%CMAPM Compute some special fixed mappings
%
% W = CMAPM(...)
% B = A*CMAPM(..)
%
% INPUT
% Various, see below
%
% OUTPUT
% W Mapping
% B Dataset
%
% DESCRIPTION
% CMAPM computes some special data-independent maps for scaling, selecting or
% rotating K-dimensional feature spaces.
%
% W = CMAPM(K,N) Selects the features listed in the vector N
% Deprecated, use FEATSEL(K,N)
% W = CMAPM(K,P) Polynomial feature map. P should be an N*K matrix
% in which each row defines the exponents for the
% original features in a polynomial term. Note: for
% N = 1 and/or K = 1, feature selection is applied!
% W = CMAPM(K,'EXP') Exponential mapping.
% Deprecated, use MAPM('EXP')
% W = CMAPM(K,'NEXP') Negative exponential mapping.
% Deprecated, use MAPM('NEXP')
% W = CMAPM(K,'LOG') Logarithmic mapping.
% Deprecated, use MAPM('LOG')
% W = CMAPM(K,'RANDROT') Defines a random K-dimensional rotation.
% W = CMAPM(F,'ROT') The N*K matrix F defines N linear combinations
% to be computed by X*F'.
% W = CMAPM(X,'SHIFT') Defines a shift of the origin by X.
% W = CMAPM(S,'SCALE') Divides the features by the components of the
% vector S.
% W = CMAPM({X,S},'SCALE') Shift by X and scale by S.
%
% EXAMPLES
% For the polynomial feature map, CMAPM(K,P), P defines exponents for each
% feature. So P = [1 0; 0 1; 1 1; 2 0; 0 2; 3 0; 0 3] defines 7 features,
% the original 2 (e.g. x and y), a mixture (xy) and all powers of the second
% (x^2,y^2) and third (x^3,y^3) order. Another example is P = diag([0.5 0.5
% 0.5]), defining 3 features to be the square roots of the original ones.
%
% Note that this is an old, complicated routine. For various options more
% logical alternatives are available, e.g. using FEATSEL, FILTM or MAPM.
%
% SEE ALSO (<a href="http://37steps.com/prtools">PRTools Guide</a>)
% MAPPINGS, SCALEM, FEATSELM, KLM
% 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: cmapm.m,v 1.5 2010/02/08 15:31:48 duin Exp $
function w = cmapm(arg1,arg2,par1,par2,par3)
if (nargin < 2)
error('insufficient arguments');
end
if (~(isa(arg1,'prdataset')||(isa(arg1,'double')&&numel(arg1)>1))) || ...
(isstr(arg2)&&(strcmp(arg2,'scale')||strcmp(arg2,'rot')||strcmp(arg2,'shift')))
% First form: ARG1 is a matrix, construct a mapping.
data = arg1;
if (isstr(arg2))
type = arg2;
switch (type)
case {'exp','nexp','log'} % Function mappings.
w = prmapping(mfilename,'fixed',{type},[],data,data);
w = setname(w,type);
case 'randrot' % Random rotation matrix.
[F,V] = preig(covm(randn(100*data,data)));
w = affine(F,zeros(1,data));
w = setname(w,'Random Rotation');
case 'rot' % Rotation by given matrix.
[n,k] = size(data);
w = affine(data',zeros(1,n));
w = setname(w,'Rotation');
case 'shift' % Shift by given vector.
k = length(data);
w = affine(eye(k),-data);
w = setname(w,'Shift');
w = setlabels(w); % avoid feature labels
case 'scale' % Shift, scale & (optionally) clip.
if (iscell(data))
% Extract and check parameters.
shift = data{1}; scale = data{2};
if (length(data) == 3), clip = data{3}; else, clip = 0; end
k = length(scale);
if (~isempty(scale)) & (length(shift) ~= k)
error('shift and scale should have same dimension')
end
else
% Only a scale is specified; set shift and clip to 0.
scale = data; k = length(scale);
shift = zeros(1,k); clip = 0;
end
% Create mapping
if (clip)
w = prmapping(mfilename,'fixed',{'normalize',shift,ones(1,k)./scale,clip},[],k,k);
w = setname(w,'Scaling');
else
w = affine(1./scale,-shift./scale);
w = setlabels(w); % avoid feature labels
end
otherwise
error(['unknown option ' arg2])
end
else
% ARG2 is not a string: feature selection or polynomial mapping.
if (min(size(arg2)) == 1)
% ARG2 is a vector: feature selection, DATA is input feature size
prwarning(4,'second input argument is a vector: performing feature selection');
if (min(arg2) < 1) | (max(arg2) > data)
error('Selected features out of range')
end
w = prmapping(mfilename,'fixed',{'featsel',arg2},[],data,length(arg2));
w = setname(w,'Feature Selection');
else
% ARG2 is a matrix: polynomial mapping.
prwarning(4,'second input argument is a matrix: performing polynomial mapping');
[n,k] = size(arg2);
if (data ~= k)
error('matrix has wrong size')
else
w = prmapping(mfilename,'fixed',{'polynomial',arg2},[],k,n);
w = setname(w,'Polynomial');
end
end
end
else
% Second form: ARG1 is a dataset, execute some fixed mappings
if ~isdataset(arg1)
% we need a dataset here to avoid problems (RD)
a = arg1;
arg1 = prdataset(arg1);
else
a = +arg1; % Extract dataset.
end
[m,k] = size(a);
type = arg2;
featlist = getfeatlab(arg1);
switch (type)
case 'exp'
b = exp(a);
case 'nexp'
b = exp(-a);
case 'log'
b = log(a);
case 'normalize'
b = a - repmat(par1,m,1); % Subtract mean (par1).
% Multiply by scale; use different ways of looping for small and
% P = diag([0.5 0.5 0.5])
% large feature sizes
if (m > k), for j = 1:k, b(:,j) = b(:,j)*par2(j); end
else, for i = 1:m, b(i,:) = b(i,:).*par2; end
end
% Clip, if necessary (par3 ~= 0, see SCALEM).
if (exist('par3')) & (par3)
J = find(b < 0); b(J) = zeros(size(J)); % Set values < 0 to 0...
J = find(b > 1); b(J) = ones(size(J)); % ...and values > 1 to 1.
end
case 'featsel'
featlist = getfeatlab(arg1);
b = a(:,par1); % Select feature indices (par1).
if ~isempty(featlist)
featlist = featlist(par1,:);
end
case 'polynomial'
[n,k] = size(par1); % Create polynomial features.
b = zeros(m,n);
for i = 1:n
b(:,i) = prod((a .^ (repmat(par1(i,:),m,1))),2);
end
featlist = [1:n]';
otherwise
error(['unknown mapping: ' type])
end
w = setdata(arg1,b,featlist);
end
return