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AFFINE
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 |
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.
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