%NU_SVR Support Vector Classifier: NU algorithm
%
% [W,J,C] = NU_SVR(A,TYPE,PAR,C,SVR_TYPE,NU_EPS,MC,PD)
%
% INPUT
% A Dataset
% TYPE Type of the kernel (optional; default: 'p')
% PAR Kernel parameter (optional; default: 1)
% C Regularization parameter (0 < C < 1): expected fraction of SV
% (optional; default: 0.25)
% SVR_TYPE This type can be 'nu' or 'epsilon'
% NU_EPS The corresponding value for NU or epsilon
% MC Do or do not data mean-centering (optional; default: 1 (to do))
% PD Do or do not the check of the positive definiteness (optional;
% default: 1 (to do))
%
% OUTPUT
% W Mapping: Support Vector Classifier
% J Object identifiers of support objects
% C Equivalent C regularization parameter of SVM-C algorithm
%
% DESCRIPTION
% Optimizes a support vector classifier for the dataset A by
% quadratic programming. The classifier can be of one of the types
% as defined by PROXM. Default is linear (TYPE = 'p', PAR = 1). In J
% the identifiers of the support objects in A are returned.
%
% C belogs to the interval (0,1). C close to 1 allows for more class
% overlap. Default C = 0.25.
%
% C is bounded from above by NU_MAX = (1 - ABS(Lp-Lm)/(Lp+Lm)), where
% Lp (Lm) is the number of positive (negative) samples. If NU > NU_MAX
% is supplied to the routine it will be changed to the NU_MAX.
%
% If C is less than some NU_MIN which depends on the overlap between
% classes algorithm will typically take long time to converge (if at
% all). So, it is advisable to set NU larger than expected overlap.
%
% Output is rescaled in a such manner as if it were returned by SVC with
% the parameter C.
%
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% NU_SVRO, SVO, SVC, MAPPINGS, DATASETS, PROXM
% Copyright: S.Verzakov, s.verzakov@ewi.tudelft.nl
% Based on SVC.M by D.M.J. Tax, D. de Ridder, R.P.W. Duin
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
% $Id: nu_svr.m,v 1.2 2009/01/31 18:43:11 duin Exp $
function [W, J, epsilon_or_nu] = nu_svcr(a,type,par,C,svr_type,nu_or_epsilon,mc,pd)
if nargin < 2 | ~isa(type,'prmapping')
if nargin < 8
pd = 1;
end
if nargin < 7
mc = 1;
end
if nargin < 6
nu_or_epsilon = [];
end
if nargin < 5 | isempty(svr_type)
svr_type = 'epsilon';
end
switch svr_type
case 'nu'
if isempty(nu_or_epsilon)
prwarning(3,'nu is not specified, assuming 0.25.');
nu_or_epsilon = 0.25;
end
%nu = nu_or_epsilon;
case {'eps', 'epsilon'}
svr_type = 'epsilon';
if isempty(nu_or_epsilon)
prwarning(3,'epsilon is not specified, assuming 1e-2.');
nu_or_epsilon = 1e-2;
end
%epsilon = nu_or_epsilon;
end
if nargin < 4 | isempty(C)
prwarning(3,'C set to 1\n');
C = 1;
end
if nargin < 3 | isempty(par)
par = 1;
prwarning(3,'Kernel parameter par set to 1\n');
end
if nargin < 2 | isempty(type)
type = 'p';
prwarning(3,'Polynomial kernel type is used\n');
end
if nargin < 1 | isempty(a)
W = prmapping(mfilename,{type,par,C,svr_type,nu_or_epsilon,mc,pd});
W = setname(W,['Support Vector Regression (' svr_type ' algorithm)']);
return;
end
islabtype(a,'targets');
[m,k] = getsize(a);
y = gettargets(a);
% The 1-dim SVR
if size(y,2) == 1 % 1-dim regression
uy = mean(y);
y = y - uy;
if mc
u = mean(a);
a = a - ones(m,1)*u;
else
u = [];
end
K = a*proxm(a,type,par);
% Perform the optimization:
[v,J,epsilon_or_nu] = nu_svro(+K,y,C,svr_type,nu_or_epsilon,pd);
% Store the results:
v(end) = v(end)+uy;
W = prmapping(mfilename,'trained',{u,a(J,:),v,type,par},getlablist(a),k,1);
W = setname(W,['Support Vector Regression (' svr_type ' algorithm)']);
%W = setcost(W,a);
J = getident(a,J);
%J = a.ident(J);
else
error('multivariate SVR is not supported');
end
else % execution
w = +type;
m = size(a,1);
% 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})
d = a*proxm(w{2},w{4},w{5});
else
d = (a-ones(m,1)*w{1})*proxm(w{2},w{4},w{5});
end
% When Data is mapped by the kernel, now we just have a linear
% regression w*x+b:
d = [d ones(m,1)] * w{3};
W = setdat(a,d,type);
end
return;