%STACKED Combining classifiers in the same feature space
%
% WC = STACKED(W1,W2,W3, ....) or WC = [W1,W2,W3, ...]
% WC = STACKED({W1,W2,W3, ...}) or WC = [{W1,W2,W3, ...}]
% WC = STACKED(WC,W1,W2, ....) or WC = [WC,W2,W3, ...]
%
% INPUT
% W1,W2,W3 Set of classifiers
%
% OUTPUT
% WC Combined classifier
%
% DESCRIPTION
% The base classifiers (or mappings) W1, W2, W3, ... defined in the same
% feature space are combined in WC. This is a classifier defined for the
% same number of features as each of the base classifiers and with the
% combined set of outputs. So, for three two class classifiers defined for
% the classes 'c1' and 'c2', a dataset A is mapped by D = A*WC on the outputs
% 'c1','c2','c1','c2','c1','c2', which are the feature labels of D. Note that
% classification by LABELD(D) finds for each vector in D the feature label
% of the column with the maximum value. This is equivalent to using the
% maximum combiner MAXC,
%
% Other fixed combining rules like PRODC, MEANC, and VOTEC can be applied by
% D = A*WC*PRODC. A trained combiner like FISHERC has to be supplied with
% the appropriate training set by AC = A*WC; VC = AC*FISHERC. So the
% expression VC = A*WC*FISHERC yields a classifier, not a dataset as with
% fixed combining rules. This classifier operates in the intermediate
% feature space, the output space of the set of base classifiers. A new
% dataset B has to be mapped to this intermediate space first by BC = B*WC
% before it can be classified by D = BC*VC. As this is equivalent to D =
% B*WC*VC, the total trained combiner is WTC = WC*VC = WC*A*WC*FISHERC. To
% simplify this procedure PRTools executes the training of a combined
% classifier by WTC = A*(WC*FISHERC) as WTC = WC*A*WC*FISHERC.
%
% It is also possible to combine a set of untrained classifiers, e.g. WC =
% [LDC NMC KNNC([],1)]*CLASSC, in which CLASSC takes care that all outputs
% will be transformed to appropriate posterior probabilities. Training of
% all base classifiers is done by WC = A*WC. Again, this may be combined
% with training of a combiner by WTC = A*(WC*FISHERC).
%
% EXAMPLES
% PREX_COMBINING
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, DATASETS, MAXC, MINC, MEANC,
% MEDIANC, PRODC, FISHERC, PARALLEL
% Copyright: R.P.W. Duin, r.p.w.duin@37steps.com
function w = stacked(varargin)
% No arguments given: just return map information.
if (nargin == 0)
w = prmapping(mfilename,'combiner');
return
end
% Single argument: should be a mapping or cell array of mappings.
if (nargin == 1)
v = varargin{1};
% If V is a single mapping, process it directly.
if (~iscell(v))
if (~isa(v,'prmapping'))
error('Mapping expected.')
end
w = prmapping('stacked',getmapping_type(v),{v},getlabels(v));
w = set(w,'size',getsize(v));
else
% If V is a cell array of mappings, call this function recursively.
if (size(v,1) ~= 1)
error('Row of cells containing mappings expected')
end
w = feval(mfilename,v{:});
end
return
end
% Multiple arguments, all of which are mappings: combine them.
if (~(isa(varargin{1},'prdataset') | (isa(varargin{1},'double') & ~isempty(varargin{1}))))
% Get the first mapping.
v1 = varargin{1};
if (isempty(v1))
start = 3;
v1 = varargin{2};
else
start = 2;
end
ismapping(v1); % Assert V1 is a mapping.
k = prod(getsize_in(v1));
labels = getlabels(v1);
type = getmapping_type(v1);
% If V1 is already a stacked mapping without output conversion,
% unpack it to re-stack.
if (~strcmp(getmapping_file(v1),mfilename)) | getout_conv(v1) > 1
v = {v1};
else
v = getdata(v1);
end
% Now stack the second to the last mapping onto the first.
for j = start:nargin
v2 = varargin{j};
if (~strcmp(type,getmapping_type(v2)))
error('All mappings should be of the same type.')
end
if (getsize(v2,1) ~= k)
error('Mappings should have equal numbers of inputs.')
end
v = [v {v2}];
if ischar(labels)
labels = char(labels,getlabels(v2));
elseif iscell(labels)
labels = {labels{:} getlabels(v2)};
else
labels = [labels;getlabels(v2)];
end
end
w = prmapping('stacked',type,v,labels,k);
elseif isdatafile(varargin{1})
% datafile * stacked mapping: store it as postprocessing
w = addpostproc(varargin{1},stacked(varargin{2:end}));
else
% The first argument is a dataset: apply the stacked mapping.
a = varargin{1};
v = varargin{2};
if (~isa(v,'prmapping'))
error('Mapping expected as second argument.')
end
if nargin==2 & isstacked(v)
n = length(v.data);
else
v = varargin(2:end);
n = nargin-1;
end
% Calculate W, the output of the stacked mapping on A.
w = [];
if n > 2
s = sprintf('Concatenating %i mappings: ',n);
prwaitbar(n,s);
end
for j = 1:n
if n > 2, prwaitbar(n,j,[s int2str(j)]); end
b = a*v{j};
% If, for a mapping to 1D (e.g. a 2-class discriminant)
% more than 1 output is returned, truncate.
if (size(v{j},2) == 1)
b = b(:,1);
end
w = [w b]; % Concatenate the outputs.
end
if n > 2
prwaitbar(0);
end
end
return