%AFFINE Construct affine (linear) mapping from parameters % % W = AFFINE(R,OFFSET,LABLIST_IN,LABLIST_OUT,SIZE_IN,SIZE_OUT) % W = AFFINE(R,OFFSET,A) % W = AFFINE(W1,W2) % % INPUT % R Matrix of a linear mapping from a K- to an L-dimensional space % OFFSET Shift applied after R; a row vector of the length L % (optional; default: zeros(1,L)) % LABLIST_IN Labels of the features of the input space % (optional; default: (1:K)') % LABLIST_OUT Labels of the features of the output space, e.g. class names % for linear classifiers (optional; default: (1:L)') % SIZE_IN If based on images: size vector of the input dimensionality % (optional; default: K) % SIZE_OUT If based on images: size vector of the output dimensionality % (optional; default: L) % A Dataset (LAB_IN_LIST and SIZE_IN are derived from A) % W1,W2 Affine mappings % % OUTPUT % W Affine mapping % % DESCRIPTION % Defines a mapping W based on a linear transformation R and an offset. % R should be a [K x L] matrix describing a linear transformation from % a K-dimensional space to an L-dimensional space. If K=1, then R is % interpreted as the diagonal of an [L x L] diagonal matrix. OFFSET is % a row vector of the length L, added afterwords. % % Affine mappings are treated by PRTools in a special way. A scaling % defined for an affine mapping, e.g. by W = SETSCALE(W,SCALE) is directly % executed by a multiplication of the coefficients. Also, the product of % two affine mappings is directly converted to a new affine mapping. % Finally, the transpose of an affine mapping exists and is defined as % an another affine mapping. Consequently, this routine also executes % W = AFFINE(W1,W2) if W1 and W2 are affine and B = AFFINE(A,W), if A % is a dataset and W is an affine mapping. % % An [M x K] dataset A can be mapped as D = A*W. The result is equivalent % to [+A, ones(M,1)]*[R; OFFSET]. The dataset D has feature labels stored % in LABLIST. The number of this labels should, thereby, be at least L. % % SEE ALSO % DATASETS, MAPPINGS % Copyright: R.P.W. Duin, r.p.w.duin@prtools.org % Faculty EWI, Delft University of Technology % P.O. Box 5031, 2600 GA Delft, The Netherlands % $Id: affine.m,v 1.6 2007/04/16 08:33:19 duin Exp $ function w = affine(R,offset,lablist_in, lablist_out,size_in,size_out) prtrace(mfilename); if (nargin == 1) | (~isa(offset,'mapping')) % Definition of an affine mapping [m,k] = size(R); if (nargin < 6) prwarning(5,'SIZE_OUT is not specified. The number of columns of R, %d, is assumed.', k); size_out = k; end if (nargin < 5) prwarning(5,'SIZE_IN is not specified. The number of rows of R, %d, is assumed.', m); size_in = m; end if (nargin < 4) prwarning(5,'LABLIST_OUT is not specified, [1:%d]'' assumed.', k); lablist_out = []; end if (nargin < 3) prwarning(5,'LABLIST_IN is not specified, [1:%d]'' assumed.', m); lablist_in = []; end if (nargin < 2) | (isempty(offset)) prwarning(3,'OFFSET not specified, a zero vector assumed.'); offset = zeros(1,k); end % Check consistencies if (~isa(R,'double')) error('No proper transformation matrix stored.') end if (size_in == 1) & nargin < 3 % R is a scaling vector size_in = size_out; end if (isempty(lablist_in)) lablist_in = genlab(1,[1:size_in]'); end cost = []; if (isa(lablist_in,'dataset')) % Copy labels from dataset/datafile cost = lablist_in.cost; size_in = getfeatsize(lablist_in); lablist_in = getfeatlab(lablist_in); % size_out = k; % Wrong for classifiers defined for 1D datasets end if (size(lablist_in,1) < m) error('Wrong number of input labels supplied.') end if isempty(lablist_out) lablist_out = genlab(1,[1:size_out]'); end if (size(lablist_out,1) < k) error('Wrong number of output labels supplied.') end if any(size(offset) ~= [1,k]) error('Offset is not a row vector of the correct size.') end % Store the results: d.rot = R; d.offset = offset; d.lablist_in = lablist_in; w = mapping(mfilename,'trained',d,lablist_out,size_in,size_out); w = setcost(w,cost); elseif isa(R,'mapping') % Two mappings, stored in R and OFFSET, should be combined. w1 = R; w2 = offset; if (~isclassifier(w1)) & (~isclassifier(w2)) & (strcmp(getmapping_file(w1),'affine')) & (strcmp(getmapping_file(w2),'affine')) % Combine two affine mappings % If d1.rot or d2.rot are vectors, they have to be interpreted as % the diagonal matrices, unless the inner dimension does not fit. d1 = +w1; d2 = +w2; if (size(d1.rot,1) == 1) % d1.rot is a vector if (size(d2.rot) == 1) % d2.rot is a vector d.rot = d1.rot.*d2.rot; d.offset = d1.offset.*d2.rot + d2.offset; else % d2.rot is a matrix d.rot = repmat(d1.rot',1,size(d2.rot,2)).*d2.rot; d.offset = d1.offset*d2.rot + d2.offset; end else % d1.rot is a matrix %RD Here comes a bug fix that I needed to continue, I am not sure it %RD is sufficient It may even introduce new problems, especially for % 1D datasets. %if size(d2.rot,1) == 1 % d2.rot is vector if (size(d1.rot,2) > 1) & (size(d2.rot,1) == 1) % d2.rot is a vector d.rot = d1.rot.*repmat(d2.rot,size(d1.rot,1),1); d.offset = d1.offset.*d2.rot + d2.offset; else % d2.rot is a matrix d.rot = d1.rot*d2.rot; d.offset = d1.offset*d2.rot + d2.offset; end end d.lablist_in = d1.lablist_in; w = mapping(mfilename,'trained',d,getlabels(w2),getsize_in(w1),getsize_out(w2)); else % Store a sequential mapping. w = sequential(w1,w2); end else % Execution of the affine mapping. % R is a dataset, OFFSET defines the mapping. v = offset; [m,k] = size(R); d = +v; if (size(d.rot,1) == 1) & (k > 1) % No rotation, just a scaling x = zeros(m,k); Rdat = +R; if (m > k) % Necessary switch for handling large feature sizes. for j=1:k x(:,j) = Rdat(:,j)*d.rot(j); end else for i=1:m x(i,:) = Rdat(i,:).*d.rot; end end x = x + repmat(d.offset,m,1); else % Rotation. x = [+R,ones(m,1)] * [d.rot;d.offset]; end if size(v,2) == 2 & size(x,2) == 1 x = [x -x]; end w = setdat(R,x,v); end return;
