%NUSVC Trainable classifier: Support Vector Machine, nu-algorithme
%
% [W,J,NU] = NUSVC(A,KERNEL,NU)
% [W,J,NU] = A*NUSVC([],KERNEL,NU)
% [W,J,NU] = A*NUSVC(KERNEL,NU)
%
% 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));
% NU Regularization parameter (0 < NU < 1): expected fraction of SV
% (optional; default: max(leave-one-out 1_NN error,0.01))
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object indices of support objects
% NU Actual nu_value used
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by quadratic
% programming. The difference with the standard SVC routine is the use and
% interpretation of the regularisation parameter NU. It is an upperbound
% for the expected classification error. By default NU is estimated by the
% leave-one-error of the 1_NN rule. For NU = NaN an automatic optimisation
% is performed using REGOPTC.
%
% 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.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, SVC, NUSVO, PROXM, USERKERNEL, REGOPTC
% Copyright: S.Verzakov, s.verzakov@ewi.tudelft.nl
% Based on SVC byby: D. de Ridder, D. Tax, 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
% $Id: nusvc.m,v 1.6 2010/06/25 09:50:40 duin Exp $
function [W,J,nu,C,alginf] = nusvc(varargin)
mapname = 'nuSVM';
argin = shiftargin(varargin,{'prmapping','char','cell'});
argin = setdefaults(argin,[],proxm([],'p',1),[],[]);
if mapping_task(argin,'definition')
W = define_mapping(argin,'untrained',mapname);
elseif mapping_task(argin,'training') % Train a mapping.
[a,kernel,nu,Options] = check_for_old_call(argin);
DefOptions.mean_centering = 1;
DefOptions.pd_check = 1;
DefOptions.bias_in_admreg = 1;
DefOptions.allow_ub_bias_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);
if isempty(nu)
nu = 2*min(max(testk(a,1),0.01),(0.8*min(classsizes(a))/size(a,1)));
end
% The SVC is basically a 2-class classifier. More classes are
% handled by mclassc.
if c == 2 % two-class classifier
if (isnan(nu)) % optimize trade-off parameter
defs = {proxm([],'p',1),[],[]};
parmin_max = [0,0;0.001,0.999;0,0]; % kernel and Options can not be optimised
[W,J,nu,C,alginf] = regoptc(a,mfilename,{kernel,nu,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,nu,C] = nusvo(+K,y,nu,Options);
% Store the results:
if ~isequal(kernel,0)
s = a(J,:);
end
% Store the results, use SVC for execution
W = prmapping('svc','trained',{u,s,v,kernel,J},getlablist(a),in_size,2);
W = cnormc(W,a);
W = setcost(W,a);
alginf.svc_type = 'nu-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(C);
end
else % multi-class classifier:
[W,J,nu,C,alginf] = mclassc(a,prmapping(mfilename,{kernel,nu,Options}),'single');
end
W = setname(W,mapname);
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 isstr(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,NU,par] = check_for_old_call(argin)
[a,kernel,NU,par] = deal(argin{:});
if ischar(kernel) && exist(kernel,'file') ~= 2
kernel = proxm(kernel,NU);
NU = par;
end