l} = model.A{l} / nnet.layers{l}.normFact;
end
[~, ind] = max(model.A{nnet.nLayers});
model.trainAcc = [model.trainAcc; sum(ind == data.T)/N*100];
% backward
if strcmpi(algOptions.loss, 'linear')
B = model.A{nnet.nLayers};
loss = sum(B(logical(data.Y)))/N;
regularizer = algOptions.regul * sum(sum(bsxfun(@times, model.A{nnet.nLayers}, nnet.Vec)))/N;
model.trainScore = [model.trainScore; loss + regularizer];
model.trainLoss = [model.trainLoss; loss];
model.Delta{nnet.nLayers} = data.Y .* bsxfun(@times, bsxfun(@power, model.Z{nnet.nLayers}, nnet.layers{nnet.nLayers}.alpha-1), nnet.layers{nnet.nLayers}.alpha);
elseif strcmpi(algOptions.loss, 'logistic')
B = exp( bsxfun(@minus, model.A{nnet.nLayers}, max(model.A{nnet.nLayers})) );
B = bsxfun(@rdivide, B, sum(B));
loss = sum(log(B(logical(data.Y))))/N;
regularizer = algOptions.regul*sum(sum(bsxfun(@times, model.A{nnet.nLayers}, nnet.Vec)))/N;
model.trainScore = [model.trainScore; loss + regularizer];
model.trainLoss = [model.trainLoss; loss];
model.Delta{nnet.nLayers} = (data.Y-B) .* bsxfun(@times, bsxfun(@power, model.Z{nnet.nLayers}, nnet.layers{nnet.nLayers}.alpha-1), nnet.layers{nnet.nLayers}.alpha);
end
% back-propagate derivatives
model.Delta{nnet.nLayers} = model.Delta{nnet.nLayers} + ...
algOptions.regul * bsxfun(@times, bsxfun(@times, bsxfun(@power, model.Z{nnet.nLayers}, nnet.layers{nnet.nLayers}.alpha-1), nnet.layers{nnet.nLayers}.alpha), nnet.Vec);
model.Delta{nnet.nLayers} = model.Delta{nnet.nLayers} / nnet.layers{nnet.nLayers}.normFact;
for l = nnet.nLayers-1:-1:2
model.Delta{l} = (model.W{l+1}' * model.Delta{l+1}) .* bsxfun(@times, bsxfun(@power, model.Z{l}, nnet.layers{l}.alpha-1), nnet.layers{l}.alpha);
model.Delta{l} = model.Delta{l} / nnet.layers{l}.normFact;
end
% compute gradients
Wgrad = cell(nnet.nLayers, 1);
for l = 2:nnet.nLayers
Wgrad{l} = (model.Delta{l} * model.A{l-1}') ./ N;
Wgrad{l}(~nnet.layers{l}.mask) = 0;
if min(min(Wgrad{l}(nnet.layers{l}.mask))) < 0
Wgrad{l}
Wgrad{l}(nnet.layers{l}.mask)
disp(['Wgrad', num2str(l), ' must be nonnegative: ', min(min(Wgrad{l}(nnet.layers{l}.mask)))]);
success = false; pause(5); break;
end
end
if ~success; break; end
% update weights
for l = 2:nnet.nLayers
model.W{l} = (abs(Wgrad{l}).^(1/(nnet.layers{l}.pNorm-1))) .* sign(Wgrad{l});
model.W{l} = normalize(model.W{l}, nnet.layers{l}.pNorm, nnet.layers{l}.rho, nnet.layers{l}.normType);
end
% update stopping criteria
stopCrit = max(arrayfun(@(l) norm(model.W{l}(nnet.layers{l}.mask)-oldW{l}(nnet.layers{l}.mask), inf)/norm(model.W{l}(nnet.layers{l}.mask), inf), 2:nnet.nLayers));
if algOptions.debug
disp(['score = ', num2str(model.trainScore(end)), ', acc = ', num2str(model.trainAcc(end))]);
disp(['StopCrit: ', num2str(stopCrit, 16)]);
end
end % end while
% evaluate final model
[score, loss, acc] = getScore(nnet, model, algOptions, data, 'train');
model.trainScore = [model.trainScore; score];
model.trainLoss = [model.trainLoss; loss];
model.trainAcc = [model.trainAcc; acc];
[score, loss, acc] = getScore(nnet, model, algOptions, data, 'test');
model.testScore = [model.testScore; score];
model.testLoss = [model.testLoss; loss];
model.testAcc = [model.testAcc; acc];
% lp-norm sphere normalization
function D = normalize(C, p, rho, normType)
if normType == 0
D = rho * C ./ norm(C(:), p);
elseif normType == 1
D = rho * bsxfun(@rdivide, C, sum(C.^p, 2).^(1/p));
elseif normType == 2
D = rho * bsxfun(@rdivide, C, sum(C.^p, 1).^(1/p));
end
end
% objective score on training/test data
function [score, loss, acc] = getScore(nnet, model, algOptions, data, type)
if strcmpi(type, 'train')
X = data.X; Y = data.Y; T = data.T;
elseif strcmpi(type, 'test')
if ~(isfield(data, 'X_test') && isfield(data, 'Y_test') && isfield(data, 'T_test'))
score = 0; loss = 0; acc = 0;
return;
end
X = data.X_test; Y = data.Y_test; T = data.T_test;
end
A = X;
for u = 2:nnet.nLayers
Z = abs(model.W{u} * A);
A = bsxfun(@power, Z, nnet.layers{u}.alpha);
if isfield(nnet.layers{u}, 'normFact')
A = A / nnet.layers{u}.normFact;
end
end
[~, ind] = max(A);
acc = sum(ind == T)/size(X, 2)*100;
if strcmpi(algOptions.loss, 'linear')
loss = sum(A(logical(Y)))/size(X, 2);
score = loss + algOptions.regul*sum(sum(bsxfun(@times, A, nnet.Vec)))/size(X, 2);
elseif strcmpi(algOptions.loss, 'logistic')
BB = exp( bsxfun(@minus, A, max(A)) );
BB = bsxfun(@rdivide, BB, sum(BB));
loss = sum(log(BB(logical(Y))))/size(X, 2);
score = loss + algOptions.regul*sum(sum(bsxfun(@times, A, nnet.Vec)))/size(X, 2);
end
end
end % end main func