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Construct affine (linear) mapping from parameters

    W = AFFINE(W1,W2)

 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

 W Affine mapping


This is a low level basic PRTools routine, not intended for direct use.  It 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 afterwards.

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.  This routine also executes W = AFFINE(W1,W2), if W1 and W2 are affine.  B = AFFINE(A,W), if A is a dataset and W is an affine mapping.  Finally, the transpose of an affine mapping exists and is defined as  an another 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,

PRTools Contents

PRTools User Guide

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