Add WQEISS for regression problems

ELMregression.m

@@ -0,0 +1,74 @@
+function [trYhat, valYhat,W1,W2,bias] =...
+    ELMregression(trX, trY, valX, nUnits)
+
+% This function implements an ELM classifier with tanh activation function.
+%
+% Inputs:     trX    <- array of training inputs with size  = num. features x num. training patterns 
+%             trY    <- array of training targets with size = num. categories x num. training patterns 
+%                       (for each i-th column of trY only the entry relative to the correct category is 1)
+%             valX   <- array of validation inputs with size  = num. features x num. training patterns  
+%             nUnits <- num. hidden units of ELM
+%
+% Output:
+%             trYhat  <- array of training target predictions with size = 1 x num. training patterns 
+%                      (each i-th is an integer = predicted category) 
+%             valYhat <- array of validaiton target predictions with size = 1 x num. validation patterns 
+%                      (each i-th is an integer = predicted category) 
+%          W1,W2,bias <- the trained parameters of the ELM
+%
+% Reference:  Huang, G.-B., Zhu, Q.-Y., Siew, C.-K., 2006. Extreme learning machine: Theory and applications. 
+%             Neurocomputing 70, 489–501. doi:10.1016/j.neucom.2005.12.126
+%
+%
+%
+%
+% Copyright 2016 Riccardo Taormina (riccardo_taormina@sutd.edu.sg), 
+%      Gulsah Karakaya (gulsahkilickarakaya@gmail.com;), 
+%      Stefano Galelli (stefano_galelli@sutd.edu.sg),
+%      and Selin Damla Ahipasaoglu (ahipasaoglu@sutd.edu.sg;. 
+%
+% Please refer to README.txt for further information.
+%
+%
+% This file is part of Matlab-Multi-objective-Feature-Selection.
+% 
+%     Matlab-Multi-objective-Feature-Selection is free software: you can redistribute 
+%     it and/or modify it under the terms of the GNU General Public License 
+%     as published by the Free Software Foundation, either version 3 of the 
+%     License, or (at your option) any later version.     
+% 
+%     This code is distributed in the hope that it will be useful,
+%     but WITHOUT ANY WARRANTY; without even the implied warranty of
+%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%     GNU General Public License for more details.
+% 
+%     You should have received a copy of the GNU General Public License
+%     along with MATLAB_IterativeInputSelection.  
+%     If not, see <http://www.gnu.org/licenses/>.
+%
+
+% get number of features and number of patterns for training and validation
+[nFeatures,nPatternsTr]   = size(trX);
+nPatternsVal              = size(valX,2);
+
+% generate random input->hidden weights W1 (between -1 and 1) 
+W1 = rand(nUnits,nFeatures)*2-1;
+
+% generate random biases (between 0 and 1) 
+bias  = rand(nUnits,1);
+
+% compute hidden neuron output matrix H
+H = sigActFun(W1*trX + repmat(bias,[1,nPatternsTr]));
+
+% compute hidden->output weights W2
+Hinv = pinv(H');
+W2  = Hinv * trY';
+
+% get ELM response on training
+temp     = (H' * W2)';  
+[~,temp] = max(temp,[],1);
+trYhat   = temp';
+
+% ...  and validation dataset
+Hval     = sigActFun(W1*valX + repmat(bias,[1,nPatternsVal]));
+valYhat  = (Hval' * W2)';

computeSU.m

@@ -0,0 +1,48 @@
+function SU = computeSU(x,y)
+% Computes simmetric uncertainty between two variables
+%
+%
+% Copyright 2016 Riccardo Taormina (riccardo_taormina@sutd.edu.sg), 
+%      Gulsah Karakaya (gulsahkilickarakaya@gmail.com;), 
+%      Stefano Galelli (stefano_galelli@sutd.edu.sg),
+%      and Selin Damla Ahipasaoglu (ahipasaoglu@sutd.edu.sg;. 
+%
+% Please refer to README.txt for further information.
+%
+%
+% This file is part of Matlab-Multi-objective-Feature-Selection.
+% 
+%     Matlab-Multi-objective-Feature-Selection is free software: you can redistribute 
+%     it and/or modify it under the terms of the GNU General Public License 
+%     as published by the Free Software Foundation, either version 3 of the 
+%     License, or (at your option) any later version.     
+% 
+%     This code is distributed in the hope that it will be useful,
+%     but WITHOUT ANy WARRANTy; without even the implied warranty of
+%     MERCHANTABILITy or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%     GNU General Public License for more details.
+% 
+%     you should have received a copy of the GNU General Public License
+%     along with MATLAB_IterativeInputSelection.  
+%     If not, see <http://www.gnu.org/licenses/>.
+
+% discretization options
+nBins     = 20;
+quantType = 'equalwidth'; 
+
+% quantize variables
+x = quantizeVariable(x,nBins,quantType);
+y = quantizeVariable(y,nBins,quantType);
+
+% compute entropies
+hX  = entropy(x);
+hy  = entropy(y);
+hXy = jointentropy(x, y);
+
+% compute mutual information
+MI = hX+hy-hXy;
+
+% compute symmetric uncertainty
+SU = 2*MI/(hX+hy);
+
+

getAlgorithmOptions.m

@@ -1,9 +1,9 @@
-function [options,objFunOptions] = getAlgorithmOptions(algorithm,data)
+function [options,objFunOptions] = getAlgorithmOptions(algorithm,data,varargin)
 % Options for the algorithms (NSGAII/BORG) and the objective function
 %
 %
 %
-% Copyright 2015 Riccardo Taormina (riccardo_taormina@sutd.edu.sg), 
+% Copyright 2016 Riccardo Taormina (riccardo_taormina@sutd.edu.sg), 
 %      Gulsah Karakaya (gulsahkilickarakaya@gmail.com;), 
 %      Stefano Galelli (stefano_galelli@sutd.edu.sg),
 %      and Selin Damla Ahipasaoglu (ahipasaoglu@sutd.edu.sg;. 
@@ -28,29 +28,44 @@
 %     If not, see <http://www.gnu.org/licenses/>.
 %
 
+% check nargin
+if nargin == 2
+    problem_type = 'CLASSIFICATION';
+elseif (nargin == 3) && varargin{1} == true 
+    problem_type = 'REGRESSION';
+else
+    error('Problem type not recognized!')
+end
+
+
+
 % extract attributes (PHI) and predictand (Y)
 PHI    = data(:,1:end-1);
 [nPatterns,nAttrs] = size(PHI);
 tempY  = data(:,end);
 
-% restructure predictand (array with same number of columns of number of classes) 
-classes  = unique(tempY);
-nClasses = numel(classes);
-Y = zeros(nPatterns,nClasses);
-for i = 1 : nClasses
-    thisClass = classes(i);
-    ixes = (tempY == thisClass);
-    Y(ixes,i) = 1;
+if strcmp(problem_type, 'CLASSIFICATION')
+    % restructure predictand (array with same number of columns of number of classes) 
+    classes  = unique(tempY);
+    nClasses = numel(classes);
+    Y = zeros(nPatterns,nClasses);
+    for i = 1 : nClasses
+        thisClass = classes(i);
+        ixes = (tempY == thisClass);
+        Y(ixes,i) = 1;
+    end
+else
+    Y = tempY;  
 end
 
 
 % Objective Function options
-objFunOptions.Y              = Y;               % predictand
-objFunOptions.PHI            = PHI;             % attributes
-objFunOptions.nFolds         = 10;              % folds for k-fold cross-validation
-objFunOptions.nELM           = 5;               % size of ELM ensemble        
-objFunOptions.nUnits         = 10;              % number of units in ELM
-objFunOptions.maxCardinality = 20;              % maximum cardinality (important for large datasets)
+objFunOptions.Y              = Y;           % predictand
+objFunOptions.PHI            = PHI;         % attributes
+objFunOptions.nFolds         = 10;          % folds for k-fold cross-validation
+objFunOptions.nELM           = 10;          % size of ELM ensemble        
+objFunOptions.nUnits         = 50;          % number of units in ELM
+objFunOptions.maxCardinality = 20;          % maximum cardinality (important for large datasets)
 
 % Algorithm options
 if strcmp(algorithm,'NSGA2')
@@ -73,7 +88,7 @@
     options.nvars       = nAttrs;              % number of design variables
     options.nconstrs    = 0;                   % number of contraints
     options.NFE         = 5000;                % number of functions evaluations
-    options.lowerBounds = zeros(1,nAttrs);     % lower bound of design variables (0)
+    options.lowerBounds = -ones(1,nAttrs);     % lower bound of design variables (-1)
     options.upperBounds = ones(1,nAttrs);      % upper bound of design variables (1)    
 else
     error('Algorithm not supported!')

objFunWQEISS_regression.m

@@ -0,0 +1,108 @@
+function [fval,dummy] = objFunWQEISS_regression(X,varargin)
+global archive fvals objFunOptions suREL suRED ix_solutions
+% objective function for developing WQEISS wrappers
+%
+%
+%
+% Copyright 2016 Riccardo Taormina (riccardo_taormina@sutd.edu.sg), 
+%      Gulsah Karakaya (gulsahkilickarakaya@gmail.com;), 
+%      Stefano Galelli (stefano_galelli@sutd.edu.sg),
+%      and Selin Damla Ahipasaoglu (ahipasaoglu@sutd.edu.sg;. 
+%
+% Please refer to README.txt for further information.
+%
+%
+% This file is part of Matlab-Multi-objective-Feature-Selection.
+% 
+%     Matlab-Multi-objective-Feature-Selection is free software: you can redistribute 
+%     it and/or modify it under the terms of the GNU General Public License 
+%     as published by the Free Software Foundation, either version 3 of the 
+%     License, or (at your option) any later version.     
+% 
+%     This code is distributed in the hope that it will be useful,
+%     but WITHOUT ANY WARRANTY; without even the implied warranty of
+%     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+%     GNU General Public License for more details.
+% 
+%     You should have received a copy of the GNU General Public License
+%     along with MATLAB_IterativeInputSelection.  
+%     If not, see <http://www.gnu.org/licenses/>.
+%
+
+
+% initialize fitness values
+fval = zeros(1,4);
+
+% unpack data and parameters
+Y       = objFunOptions.Y;         % targets
+PHI     = objFunOptions.PHI;       % inputs
+nFolds  = objFunOptions.nFolds;    % nFolds for k-fold cross validation
+nELM    = objFunOptions.nELM;      % number of repeats for computing the accuracy obj function
+nUnits  = objFunOptions.nUnits;    % info on dataset
+maxCardinality = objFunOptions.maxCardinality;  % maximum cardinality
+
+% retrieve populations size and number of attributes
+nAttrs = size(X,2);
+
+% transform decision variables from continuous to discrete
+% 0 or 1 assigned depending on ratio of maxCardinality/nAttrs
+% (This has no effect if the search algorithm is binary-coded already!) 
+varRatio = maxCardinality/nAttrs;
+if varRatio > 0.5
+    X = X>0.5;
+else
+    X = X>(1 - varRatio);
+end
+
+% get selected features from genotype
+featIxes = find(X);
+
+% get cardinality
+cardinality = numel(featIxes);
+
+
+% check if this combination of inputs is already in archive
+% if so, assign existing fitness values to this genotype
+temp = cellfun(@(x) isequal(x,featIxes),archive,'UniformOutput',false);    
+archiveIx = find([temp{:}]);
+if ~isempty(archiveIx);
+    % get fval from lookup table
+    fval = fvals(archiveIx,:);
+    ix_solutions(archiveIx) = 1;
+else
+    if cardinality > maxCardinality
+        % if cardinality > maxCardinality do not evaluate and assign very
+        % high values of the obj functions
+        fval = [Inf,Inf,Inf,numel(featIxes)];
+    elseif cardinality == 0
+        % no inputs selected, irregular solution
+        fval = [Inf,Inf,Inf,numel(featIxes)];
+    else       
+        % found new combination, compute values of obj. functions
+
+        % relevance
+        REL = sum(suREL(featIxes));               
+
+        % redundancy
+        if cardinality == 1
+            % 1 input selected, no redundancy
+            RED = 0;
+        else
+            temp = nchoosek(featIxes,2); 
+            ixes = (temp(:,2)-1)*nAttrs+temp(:,1);        
+            RED = sum(suRED(ixes));
+        end
+
+        % compute ELM classifier accuracy
+        SU = trainAndValidateELM_regression(PHI,Y,featIxes,nFolds,nELM,nUnits);
+
+        % fitness values (- for those obj. functions to maximize)                
+        fval = [-REL,RED,-SU,cardinality];            
+        % add solution to archive and fvals
+        archive = cat(1,archive,featIxes);
+        fvals   = cat(1,fvals,[-REL,RED,-SU,cardinality]);
+        ix_solutions = cat(1,ix_solutions,1);
+    end  
+end
+
+dummy = [];