PRTools Contents PRTools User Guide
cmapm

CMAPM

### Compute some special fixed mappings

W = CMAPM(...)
B = A*CMAPM(..)

Various, see below
 Input

 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.

### Example(s)

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.
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