%SVMR SVM regression
%
% W = SVMR(X,NU,KTYPE,KPAR,EP)
% W = X*SVMR([],NU,KTYPE,KPAR,EP)
% W = X*SVMR(NU,KTYPE,KPAR,EP)
%
% INPUT
% X Regression dataset
% NU Fraction of objects outside the 'data tube'
% KTYPE Kernel type (default KTYPE='p', for polynomial)
% KPAR Extra parameter for the kernel
% EP Epsilon, with of the 'data tube'
%
% OUTPUT
% W Support vector regression
%
% DESCRIPTION
% Train an nu-Support Vector Regression on dataset X with parameter NU.
% The kernel is defined by kernel type KTYPE and kernel parameter KPAR.
% For the definitions of these kernels, have a look at proxm.m.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% LINEARR, PROXM, GPR, SVC
% Copyright: D.M.J. Tax, D.M.J.Tax@37steps.com
% Faculty EWI, Delft University of Technology
% P.O. Box 5031, 2600 GA Delft, The Netherlands
function y = svmr(varargin)
argin = shiftargin(varargin,{'scalar','char'},1);
argin = shiftargin(argin,'char',2);
argin = setdefaults(argin,[],0.01,'p',1,0.2);
if mapping_task(argin,'definition')
y = define_mapping(argin,'untrained');
y = setname(y,'SVM regression');
elseif mapping_task(argin,'training') % Train a mapping.
[x,nu,ktype,kpar,ep] = deal(argin{:});
[n,d] = size(x);
y = gettargets(x);
% kernel mapping:
wk = proxm(+x,ktype,kpar);
K = +(x*wk);
% setup optimization:
tol = 1e-6;
C = 1/(n*nu);
H = [K -K; -K K];
f = repmat(ep,2*n,1) - [y; -y];
A = [];
b = [];
Aeq = [ones(1,n) -ones(1,n)];
beq = 0;
lb = zeros(2*n,1);
ub = repmat(C,2*n,1);
%do the optimization:
if exist('qld')
alf = qld(H,f,Aeq,beq,lb,ub,[],1);
else
alf = quadprog(H,f,A,b,Aeq,beq,lb,ub);
end
% find SV's
w = alf(1:n)-alf((n+1):end); % the real weights
Isv = find(abs(w)>tol);
Ibnd = find(abs(w(Isv))<C-tol);
% for the 'real' sv's, we want the classifier output to compute the
% offset:
I = Isv(Ibnd);
out1 = sum(repmat(w',length(Ibnd),1).*K(I,:),2);
sw = sign(w);
out = y(I) - out1 - sw(I).*ep;
% store the useful parameters:
W.b = mean(out);
W.wk = proxm(+x(Isv,:),ktype,kpar);
W.w = w(Isv);
y = prmapping(mfilename,'trained',W,1,d,1);
y = setname(y,'Linear regression');
else
% evaluation
[x,v] = deal(argin{1:2});
W = getdata(v);
[n,d] = size(x);
Kz = +(x*W.wk);
out = sum(repmat(W.w',n,1).*Kz,2) + repmat(W.b,n,1);
y = setdat(x,out);
end
return