Analog Outputs

[David J. Burr]

Regarding the question of networks  with  analog  outputs  I
recommend  some earlier papers on elastic mapping algorithms
(below).  These have true  analog  outputs  since  they  are
based on Green's function solutions in continuous media.  In
contrast to similar self-organized mapping schemes, they ex-
hibit  full  symmetry  on the input spaces in the sense that
the distance from pattern A to B is equal  to  the  distance
from  B  to  A.   This  is  based on a generalization of the
"winner-take-all" arrangement to a  "symmetric  winner-take-
all".   Extension to an "average of k winners" was suggested
in the CGIP paper.

Symmetry is important as it uses a "push-pull"  force  field
for  more  accurate  correspondence and hence faster conver-
gence.  This is useful for pulling together  extremities  of
strokes  in  character recognition.  Popular self-organizing
feature maps can be viewed as a special case of elastic map-
ping without the symmetry component.  Symmetric elastic map-
ping recently found optimum solutions to travelling salesman
problems  using  fewer  iterations  than  a competing analog
method (Burr, Snowbird, April 1988).


D. J. Burr, Computer Graphics and Image Processing, Vol. 15,
102-112, 1981.

D. J.  Burr,  IEEE  Transactions  on  Pattern  Analysis  and
Machine  Intelligence,  Vol.  PAMI-3,  No.  6, 708-713, Nov.
1981.