PROXM

Proximity mapping

   W = PROXM(A,TYPE,P,WEIGHTS)
   W = A*PROXM([],TYPE,P,WEIGHTS)

Input
A	Dataset
TYPE	Type of the proximity (optional; default: 'distance')
P	Parameter of the proximity (optional; default: 1)
WEIGHTS	Weights (optional; default: all 1)

Output
W	Proximity mapping

Description

Computation of the [K x M] proximity mapping (or kernel) defined by  the [M x K] dataset A. Unlabeled objects in A are neglected.  If B is an [N x K] dataset, then D=B*W is the [N x M] proximity matrix  between B and A. The proximities can be defined by the following types

     'POLYNOMIAL'   | 'P': SIGN(A*B'+1).*(A*B'+1).^P
     'HOMOGENEOUS'  | 'H': SIGN(A*B').*(A*B').^P
     'EXPONENTIAL'  | 'E': EXP(-(||A-B||)/P)
     'RADIAL_BASIS' | 'R': EXP(-(||A-B||.^2)/(P*P))
     'SIGMOID'      | 'S': SIGM((SIGN(A*B').*(A*B'))/P)
     'DISTANCE'     | 'D': ||A-B||.^P
     'MINKOWSKI'    | 'M': SUM(|A-B|^P).^(1/P)
     'CITY-BLOCK'   | 'C': SUM(|A-B|)
     'COSINE'       | 'O': 1 - (A*B')/||A||*||B||

In the polynomial case for a non-integer P, the proximity is computed  as D = SIGN(S+1).*ABS(S+1).^P, in order to avoid problems with negative  inner products S = A*B'. The features of the objects in A and B may be  weighted by the weights in the vector WEIGHTS.

See also

mappings, datasets,