range_svdd.m

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function sigma = range_svdd(a,frac_rej,frac_err)
% RANGE_SVDD compute SVDD over a range of sigma's.
%
% sigma = range_svdd(A,frac_rej,frac_err)
%
% The SVDD is optimized for a complete range of frac_rej by trying a
% range of sigma's in the Gaussian kernel and matching a good sigma
% with each frac_rej. This routine is internally used in dd_roc for
% speed-up.
%
% see also dd_roc

% Copyright: D. Tax, R.P.W. Duin, [e-mail]
% Faculty of Applied Physics, Delft University of Technology
% P.O. Box 5046, 2600 GA Delft, The Netherlands

if (nargin<3)
  frac_err = 0;
end
if (length(frac_rej)==1)
  warning('Please use range_svdd for a VECTOR of frac_rej.');
end

% number of steps over the sigma range
nrs = 40;

% find the range of useful distance in the data
D = distm(+a);
maxD = sqrt(max(max(D)));
%D = D + maxD*eye(size(D,1));
I = find(D==0); D(I) = maxD;
minD = sqrt(min(min(D)));

% find a range of sigmas:
step_s = (log(maxD) - log(minD))/(nrs-1);
list_s = exp(log(minD):step_s:log(maxD));

% set up variables:
[nlab,lablist,m,k,c] = dataset(a);
laba = -ones(m,1); laba(find_target(a)) = 1;
%laba = nlab; laba(nlab>1) = -1;
svdd_rej = zeros(nrs,1);

% loop over the sigma:
alf = [];
Da = +distm(a);
for s=1:nrs

%  [frac_SV2,alf,R2,I] = f_svs(list_s(s),Da,laba,frac_err);
  [frac_SV2,alf,R2,I] = new_f_svs(list_s(s),+a,laba,frac_err);
  svdd_rej(s) = sqrt(frac_SV2);

  if (svdd_rej(s)<min(frac_rej)) % stop increasing s: not necessary
    svdd_rej = svdd_rej(1:s);
    break;
  end
end
%[list_s(1:s)' svdd_rej]

% now we have to find the final value(s) for the given fracsv's,
% interpolate if necessary
nrsigma = length(frac_rej);
sigma = zeros(nrsigma,1);

for s=1:nrsigma

  I = find(svdd_rej<=frac_rej(s));
  if isempty(I)                             % all solutions are bad
    [mins,Imin] = min(svdd_rej);
    sigma(s) = list_s(Imin);
  else
%    [I svdd_rej(I) list_s(I)']
    if ((length(I)==1)|(I(1)<2))                 % in the beginning
      sigma(s) = list_s(I(1));
    else                        % somewhere in between: interpolate
      I = I(1);
      sigma(s) = list_s(I-1) + ...
      (frac_rej(s)-svdd_rej(I-1))*(list_s(I)-list_s(I-1))/...
                                      (svdd_rej(I)-svdd_rej(I-1));
    end
  end
end

return