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% 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
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