PROXXM

Proximity Mapping

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

Input
A	MxK 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 KxM proximity mapping (or kernel) defined by the  MxK dataset A. Unlabeled objects in A are neglected. If B is an NxK  dataset, then D=B*W is the NxM proximity matrix between B and A. The  proximities can be defined by the following types

     'POLYNOMIAL'   | 'P':  SIGN(A*B').*(A*B').^P
     'HOMOGENEOUS'  | 'H':  SIGN(A*B').*(A*B').^P
     'EXP'          | 'E':  EXP(-(||A-B||)/P)
     'EXP-SUM'      | 'ES': SUM_Z SIGN(P(Z)) * EXP(-(||A-B||)/P(Z))
     'RBF'          | 'R':  EXP(-(||A-B||.^2)/(P*P))
     'RBF-SUM'      | 'RS': SUM_Z SIGN(P(Z)) * EXP(-(||A-B||.^2)/(P(Z)^2))
     'SIGMOID'      | 'S':  SIGM(A*B'/P)
     'DSIGMOID'     | 'DS': SIGM(||A-B||^(2P(1))/P(2))
     'DISTANCE'     | 'D':  ||A-B||.^P
     'MULTIQUADRIC' | 'MQ': SQRT(||A-B||.^2/P(1) + P(2))
     'THIN-PLATE'   | 'TP': ||A-B||.^(2*P(1))/P(2) * LOG(1+||A-B||.^(2*P(1))/P(2))
     'N-THIN-PLATE' | 'NTP': -||A-B||.^(2*P(1))/P(2) * LOG(1+||A-B||.^(2*P(1))/P(2))
     'MINKOWSKI'    | 'M':  SUM(|A-B|^P).^(1/P)
     'CITY-BLOCK'   | 'C':  SUM(|A-B|)
     'COSINE'       | 'O':  1 - (A*B')/||A||*||B||
     'FOURIER'      | 'F'
     'TANH'         | 'T':  TANH(P*(A*B')/LENGTH(A) + P);
     'ANOVA'        | 'A':  ANOVA MODEL
     'BSPLINE'      | 'B':  BSPLINE MODEL, ORDER P
     'ANOVABSPLINE' | 'AB': ANOVA-BSPLINE MODEL, ORDER P
     'ANOVASPLINE1' | 'AS1':ANOVA-SPLINE MODEL, ORDER 1
     'ANOVASPLINE2' | 'AS2':ANOVA-SPLINE MODEL, ORDER 2
     'ANOVASPLINE3' | 'AS3':ANOVA-SPLINE MODEL, ORDER 3

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

proxm, mappings, datasets,