%SVC Trainable classifier: Support Vector Machine
%
% [W,J] = SVC(A,KERNEL,C)
% [W,J] = A*SVC([],KERNEL,C)
% [W,J] = A*SVC(KERNEL,C)
%
% INPUT
% A Dataset
% KERNEL - Untrained mapping to compute kernel by A*(A*KERNEL) during
% training, or B*(A*KERNEL) during testing with dataset B.
% - String to compute kernel matrices by FEVAL(KERNEL,B,A)
% Default: linear kernel (PROXM('p',1))
% C Regularization parameter (optional; default: 1)
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object indices of support objects
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by quadratic
% programming. The non-linearity is determined by the kernel.
% If KERNEL = 0 it is assumed that A is already the kernelmatrix (square).
% In this case also a kernel matrix B should be supplied at evaluation by
% B*W or PRMAP(B,W).
%
% There are several ways to define KERNEL, e.g. PROXM('r',1) for a
% radial basis kernel or by USERKERNEL for a user defined kernel.
%
% If C is NaN this regularisation parameter is optimised by REGOPTC.
%
% See for more possibilties SVCINFO
%
% EXAMPLE
% a = gendatb; % generate banana classes
% [w,J] = a*svc(proxm('p',3)); % compute svm with 3rd order polynomial
% a*w*testc % show error on train set
% scatterd(a) % show scatterplot
% plotc(w) % plot classifier
% hold on;
% scatterd(a(J,:),'o') % show support objcts
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, PROXM, USERKERNEL, NUSVC, RBSVC, LIBSVC, REGOPTC
% Copyright: D. de Ridder, D. Tax, S. Verzakov, R.P.W. Duin, r.p.w.duin@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
function [W,J,C,nu,alginf] = svc(varargin)
mapname = 'SVC';
argin = shiftargin(varargin,{'prmapping','char','cell'});
argin = setdefaults(argin,[],proxm([],'p',1),1,1);
if mapping_task(argin,'definition')
W = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a,kernel,C,Options] = check_for_old_call(argin);
if isequal(Options,1), Options = []; end
DefOptions.mean_centering = 1;
DefOptions.pd_check = 1;
DefOptions.bias_in_admreg = 1;
DefOptions.pf_on_failure = 1;
DefOptions.multiclass_mode = 'single';
Options = updstruct(DefOptions,Options,1);
islabtype(a,'crisp');
isvaldfile(a,1,2); % at least 1 object per class, 2 classes
a = testdatasize(a,'objects');
[m,k,c] = getsize(a);
nlab = getnlab(a);
% The SVC is basically a 2-class classifier. More classes are
% handled by mclassc.
if c == 2 % two-class classifier
if (isnan(C))|length(C)>1 % optimize trade-off parameter
defs = {proxm([],'p',1),1,[]};
if isnan(C) % use a default range of C values
parmin_max = [0,0;1e-2,1e2;0,0]; % kernel and Options can not be optimised
else % use the range that is supplied by the user
parmin_max = [0 0; min(C) max(C); 0 0];
C = NaN;
end
[W,J,C,nu,alginf] = regoptc(a,mfilename,{kernel,C,Options},defs,[2],parmin_max,testc([],'soft'));
else
% Compute the parameters for the optimization:
y = 3 - 2*nlab;
if isequal(kernel,0)
s = [];
u = [];
in_size = 0; % to allow old and new style calls
else
if Options.mean_centering
u = mean(a); % shift origin for better accuracy
a = a - repmat(u,[m,1]);
else
u = [];
end
in_size = k;
end
K = compute_kernel(a,a,kernel);
K = min(K,K'); % make sure kernel is symmetric
[v,J,C,nu] = svo(+K,y,C,Options);
% Store the results:
if ~isequal(kernel,0)
s = a(J,:);
end
W = prmapping(mfilename,'trained',{u,s,v,kernel,J},getlablist(a),in_size,2);
% Note: even in case kernel is a mapping, we store the untrained
% mapping, as training is just administration
W = cnormc(W,a);
W = setcost(W,a);
alginf.svc_type = 'C-SVM';
alginf.kernel = kernel;
alginf.C = C;
alginf.nu = nu;
alginf.nSV = length(J);
alginf.classsizes = [nnz(y==1), nnz(y==-1)];
alginf.pf = isnan(nu);
W = setname(W,'SVM');
end
else % multi-class classifier:
[W,J,C,nu,alginf] = mclassc(a,prmapping(mfilename,{kernel,C,Options}),Options.multiclass_mode);
W = W*classc;
end
W = setname(W,mapname);
else % Evaluation
[a,v] = deal(argin{1:2});
w = +v;
m = size(a,1);
if isempty(w{2})
K = a; % user supplied testkernel
J = w{5};
if size(K,2) > length(J) & size(K,2) >= max(J)
K = K(:,J); % probably full test kernel
elseif size(K,2) ~= length(J)
error('Wrong test kernel supplied')
end
else
% The first parameter w{1} stores the mean of the dataset. When it
% is supplied, remove it from the dataset to improve the numerical
% precision. Then compute the kernel matrix using proxm:
if isempty(w{1})
K = a*(w{2}*w{4});
else
K = (a-ones(m,1)*w{1})*(w{2}*w{4});
end
end
% Data is mapped by the kernel, now we just have a linear
% classifier w*x+b:
d = [K ones(m,1)] * w{3};
W = setdat(a,[d -d],v);
end
return
function K = compute_kernel(a,s,kernel)
% compute a kernel matrix for the objects a w.r.t. the support objects s
% given a kernel description
if ischar(kernel) % routine supplied to compute kernel
K = feval(kernel,a,s);
elseif iscell(kernel)
K = feval(kernel{1},a,s,kernel{2:end});
elseif ismapping(kernel)
K = a*prmap(s,kernel);
elseif kernel == 0 % we have already a kernel
K = a;
else
error('Do not know how to compute kernel matrix')
end
K = +K;
return
function [a,kernel,C,par] = check_for_old_call(argin)
[a,kernel,C,par] = deal(argin{:});
if ischar(kernel) && exist(kernel,'file') ~= 2
kernel = proxm(kernel,C);
C = par;
par = [];
end
return