--- /dev/null
+function [CC]=train_sc(D,classlabel,MODE,W)
+% Train a (statistical) classifier
+%
+% CC = train_sc(D,classlabel)
+% CC = train_sc(D,classlabel,MODE)
+% CC = train_sc(D,classlabel,MODE, W)
+% weighting D(k,:) with weight W(k) (not all classifiers supported weighting)
+%
+% CC contains the model parameters of a classifier which can be applied
+% to test data using test_sc.
+% R = test_sc(CC,D,...)
+%
+% D training samples (each row is a sample, each column is a feature)
+% classlabel labels of each sample, must have the same number of rows as D.
+% Two different encodings are supported:
+% {-1,1}-encoding (multiple classes with separate columns for each class) or
+% 1..M encoding.
+% So [1;2;3;1;4] is equivalent to
+% [+1,-1,-1,-1;
+% [-1,+1,-1,-1;
+% [-1,-1,+1,-1;
+% [+1,-1,-1,-1]
+% [-1,-1,-1,+1]
+% Note, samples with classlabel=0 are ignored.
+%
+% The following classifier types are supported MODE.TYPE
+% 'MDA' mahalanobis distance based classifier [1]
+% 'MD2' mahalanobis distance based classifier [1]
+% 'MD3' mahalanobis distance based classifier [1]
+% 'GRB' Gaussian radial basis function [1]
+% 'QDA' quadratic discriminant analysis [1]
+% 'LD2' linear discriminant analysis (see LDBC2) [1]
+% MODE.hyperparameter.gamma: regularization parameter [default 0]
+% 'LD3', 'FDA', 'LDA', 'FLDA'
+% linear discriminant analysis (see LDBC3) [1]
+% MODE.hyperparameter.gamma: regularization parameter [default 0]
+% 'LD4' linear discriminant analysis (see LDBC4) [1]
+% MODE.hyperparameter.gamma: regularization parameter [default 0]
+% 'LD5' another LDA (motivated by CSP)
+% MODE.hyperparameter.gamma: regularization parameter [default 0]
+% 'RDA' regularized discriminant analysis [7]
+% MODE.hyperparameter.gamma: regularization parameter
+% MODE.hyperparameter.lambda =
+% gamma = 0, lambda = 0 : MDA
+% gamma = 0, lambda = 1 : LDA [default]
+% Hint: hyperparameter are used only in test_sc.m, testing different
+% the hyperparameters do not need repetitive calls to train_sc,
+% it is sufficient to modify CC.hyperparameter before calling test_sc.
+% 'GDBC' general distance based classifier [1]
+% '' statistical classifier, requires Mode argument in TEST_SC
+% '###/DELETION' if the data contains missing values (encoded as NaNs),
+% a row-wise or column-wise deletion (depending on which method
+% removes less data values) is applied;
+% '###/GSVD' GSVD and statistical classifier [2,3],
+% '###/sparse' sparse [5]
+% '###' must be 'LDA' or any other classifier
+% 'PLS' (linear) partial least squares regression
+% 'REG' regression analysis;
+% 'WienerHopf' Wiener-Hopf equation
+% 'NBC' Naive Bayesian Classifier [6]
+% 'aNBC' Augmented Naive Bayesian Classifier [6]
+% 'NBPW' Naive Bayesian Parzen Window [9]
+%
+% 'PLA' Perceptron Learning Algorithm [11]
+% MODE.hyperparameter.alpha = alpha [default: 1]
+% w = w + alpha * e'*x
+% 'LMS', 'AdaLine' Least mean squares, adaptive line element, Widrow-Hoff, delta rule
+% MODE.hyperparameter.alpha = alpha [default: 1]
+% 'Winnow2' Winnow2 algorithm [12]
+%
+% 'PSVM' Proximal SVM [8]
+% MODE.hyperparameter.nu (default: 1.0)
+% 'LPM' Linear Programming Machine
+% uses and requires train_LPM of the iLog CPLEX optimizer
+% MODE.hyperparameter.c_value =
+% 'CSP' CommonSpatialPattern is very experimental and just a hack
+% uses a smoothing window of 50 samples.
+% 'SVM','SVM1r' support vector machines, one-vs-rest
+% MODE.hyperparameter.c_value =
+% 'SVM11' support vector machines, one-vs-one + voting
+% MODE.hyperparameter.c_value =
+% 'RBF' Support Vector Machines with RBF Kernel
+% MODE.hyperparameter.c_value =
+% MODE.hyperparameter.gamma =
+% 'SVM:LIB' libSVM [default SVM algorithm)
+% 'SVM:bioinfo' uses and requires svmtrain from the bioinfo toolbox
+% 'SVM:OSU' uses and requires mexSVMTrain from the OSU-SVM toolbox
+% 'SVM:LOO' uses and requires svcm_train from the LOO-SVM toolbox
+% 'SVM:Gunn' uses and requires svc-functios from the Gunn-SVM toolbox
+% 'SVM:KM' uses and requires svmclass-function from the KM-SVM toolbox
+% 'SVM:LINz' LibLinear [10] (requires train.mex from LibLinear somewhere in the path)
+% z=0 (default) LibLinear with -- L2-regularized logistic regression
+% z=1 LibLinear with -- L2-loss support vector machines (dual)
+% z=2 LibLinear with -- L2-loss support vector machines (primal)
+% z=3 LibLinear with -- L1-loss support vector machines (dual)
+% 'SVM:LIN4' LibLinear with -- multi-class support vector machines by Crammer and Singer
+% 'DT' decision tree - not implemented yet.
+%
+% {'REG','MDA','MD2','QDA','QDA2','LD2','LD3','LD4','LD5','LD6','NBC','aNBC','WienerHopf','LDA/GSVD','MDA/GSVD', 'LDA/sparse','MDA/sparse', 'PLA', 'LMS','LDA/DELETION','MDA/DELETION','NBC/DELETION','RDA/DELETION','REG/DELETION','RDA','GDBC','SVM','RBF','PSVM','SVM11','SVM:LIN4','SVM:LIN0','SVM:LIN1','SVM:LIN2','SVM:LIN3','WINNOW', 'DT'};
+%
+% CC contains the model parameters of a classifier. Some time ago,
+% CC was a statistical classifier containing the mean
+% and the covariance of the data of each class (encoded in the
+% so-called "extended covariance matrices". Nowadays, also other
+% classifiers are supported.
+%
+% see also: TEST_SC, COVM, ROW_COL_DELETION
+%
+% References:
+% [1] R. Duda, P. Hart, and D. Stork, Pattern Classification, second ed.
+% John Wiley & Sons, 2001.
+% [2] Peg Howland and Haesun Park,
+% Generalizing Discriminant Analysis Using the Generalized Singular Value Decomposition
+% IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(8), 2004.
+% dx.doi.org/10.1109/TPAMI.2004.46
+% [3] http://www-static.cc.gatech.edu/~kihwan23/face_recog_gsvd.htm
+% [4] Jieping Ye, Ravi Janardan, Cheong Hee Park, Haesun Park
+% A new optimization criterion for generalized discriminant analysis on undersampled problems.
+% The Third IEEE International Conference on Data Mining, Melbourne, Florida, USA
+% November 19 - 22, 2003
+% [5] J.D. Tebbens and P. Schlesinger (2006),
+% Improving Implementation of Linear Discriminant Analysis for the Small Sample Size Problem
+% Computational Statistics & Data Analysis, vol 52(1): 423-437, 2007
+% http://www.cs.cas.cz/mweb/download/publi/JdtSchl2006.pdf
+% [6] H. Zhang, The optimality of Naive Bayes,
+% http://www.cs.unb.ca/profs/hzhang/publications/FLAIRS04ZhangH.pdf
+% [7] J.H. Friedman. Regularized discriminant analysis.
+% Journal of the American Statistical Association, 84:165–175, 1989.
+% [8] G. Fung and O.L. Mangasarian, Proximal Support Vector Machine Classifiers, KDD 2001.
+% Eds. F. Provost and R. Srikant, Proc. KDD-2001: Knowledge Discovery and Data Mining, August 26-29, 2001, San Francisco, CA.
+% p. 77-86.
+% [9] Kai Keng Ang, Zhang Yang Chin, Haihong Zhang, Cuntai Guan.
+% Filter Bank Common Spatial Pattern (FBCSP) in Brain-Computer Interface.
+% IEEE International Joint Conference on Neural Networks, 2008. IJCNN 2008. (IEEE World Congress on Computational Intelligence).
+% 1-8 June 2008 Page(s):2390 - 2397
+% [10] R.-E. Fan, K.-W. Chang, C.-J. Hsieh, X.-R. Wang, and C.-J. Lin.
+% LIBLINEAR: A Library for Large Linear Classification, Journal of Machine Learning Research 9(2008), 1871-1874.
+% Software available at http://www.csie.ntu.edu.tw/~cjlin/liblinear
+% [11] http://en.wikipedia.org/wiki/Perceptron#Learning_algorithm
+% [12] Littlestone, N. (1988)
+% "Learning Quickly When Irrelevant Attributes Abound: A New Linear-threshold Algorithm"
+% Machine Learning 285-318(2)
+% http://en.wikipedia.org/wiki/Winnow_(algorithm)
+
+% $Id: train_sc.m 9601 2012-02-09 14:14:36Z schloegl $
+% Copyright (C) 2005,2006,2007,2008,2009,2010 by Alois Schloegl <alois.schloegl@gmail.com>
+% This function is part of the NaN-toolbox
+% http://pub.ist.ac.at/~schloegl/matlab/NaN/
+
+% This program 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 program 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 this program; if not, write to the Free Software
+% Foundation, Inc., 51 Franklin Street - Fifth Floor, Boston, MA 02110-1301, USA.
+
+ if nargin<2,
+ error('insufficient input arguments\n\tusage: train_sc(D,C,...)\n');
+ end
+ if nargin<3, MODE = 'LDA'; end
+ if nargin<4, W = []; end
+ if ischar(MODE)
+ tmp = MODE;
+ clear MODE;
+ MODE.TYPE = tmp;
+ elseif ~isfield(MODE,'TYPE')
+ MODE.TYPE='';
+ end
+
+ if isfield(MODE,'hyperparameters') && ~isfield(MODE,'hyperparameter'),
+ %% for backwards compatibility, this might become obsolete
+ warning('MODE.hyperparameters are used, You should use MODE.hyperparameter instead!!!');
+ MODE.hyperparameter = MODE.hyperparameters;
+ end
+
+ sz = size(D);
+ if sz(1)~=size(classlabel,1),
+ error('length of data and classlabel does not fit');
+ end
+
+ % remove all NaN's
+ if 1,
+ % several classifier can deal with NaN's, there is no need to remove them.
+ elseif isempty(W)
+ %% TODO: some classifiers can deal with NaN's in D. Test whether this can be relaxed.
+ %ix = any(isnan([classlabel]),2);
+ ix = any(isnan([D,classlabel]),2);
+ D(ix,:) = [];
+ classlabel(ix,:)=[];
+ W = [];
+ else
+ %ix = any(isnan([classlabel]),2);
+ ix = any(isnan([D,classlabel]),2);
+ D(ix,:)=[];
+ classlabel(ix,:)=[];
+ W(ix,:)=[];
+ warning('support for weighting of samples is still experimental');
+ end
+
+ sz = size(D);
+ if sz(1)~=length(classlabel),
+ error('length of data and classlabel does not fit');
+ end
+ if ~isfield(MODE,'hyperparameter')
+ MODE.hyperparameter = [];
+ end
+
+ if 0,
+ ;
+ elseif ~isempty(strfind(lower(MODE.TYPE),'/delet'))
+ POS1 = find(MODE.TYPE=='/');
+ [rix,cix] = row_col_deletion(D);
+ if ~isempty(W), W=W(rix); end
+ CC = train_sc(D(rix,cix),classlabel(rix,:),MODE.TYPE(1:POS1(1)-1),W);
+ CC.G = sparse(cix, 1:length(cix), 1, size(D,2), length(cix));
+ if isfield(CC,'weights')
+ W = [CC.weights(1,:); CC.weights(2:end,:)];
+ CC.weights = sparse(size(D,2)+1, size(W,2));
+ CC.weights([1,cix+1],:) = W;
+ CC.datatype = ['classifier:statistical:',lower(MODE.TYPE)];
+ else
+ CC.datatype = [CC.datatype,'/delet'];
+ end
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'nbpw'))
+ error('NBPW not implemented yet')
+ %%%% Naive Bayesian Parzen Window Classifier.
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ for k = 1:length(CC.Labels),
+ [d,CC.MEAN(k,:)] = center(D(classlabel==CC.Labels(k),:),1);
+ [CC.VAR(k,:),CC.N(k,:)] = sumskipnan(d.^2,1);
+ h2_opt = (4./(3*CC.N(k,:))).^(2/5).*CC.VAR(k,:);
+ %%% TODO
+ end
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'nbc'))
+ %%%% Naive Bayesian Classifier
+ if ~isempty(strfind(lower(MODE.TYPE),'anbc'))
+ %%%% Augmented Naive Bayesian classifier.
+ [CC.V,L] = eig(covm(D,'M',W));
+ D = D*CC.V;
+ else
+ CC.V = eye(size(D,2));
+ end
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ for k = 1:length(CC.Labels),
+ ix = classlabel==CC.Labels(k);
+ %% [d,CC.MEAN(k,:)] = center(D(ix,:),1);
+ if ~isempty(W)
+ [s,n] = sumskipnan(D(ix,:),1,W(ix));
+ CC.MEAN(k,:) = s./n;
+ d = D(ix,:) - CC.MEAN(repmat(k,sum(ix),1),:);
+ [CC.VAR(k,:),CC.N(k,:)] = sumskipnan(d.^2,1,W(ix));
+ else
+ [s,n] = sumskipnan(D(ix,:),1);
+ CC.MEAN(k,:) = s./n;
+ d = D(ix,:) - CC.MEAN(repmat(k,sum(ix),1),:);
+ [CC.VAR(k,:),CC.N(k,:)] = sumskipnan(d.^2,1);
+ end
+ end
+ CC.VAR = CC.VAR./max(CC.N-1,0);
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'lpm'))
+ if ~isempty(W)
+ error('Error TRAIN_SC: Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+ % linear programming machine
+ % CPLEX optimizer: ILOG solver, ilog cplex 6.5 reference manual http://www.ilog.com
+ MODE.TYPE = 'LPM';
+ if ~isfield(MODE.hyperparameter,'c_value')
+ MODE.hyperparameter.c_value = 1;
+ end
+ [classlabel,CC.Labels] = CL1M(classlabel);
+
+ M = length(CC.Labels);
+ if M==2, M=1; end % For a 2-class problem, only 1 Discriminant is needed
+ for k = 1:M,
+ %LPM = train_LPM(D,(classlabel==CC.Labels(k)),'C',MODE.hyperparameter.c_value);
+ LPM = train_LPM(D',(classlabel'==CC.Labels(k)));
+ CC.weights(:,k) = [-LPM.b; LPM.w(:)];
+ end
+ CC.hyperparameter.c_value = MODE.hyperparameter.c_value;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'pla')),
+ % Perceptron Learning Algorithm
+
+ [rix,cix] = row_col_deletion(D);
+ [CL101,CC.Labels] = cl101(classlabel);
+ M = size(CL101,2);
+ weights = sparse(length(cix)+1,M);
+
+ %ix = randperm(size(D,1)); %% randomize samples ???
+ if ~isfield(MODE.hyperparameter,'alpha')
+ if isfield(MODE.hyperparameter,'alpha')
+ alpha = MODE.hyperparameter.alpha;
+ else
+ alpha = 1;
+ end
+ for k = rix(:)',
+ %e = ((classlabel(k)==(1:M))-.5) - sign([1, D(k,cix)] * weights)/2;
+ e = CL101(k,:) - sign([1, D(k,cix)] * weights);
+ weights = weights + alpha * [1,D(k,cix)]' * e ;
+ end
+
+ else %if ~isempty(W)
+ if isfield(MODE.hyperparameter,'alpha')
+ W = W*MODE.hyperparameter.alpha;
+ end
+ for k = rix(:)',
+ %e = ((classlabel(k)==(1:M))-.5) - sign([1, D(k,cix)] * weights)/2;
+ e = CL101(k,:) - sign([1, D(k,cix)] * weights);
+ weights = weights + W(k) * [1,D(k,cix)]' * e ;
+ end
+ end
+ CC.weights = sparse(size(D,2)+1,M);
+ CC.weights([1,cix+1],:) = weights;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'adaline')) || ~isempty(strfind(lower(MODE.TYPE),'lms')),
+ % adaptive linear elemente, least mean squares, delta rule, Widrow-Hoff,
+
+ [rix,cix] = row_col_deletion(D);
+ [CL101,CC.Labels] = cl101(classlabel);
+ M = size(CL101,2);
+ weights = sparse(length(cix)+1,M);
+
+ %ix = randperm(size(D,1)); %% randomize samples ???
+ if isempty(W)
+ if isfield(MODE.hyperparameter,'alpha')
+ alpha = MODE.hyperparameter.alpha;
+ else
+ alpha = 1;
+ end
+ for k = rix(:)',
+ %e = (classlabel(k)==(1:M)) - [1, D(k,cix)] * weights;
+ e = CL101(k,:) - sign([1, D(k,cix)] * weights);
+ weights = weights + alpha * [1,D(k,cix)]' * e ;
+ end
+
+ else %if ~isempty(W)
+ if isfield(MODE.hyperparameter,'alpha')
+ W = W*MODE.hyperparameter.alpha;
+ end
+ for k = rix(:)',
+ %e = (classlabel(k)==(1:M)) - [1, D(k,cix)] * weights;
+ e = CL101(k,:) - sign([1, D(k,cix)] * weights);
+ weights = weights + W(k) * [1,D(k,cix)]' * e ;
+ end
+ end
+ CC.weights = sparse(size(D,2)+1,M);
+ CC.weights([1,cix+1],:) = weights;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'winnow'))
+ % winnow algorithm
+ if ~isempty(W)
+ error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+
+ [rix,cix] = row_col_deletion(D);
+ [CL101,CC.Labels] = cl101(classlabel);
+ M = size(CL101,2);
+ weights = ones(length(cix),M);
+ theta = size(D,2)/2;
+
+ for k = rix(:)',
+ e = CL101(k,:) - sign(D(k,cix) * weights - theta);
+ weights = weights.* 2.^(D(k,cix)' * e);
+ end
+
+ CC.weights = sparse(size(D,2)+1,M);
+ CC.weights(cix+1,:) = weights;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'pls')) || ~isempty(strfind(lower(MODE.TYPE),'reg'))
+ % 4th version: support for weighted samples - work well with unequally distributed data:
+ % regression analysis, can handle sparse data, too.
+
+ if nargin<4,
+ W = [];
+ end
+ [rix, cix] = row_col_deletion(D);
+ wD = [ones(length(rix),1),D(rix,cix)];
+
+ if ~isempty(W)
+ %% wD = diag(W)*wD
+ W = W(:);
+ for k=1:size(wD,2)
+ wD(:,k) = W(rix).*wD(:,k);
+ end
+ end
+ [CL101, CC.Labels] = cl101(classlabel(rix,:));
+ M = size(CL101,2);
+ CC.weights = sparse(sz(2)+1,M);
+
+ %[rix, cix] = row_col_deletion(wD);
+ [q,r] = qr(wD,0);
+
+ if isempty(W)
+ CC.weights([1,cix+1],:) = r\(q'*CL101);
+ else
+ CC.weights([1,cix+1],:) = r\(q'*(W(rix,ones(1,M)).*CL101));
+ end
+ %for k = 1:M,
+ % CC.weights(cix,k) = r\(q'*(W.*CL101(rix,k)));
+ %end
+ CC.datatype = ['classifier:statistical:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(MODE.TYPE,'WienerHopf'))
+ % Q: equivalent to LDA
+ % equivalent to Regression, except regression can not deal with NaN's
+ [CL101,CC.Labels] = cl101(classlabel);
+ M = size(CL101,2);
+ CC.weights = sparse(size(D,2)+1,M);
+ cc = covm(D,'E',W);
+ %c1 = classlabel(~isnan(classlabel));
+ %c2 = ones(sum(~isnan(classlabel)),M);
+ %for k = 1:M,
+ % c2(:,k) = c1==CC.Labels(k);
+ %end
+ %CC.weights = cc\covm([ones(size(c2,1),1),D(~isnan(classlabel),:)],2*real(c2)-1,'M',W);
+ CC.weights = cc\covm([ones(size(D,1),1),D],CL101,'M',W);
+ CC.datatype = ['classifier:statistical:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'/gsvd'))
+ if ~isempty(W)
+ error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+ % [2] Peg Howland and Haesun Park, 2004
+ % Generalizing Discriminant Analysis Using the Generalized Singular Value Decomposition
+ % IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(8), 2004.
+ % dx.doi.org/10.1109/TPAMI.2004.46
+ % [3] http://www-static.cc.gatech.edu/~kihwan23/face_recog_gsvd.htm
+
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ [rix,cix] = row_col_deletion(D);
+
+ Hw = zeros(length(rix)+length(CC.Labels), length(cix));
+ Hb = [];
+ m0 = mean(D(rix,cix));
+ K = length(CC.Labels);
+ N = zeros(1,K);
+ for k = 1:K,
+ ix = find(classlabel(rix)==CC.Labels(k));
+ N(k) = length(ix);
+ [Hw(ix,:), mu] = center(D(rix(ix),cix));
+ %Hb(k,:) = sqrt(N(k))*(mu(k,:)-m0);
+ Hw(length(rix)+k,:) = sqrt(N(k))*(mu-m0); % Hb(k,:)
+ end
+ try
+ [P,R,Q] = svd(Hw,'econ');
+ catch % needed because SVD(..,'econ') not supported in Matlab 6.x
+ [P,R,Q] = svd(Hw,0);
+ end
+ t = rank(R);
+
+ clear Hw Hb mu;
+ %[size(D);size(P);size(Q);size(R)]
+ R = R(1:t,1:t);
+ %P = P(1:size(D,1),1:t);
+ %Q = Q(1:t,:);
+ [U,E,W] = svd(P(1:length(rix),1:t),0);
+ %[size(U);size(E);size(W)]
+ clear U E P;
+ %[size(Q);size(R);size(W)]
+
+ %G = Q(1:t,:)'*[R\W'];
+ G = Q(:,1:t)*(R\W'); % this works as well and needs only 'econ'-SVD
+ %G = G(:,1:t); % not needed
+
+ % do not use this, gives very bad results for Medline database
+ %G = G(:,1:K); this seems to be a typo in [2] and [3].
+ CC = train_sc(D(:,cix)*G,classlabel,MODE.TYPE(1:find(MODE.TYPE=='/')-1));
+ CC.G = sparse(size(D,2),size(G,2));
+ CC.G(cix,:) = G;
+ if isfield(CC,'weights')
+ CC.weights = sparse([CC.weights(1,:); CC.G*CC.weights(2:end,:)]);
+ CC.datatype = ['classifier:statistical:', lower(MODE.TYPE)];
+ else
+ CC.datatype = [CC.datatype,'/gsvd'];
+ end
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'sparse'))
+ if ~isempty(W)
+ error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+ % [5] J.D. Tebbens and P.Schlesinger (2006),
+ % Improving Implementation of Linear Discriminant Analysis for the Small Sample Size Problem
+ % http://www.cs.cas.cz/mweb/download/publi/JdtSchl2006.pdf
+
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ [rix,cix] = row_col_deletion(D);
+
+ warning('sparse LDA is sensitive to linear transformations')
+ M = length(CC.Labels);
+ G = sparse([],[],[],length(rix),M,length(rix));
+ for k = 1:M,
+ G(classlabel(rix)==CC.Labels(k),k) = 1;
+ end
+ tol = 1e-10;
+
+ G = train_lda_sparse(D(rix,cix),G,1,tol);
+ CC.datatype = 'classifier:slda';
+ POS1 = find(MODE.TYPE=='/');
+ %G = v(:,1:size(G.trafo,2)).*G.trafo;
+ %CC.weights = s * CC.weights(2:end,:) + sparse(1,1:M,CC.weights(1,:),sz(2)+1,M);
+
+ CC = train_sc(D(rix,cix)*G.trafo,classlabel(rix),MODE.TYPE(1:POS1(1)-1));
+ CC.G = sparse(size(D,2),size(G.trafo,2));
+ CC.G(cix,:) = G.trafo;
+ if isfield(CC,'weights')
+ CC.weights = sparse([CC.weights(1,:); CC.G*CC.weights(2:end,:)]);
+ CC.datatype = ['classifier:statistical:',lower(MODE.TYPE)];
+ else
+ CC.datatype = [CC.datatype,'/sparse'];
+ end
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'rbf'))
+ if ~isempty(W)
+ error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+
+ % Martin Hieden's RBF-SVM
+ if exist('svmpredict_mex','file')==3,
+ MODE.TYPE = 'SVM:LIB:RBF';
+ else
+ error('No SVM training algorithm available. Install LibSVM for Matlab.\n');
+ end
+ CC.options = '-t 2 -q'; %use RBF kernel, set C, set gamma
+ if isfield(MODE.hyperparameter,'gamma')
+ CC.options = sprintf('%s -c %g', CC.options, MODE.hyperparameter.c_value); % set C
+ end
+ if isfield(MODE.hyperparameter,'c_value')
+ CC.options = sprintf('%s -g %g', CC.options, MODE.hyperparameter.gamma); % set C
+ end
+
+ % pre-whitening
+ [D,r,m]=zscore(D,1);
+ CC.prewhite = sparse(2:sz(2)+1,1:sz(2),r,sz(2)+1,sz(2),2*sz(2));
+ CC.prewhite(1,:) = -m.*r;
+
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ CC.model = svmtrain_mex(classlabel, D, CC.options); % Call the training mex File
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'svm11'))
+ if ~isempty(W)
+ error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ end
+ % 1-versus-1 scheme
+ if ~isfield(MODE.hyperparameter,'c_value')
+ MODE.hyperparameter.c_value = 1;
+ end
+
+ CC.options=sprintf('-c %g -t 0 -q',MODE.hyperparameter.c_value); %use linear kernel, set C
+ CC.hyperparameter.c_value = MODE.hyperparameter.c_value;
+
+ % pre-whitening
+ [D,r,m]=zscore(D,1);
+ CC.prewhite = sparse(2:sz(2)+1,1:sz(2),r,sz(2)+1,sz(2),2*sz(2));
+ CC.prewhite(1,:) = -m.*r;
+
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ CC.model = svmtrain_mex(classlabel, D, CC.options); % Call the training mex File
+
+ FUN = 'SVM:LIB:1vs1';
+ CC.datatype = ['classifier:',lower(FUN)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'psvm'))
+ if ~isempty(W)
+ %%% error('Classifier (%s) does not support weighted samples.',MODE.TYPE);
+ warning('Classifier (%s) in combination with weighted samples is not tested.',MODE.TYPE);
+ end
+ if ~isfield(MODE,'hyperparameter')
+ nu = 1;
+ elseif isfield(MODE.hyperparameter,'nu')
+ nu = MODE.hyperparameter.nu;
+ else
+ nu = 1;
+ end
+ [m,n] = size(D);
+ [CL101,CC.Labels] = cl101(classlabel);
+ CC.weights = sparse(n+1,size(CL101,2));
+ M = size(CL101,2);
+ for k = 1:M,
+ d = sparse(1:m,1:m,CL101(:,k));
+ H = d * [ones(m,1),D];
+ %%% r = sum(H,1)';
+ r = sumskipnan(H,1,W)';
+ %%% r = (speye(n+1)/nu + H' * H)\r; %solve (I/nu+H’*H)r=H’*e
+ [HTH, nn] = covm(H,H,'M',W);
+ r = (speye(n+1)/nu + HTH)\r; %solve (I/nu+H’*H)r=H’*e
+ u = nu*(1-(H*r));
+ %%% CC.weights(:,k) = u'*H;
+ [c,nn] = covm(u,H,'M',W);
+ CC.weights(:,k) = c';
+ end
+ CC.hyperparameter.nu = nu;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'svm:lin4'))
+ if ~isfield(MODE.hyperparameter,'c_value')
+ MODE.hyperparameter.c_value = 1;
+ end
+
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ M = length(CC.Labels);
+ CC.weights = sparse(size(D,2)+1,M);
+
+ [rix,cix] = row_col_deletion(D);
+
+ % pre-whitening
+ [D,r,m]=zscore(D(rix,cix),1);
+ sz2 = length(cix);
+ s = sparse(2:sz2+1,1:sz2,r,sz2+1,sz2,2*sz2);
+ s(1,:) = -m.*r;
+
+ CC.options = sprintf('-s 4 -B 1 -c %f -q', MODE.hyperparameter.c_value); % C-SVC, C=1, linear kernel, degree = 1,
+ model = train(W, classlabel, sparse(D), CC.options); % C-SVC, C=1, linear kernel, degree = 1,
+ weights = model.w([end,1:end-1],:)';
+
+ CC.weights([1,cix+1],:) = s * weights(2:end,:) + sparse(1,1:M,weights(1,:),sz2+1,M); % include pre-whitening transformation
+ CC.weights([1,cix+1],:) = s * CC.weights(cix+1,:) + sparse(1,1:M,CC.weights(1,:),sz2+1,M); % include pre-whitening transformation
+ CC.hyperparameter.c_value = MODE.hyperparameter.c_value;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'svm'))
+
+ if ~isfield(MODE.hyperparameter,'c_value')
+ MODE.hyperparameter.c_value = 1;
+ end
+ if any(MODE.TYPE==':'),
+ % nothing to be done
+ elseif exist('train','file')==3,
+ MODE.TYPE = 'SVM:LIN'; %% liblinear
+ elseif exist('svmtrain_mex','file')==3,
+ MODE.TYPE = 'SVM:LIB';
+ elseif (exist('svmtrain','file')==3),
+ MODE.TYPE = 'SVM:LIB';
+ fprintf(1,'You need to rename %s to svmtrain_mex.mex !! \n Press any key to continue !!!\n',which('svmtrain.mex'));
+ elseif exist('svmtrain','file')==2,
+ MODE.TYPE = 'SVM:bioinfo';
+ elseif exist('mexSVMTrain','file')==3,
+ MODE.TYPE = 'SVM:OSU';
+ elseif exist('svcm_train','file')==2,
+ MODE.TYPE = 'SVM:LOO';
+ elseif exist('svmclass','file')==2,
+ MODE.TYPE = 'SVM:KM';
+ elseif exist('svc','file')==2,
+ MODE.TYPE = 'SVM:Gunn';
+ else
+ error('No SVM training algorithm available. Install OSV-SVM, or LOO-SVM, or libSVM for Matlab.\n');
+ end
+
+ %%CC = train_svm(D,classlabel,MODE);
+ [CL101,CC.Labels] = cl101(classlabel);
+ M = size(CL101,2);
+ [rix,cix] = row_col_deletion(D);
+ CC.weights = sparse(sz(2)+1, M);
+
+ % pre-whitening
+ [D,r,m]=zscore(D(rix,cix),1);
+ sz2 = length(cix);
+ s = sparse(2:sz2+1,1:sz2,r,sz2+1,sz2,2*sz2);
+ s(1,:) = -m.*r;
+
+ for k = 1:M,
+ cl = CL101(rix,k);
+ if strncmp(MODE.TYPE, 'SVM:LIN',7);
+ if isfield(MODE,'options')
+ CC.options = MODE.options;
+ else
+ t = 0;
+ if length(MODE.TYPE)>7, t=MODE.TYPE(8)-'0'; end
+ if (t<0 || t>6) t=0; end
+ CC.options = sprintf('-s %i -B 1 -c %f -q',t, MODE.hyperparameter.c_value); % C-SVC, C=1, linear kernel, degree = 1,
+ end
+ model = train(W, cl, sparse(D), CC.options); % C-SVC, C=1, linear kernel, degree = 1,
+ w = -model.w';
+ Bias = -model.bias;
+ w = -model.w(:,1:end-1)';
+ Bias = -model.w(:,end)';
+
+ elseif strcmp(MODE.TYPE, 'SVM:LIB'); %% tested with libsvm-mat-2.9-1
+ if isfield(MODE,'options')
+ CC.options = MODE.options;
+ else
+ CC.options = sprintf('-s 0 -c %f -t 0 -d 1 -q', MODE.hyperparameter.c_value); % C-SVC, C=1, linear kernel, degree = 1,
+ end
+ model = svmtrain_mex(cl, D, CC.options); % C-SVC, C=1, linear kernel, degree = 1,
+ w = cl(1) * model.SVs' * model.sv_coef; %Calculate decision hyperplane weight vector
+ % ensure correct sign of weight vector and Bias according to class label
+ Bias = model.rho * cl(1);
+
+ elseif strcmp(MODE.TYPE, 'SVM:bioinfo');
+ % SVM classifier from bioinformatics toolbox.
+ % Settings suggested by Ian Daly, 2011-06-06
+ options = optimset('Display','iter','maxiter',20000, 'largescale','off');
+ CC.SVMstruct = svmtrain(D, cl, 'AUTOSCALE', 0, 'quadprog_opts', options, 'Method', 'LS', 'kernel_function', 'polynomial');
+ Bias = -CC.SVMstruct.Bias;
+ w = -CC.SVMstruct.Alpha'*CC.SVMstruct.SupportVectors;
+
+ elseif strcmp(MODE.TYPE, 'SVM:OSU');
+ [AlphaY, SVs, Bias] = mexSVMTrain(D', cl', [0 1 1 1 MODE.hyperparameter.c_value]); % Linear Kernel, C=1; degree=1, c-SVM
+ w = -SVs * AlphaY'*cl(1); %Calculate decision hyperplane weight vector
+ % ensure correct sign of weight vector and Bias according to class label
+ Bias = -Bias * cl(1);
+
+ elseif strcmp(MODE.TYPE, 'SVM:LOO');
+ [a, Bias, g, inds] = svcm_train(D, cl, MODE.hyperparameter.c_value); % C = 1;
+ w = D(inds,:)' * (a(inds).*cl(inds)) ;
+
+ elseif strcmp(MODE.TYPE, 'SVM:Gunn');
+ [nsv, alpha, Bias,svi] = svc(D, cl, 1, MODE.hyperparameter.c_value); % linear kernel, C = 1;
+ w = D(svi,:)' * alpha(svi) * cl(1);
+ Bias = mean(D*w);
+
+ elseif strcmp(MODE.TYPE, 'SVM:KM');
+ [xsup,w1,Bias,inds] = svmclass(D, cl, MODE.hyperparameter.c_value, 1, 'poly', 1); % C = 1;
+ w = -D(inds,:)' * w1;
+
+ else
+ fprintf(2,'Error TRAIN_SVM: no SVM training algorithm available\n');
+ return;
+ end
+
+ CC.weights(1,k) = -Bias;
+ CC.weights(cix+1,k) = w;
+ end
+ CC.weights([1,cix+1],:) = s * CC.weights(cix+1,:) + sparse(1,1:M,CC.weights(1,:),sz2+1,M); % include pre-whitening transformation
+ CC.hyperparameter.c_value = MODE.hyperparameter.c_value;
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+
+
+ elseif ~isempty(strfind(lower(MODE.TYPE),'csp'))
+ CC.datatype = ['classifier:',lower(MODE.TYPE)];
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ CC.MD = repmat(NaN,[sz(2)+[1,1],length(CC.Labels)]);
+ CC.NN = CC.MD;
+ for k = 1:length(CC.Labels),
+ %% [CC.MD(k,:,:),CC.NN(k,:,:)] = covm(D(classlabel==CC.Labels(k),:),'E');
+ ix = classlabel==CC.Labels(k);
+ if isempty(W)
+ [CC.MD(:,:,k),CC.NN(:,:,k)] = covm(D(ix,:), 'E');
+ else
+ [CC.MD(:,:,k),CC.NN(:,:,k)] = covm(D(ix,:), 'E', W(ix));
+ end
+ end
+ ECM = CC.MD./CC.NN;
+ W = csp(ECM,'CSP3');
+ %%% ### This is a hack ###
+ CC.FiltA = 50;
+ CC.FiltB = ones(CC.FiltA,1);
+ d = filtfilt(CC.FiltB,CC.FiltA,(D*W).^2);
+ CC.csp_w = W;
+ CC.CSP = train_sc(log(d),classlabel);
+
+
+ else % Linear and Quadratic statistical classifiers
+ CC.datatype = ['classifier:statistical:',lower(MODE.TYPE)];
+ [classlabel,CC.Labels] = CL1M(classlabel);
+ CC.MD = repmat(NaN,[sz(2)+[1,1],length(CC.Labels)]);
+ CC.NN = CC.MD;
+ for k = 1:length(CC.Labels),
+ ix = classlabel==CC.Labels(k);
+ if isempty(W)
+ [CC.MD(:,:,k),CC.NN(:,:,k)] = covm(D(ix,:), 'E');
+ else
+ [CC.MD(:,:,k),CC.NN(:,:,k)] = covm(D(ix,:), 'E', W(ix));
+ end
+ end
+
+ ECM = CC.MD./CC.NN;
+ NC = size(CC.MD);
+ if strncmpi(MODE.TYPE,'LD',2) || strncmpi(MODE.TYPE,'FDA',3) || strncmpi(MODE.TYPE,'FLDA',3),
+
+ %if NC(1)==2, NC(1)=1; end % linear two class problem needs only one discriminant
+ CC.weights = repmat(NaN,NC(2),NC(3)); % memory allocation
+ type = MODE.TYPE(3)-'0';
+
+ ECM0 = squeeze(sum(ECM,3)); %decompose ECM
+ for k = 1:NC(3);
+ ix = [1:k-1,k+1:NC(3)];
+ dM = CC.MD(:,1,k)./CC.NN(:,1,k) - sum(CC.MD(:,1,ix),3)./sum(CC.NN(:,1,ix),3);
+ switch (type)
+ case 2 % LD2
+ ecm0 = (sum(ECM(:,:,ix),3)/(NC(3)-1) + ECM(:,:,k));
+ case 4 % LD4
+ ecm0 = 2*(sum(ECM(:,:,ix),3) + ECM(:,:,k))/NC(3);
+ % ecm0 = sum(CC.MD,3)./sum(CC.NN,3);
+ case 5 % LD5
+ ecm0 = ECM(:,:,k);
+ case 6 % LD6
+ ecm0 = sum(CC.MD(:,:,ix),3)./sum(CC.NN(:,:,ix),3);
+ otherwise % LD3, LDA, FDA
+ ecm0 = ECM0;
+ end
+ if isfield(MODE.hyperparameter,'gamma')
+ ecm0 = ecm0 + mean(diag(ecm0))*eye(size(ecm0))*MODE.hyperparameter.gamma;
+ end
+
+ CC.weights(:,k) = ecm0\dM;
+
+ end
+ %CC.weights = sparse(CC.weights);
+
+ elseif strcmpi(MODE.TYPE,'RDA');
+ if isfield(MODE,'hyperparameter')
+ CC.hyperparameter = MODE.hyperparameter;
+ end
+ % default values
+ if ~isfield(CC.hyperparameter,'gamma')
+ CC.hyperparameter.gamma = 0;
+ end
+ if ~isfield(CC.hyperparameter,'lambda')
+ CC.hyperparameter.lambda = 1;
+ end
+ else
+ ECM0 = sum(ECM,3);
+ nn = ECM0(1,1,1); % number of samples in training set for class k
+ XC = squeeze(ECM0(:,:,1))/nn; % normalize correlation matrix
+ M = XC(1,2:NC(2)); % mean
+ S = XC(2:NC(2),2:NC(2)) - M'*M;% covariance matrix
+
+ try
+ [v,d]=eig(S);
+ U0 = v(diag(d)==0,:);
+ CC.iS2 = U0*U0';
+ end
+
+ %M = M/nn; S=S/(nn-1);
+ ICOV0 = inv(S);
+ CC.iS0 = ICOV0;
+ % ICOV1 = zeros(size(S));
+ for k = 1:NC(3),
+ %[M,sd,S,xc,N] = decovm(ECM{k}); %decompose ECM
+ %c = size(ECM,2);
+ nn = ECM(1,1,k);% number of samples in training set for class k
+ XC = squeeze(ECM(:,:,k))/nn;% normalize correlation matrix
+ M = XC(1,2:NC(2));% mean
+ S = XC(2:NC(2),2:NC(2)) - M'*M;% covariance matrix
+ %M = M/nn; S=S/(nn-1);
+
+ %ICOV(1) = ICOV(1) + (XC(2:NC(2),2:NC(2)) - )/nn
+
+ CC.M{k} = M;
+ CC.IR{k} = [-M;eye(NC(2)-1)]*inv(S)*[-M',eye(NC(2)-1)]; % inverse correlation matrix extended by mean
+ CC.IR0{k} = [-M;eye(NC(2)-1)]*ICOV0*[-M',eye(NC(2)-1)]; % inverse correlation matrix extended by mean
+ d = NC(2)-1;
+ if exist('OCTAVE_VERSION','builtin')
+ S = full(S);
+ end
+ CC.logSF(k) = log(nn) - d/2*log(2*pi) - det(S)/2;
+ CC.logSF2(k) = -2*log(nn/sum(ECM(:,1,1)));
+ CC.logSF3(k) = d*log(2*pi) + log(det(S));
+ CC.logSF4(k) = log(det(S)) + 2*log(nn);
+ CC.logSF5(k) = log(det(S));
+ CC.logSF6(k) = log(det(S)) - 2*log(nn/sum(ECM(:,1,1)));
+ CC.logSF7(k) = log(det(S)) + d*log(2*pi) - 2*log(nn/sum(ECM(:,1,1)));
+ CC.logSF8(k) = sum(log(svd(S))) + log(nn) - log(sum(ECM(:,1,1)));
+ CC.SF(k) = nn/sqrt((2*pi)^d * det(S));
+ %CC.datatype='LLBC';
+ end
+ end
+ end
+end
+
+function [CL101,Labels] = cl101(classlabel)
+ %% convert classlabels to {-1,1} encoding
+
+ if (all(classlabel>=0) && all(classlabel==fix(classlabel)) && (size(classlabel,2)==1))
+ M = max(classlabel);
+ if M==2,
+ CL101 = (classlabel==2)-(classlabel==1);
+ else
+ CL101 = zeros(size(classlabel,1),M);
+ for k=1:M,
+ %% One-versus-Rest scheme
+ CL101(:,k) = 2*real(classlabel==k) - 1;
+ end
+ end
+ CL101(isnan(classlabel),:) = NaN; %% or zero ???
+
+ elseif all((classlabel==1) | (classlabel==-1) | (classlabel==0) )
+ CL101 = classlabel;
+ M = size(CL101,2);
+ else
+ classlabel,
+ error('format of classlabel unsupported');
+ end
+ Labels = 1:M;
+ return;
+end
+
+
+function [cl1m, Labels] = CL1M(classlabel)
+ %% convert classlabels to 1..M encoding
+ if (all(classlabel>=0) && all(classlabel==fix(classlabel)) && (size(classlabel,2)==1))
+ cl1m = classlabel;
+
+ elseif all((classlabel==1) | (classlabel==-1) | (classlabel==0) )
+ CL101 = classlabel;
+ M = size(classlabel,2);
+ if any(sum(classlabel==1,2)>1)
+ warning('invalid format of classlabel - at most one category may have +1');
+ end
+ if (M==1),
+ cl1m = (classlabel==-1) + 2*(classlabel==+1);
+ else
+ [tmp, cl1m] = max(classlabel,[],2);
+ if any(tmp ~= 1)
+ warning('some class might not be properly represented - you might what to add another column to classlabel = [max(classlabel,[],2)<1,classlabel]');
+ end
+ cl1m(tmp<1)= 0; %% or NaN ???
+ end
+ else
+ classlabel
+ error('format of classlabel unsupported');
+ end
+ Labels = 1:max(cl1m);
+ return;
+end
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff