%NORMAL_MAP Map a dataset on normal-density classifiers or mappings
% Back-end routine
%
% F = NORMAL_MAP(A,W)
%
% INPUT
% A Dataset
% W Mapping
%
% OUTPUT
% F Density estimation for classes in A
%
% DESCRIPTION
% Maps the dataset A by the normal density based classifier or mapping W.
% For each object in A, F returns the densities for each of the classes or
% distributions stored in W. For classifiers, the densities are weighted
% by the class prior probabilities. This routine is automatically called for
% computing A*W if W is a normal density based classifier or a mapping.
%
% Use W = LOGDENS(W) (or W = W*LOGDENS) if absolute densities are not
% needed and a more accurate posterior probability is desired.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, QDC, UDC, LDC, GAUSSM, LOGDENS
% Copyright: 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: normal_map.m,v 1.16 2010/02/24 20:28:13 duin Exp $
function F = normal_map(varargin)
if isstruct(varargin{1}) % this is a constructor call like W = normal_map(w,nlab,k,c)
[w,nlab,k,c] = deal(varargin{:});
deg = ndims(w.cov)-1; % linear or quadratic
n = size(w.mean,1); % number of components
w.det = zeros(1,n);
if (deg == 1)
H = w.cov;
if min(size(H)) == 1 % cov matrix stored as scalar or diagonal
E = 1./H;
w.det = repmat(sum(log(real(H+1e-16))),1,n) ;
else
if (prrank(H) < size(H,1))
prwarning(2,'Singular case, pseudo-inverse of the covariance matrix is used.');
E = real(prpinv(H));
else
E = real(prinv(H));
end
w.det = repmat(sum(log(real(preig(H)+1e-16)+realmin)),1,n);
end
w.cov = E;
elseif deg == 2
w.det = zeros(1,n);
for i=1:n
H = w.cov(:,:,i);
if (prrank(H) < size(H,1))
prwarning(1,'Singular case, pseudo-inverse of the covariance matrix is used.');
E = real(prpinv(H));
else
E = real(prinv(H));
end
w.cov(:,:,i) = E;
w.det(i) = sum(log(abs(preig(H)+1e-16)+realmin));
end
else
error('Illegal value for degree')
end
F = prmapping(mfilename,'trained',w,nlab,k,c);
return
end
% Now we have an execution call like F = normal_map(A,W)
[A,W] = deal(varargin{:});
if isdatafile(A)
F = prdataset(A*W);
return
end
w = +W; % data field of W (fields: w.mean, w.cov, w.prior, w.nlab)
% each of these data fields has a mean, cov, prior for separate
% Gaussian components. The nlab field assigns each component
% to a class.
if ~isfield(w,'det') % if det-field is not available, we are dealing with an old def
F = normal_map_old(A,W);
return
end
[k,c] = size(W); % c is number of classes
% DEG = 1 indicates a common cov. matrix and DEG = 2 - separate cov. matrices.
deg = ndims(w.cov)-1;
U = w.mean; G = w.cov; p = w.prior;
if (abs(1-sum(p)) > 1e-6)
error('Class or component probabilities do not sum to one.')
end
lablist = getlab(W);
[m,ka] = size(A);
if (ka ~= k),
error('Feature sizes of the dataset and the mapping do not match.');
end
n = size(U,1); % Number of components.
F = zeros(m,n); % Gaussian densities for each component to be computed.
if (deg == 1)
E = G;
end
% Loop over components.
t = sprintf('Processing %i components: ',n);
prwaitbar(n,t);
for i=1:n
prwaitbar(n,i,[t num2str(i)]);
% Shift A such that the mean lies at the origin.
X = +A - ones(m,1)*U(i,:);
if (deg == 2)
E = G(:,:,i);
end
if min(size(E)) == 1 % diagonal or scalar of cov matrix
if max(size(E)) == 1, E = repmat(E,1,k); end
F(:,i) = -0.5*sum(X.*X.*repmat(E(:)',m,1),2) - (w.det(i) + k*log(2*pi))*0.5;
else
% Gaussian distribution for the i-th component. Take log of density to preserve tails
F(:,i) = -0.5*sum(X'.*(E*X'),1)' - (w.det(i) + k*log(2*pi))*0.5;
end
if (getout_conv(W) ~= 2) % take log of density to preserve tails
F(:,i) = exp(F(:,i));
end
end
prwaitbar(0)
if isfield(w,'nlab')
% For mixtures of Gaussians. Relates components to classes
nlab = w.nlab;
cc = max(w.nlab);
else
nlab = [1:c];
cc = c;
end
if (getout_conv(W) == 2)
Cmax = max(F(:)); % scale to gain accuracy in the tails
F = F - Cmax;
end
FF = zeros(m,cc);
% Loop over true classes. Weight the probabilities by the priors.
for j = 1:cc
J = find(nlab == j);
if (getout_conv(W) == 2) % take log of density to preserve tails
% difficult to get this right for MOGs, and moreover, probably not of
% much help. Anyway, we give it a try.
FF(:,j) = exp(F(:,J))*w.prior(J)';
% like in parzen_map, use in tails just largest component
L = find(FF(:,j) <= 1e-300);
N = find(FF(:,j) > 1e-300);
if ~isempty(L)
[FM,R] = max(F(L,J),[],2);
FF(L,j) = FM + log(w.prior(R)');
end
if ~isempty(N)
FF(N,j) = log(FF(N,j));
end
else
FF(:,j) = F(:,J) * w.prior(J)';
end
end
if (getout_conv(W) == 2) % scale to gain accuracy in the tails
Fmax = max(FF,[],2); % really needed!!!!
FF = FF - repmat(Fmax,1,cc);
FF = exp(FF);
else
FF = FF + realmin; % avoid devision by 0 in computing posterios later
end
if isdataset(A)
F = setdata(A,FF,lablist);
else
F = FF;
end
return;
%NORMAL_MAP_OLD Map a dataset on normal-density classifiers or mappings
% using an old classifier definition:
% cov inverse during execution
%
function F = normal_map_old(A,W)
w = +W; % data field of W (fields: w.mean, w.cov, w.prior, w.nlab)
% each of these data fields has a mean, cov, prior for separate
% Gaussian components. The nlab field assigns each component
% to a class.
[k,c] = size(W); % c is number of classes
% DEG = 1 indicates a common cov. matrix and DEG = 2 - separate cov. matrices.
deg = ndims(w.cov)-1;
U = w.mean; G = w.cov; p = w.prior;
if (abs(1-sum(p)) > 1e-6)
error('Class or component probabilities do not sum to one.')
end
lablist = getlab(W);
[m,ka] = size(A);
if (ka ~= k),
error('Feature sizes of the dataset and the mapping do not match.');
end
n = size(U,1); % Number of components.
F = zeros(m,n); % Gaussian densities for each component to be computed.
if (deg == 1)
H = G;
if (prrank(H) < size(H,1))
prwarning(2,'Singular case, pseudo-inverse of the covariance matrix is used.');
E = real(prpinv(H));
else
E = real(prinv(H));
end
end
% Loop over components.
for i=1:n
% Shift A such that the mean lies at the origin.
X = +A - ones(m,1)*U(i,:);
if (deg == 2)
H = G(:,:,i);
if (prrank(H) < size(H,1))
prwarning(1,'Singular case, pseudo-inverse of the covariance matrix is used.');
E = real(prpinv(H));
else
E = real(prinv(H));
end
end
% Gaussian distribution for the i-th component. Take log of density to preserve tails
F(:,i) = -0.5*sum(X'.*(E*X'),1)' - (sum(log(real(preig(H)+1e-16)+realmin)) + k*log(2*pi))*0.5;
if (getout_conv(W) ~= 2) % take log of density to preserve tails
F(:,i) = exp(F(:,i));
end
end
if isfield(w,'nlab')
% For mixtures of Gaussians. Relates components to classes
nlab = w.nlab;
cc = max(w.nlab);
else
nlab = [1:c];
cc = c;
end
if (getout_conv(W) == 2)
Cmax = max(F(:)); % scale to gain accuracy in the tails
F = F - Cmax;
end
FF = zeros(m,cc);
% Loop over true classes. Weight the probabilities by the priors.
for j = 1:cc
J = find(nlab == j);
if (getout_conv(W) == 2) % take log of density to preserve tails
% difficult to get this right for MOGs, and moreover, probably not of
% much help. Anyway, we give it a try.
FF(:,j) = exp(F(:,J))*w.prior(J)';
% like in parzen_map, use in tails just largest component
L = find(FF(:,j) <= 1e-300);
N = find(FF(:,j) > 1e-300);
if ~isempty(L)
[FM,R] = max(F(L,J),[],2);
FF(L,j) = FM + log(w.prior(R)');
end
if ~isempty(N)
FF(N,j) = log(FF(N,j));
end
else
FF(:,j) = F(:,J) * w.prior(J)';
end
end
if (getout_conv(W) == 2)
FF = exp(FF);
else
FF = FF + realmin; % avoid devision by 0 in computing posterios later
end
if isdataset(A)
F = setdata(A,FF,lablist);
else
F = FF;
end
return;