M. Heiss, ONLINE LEARNING OR TRACKING OFF DISCRETE INPUT-OUTPUT MAPS, IEEE transactions on systems, man and cybernetics. Part A. Systems and humans, 27(5), 1997, pp. 657-668
This paper shows how a slowly time-varying nonlinear mapping can be le
arned, if, for every possible input value, the corresponding estimated
output value is stored in memory, (This representation form can be ca
lled ''flash map,'' or pointwise representation, or look-up table,) Th
us, very fast access to the mapping Is provided, The learning process
is performed online during regular operation of the system and must av
oid ''adaptation holes'' which could occur when some of the points are
more frequently updated than other points, After analyzing the proble
ms of previous approaches we show how radial basis function networks c
an be modified for flash maps and present the tent roof tensioning alg
orithm which is exclusively designed for learning flash maps, The conv
ergence of the tent roof tensioning algorithm is proved, Finally, we c
ompare the two approaches concluding that under the flash map restrict
ion the tent roof tensioning algorithm is the better choice for learni
ng low-dimensional mappings, if a polygonal approximation of the desir
ed mapping is sufficiently smooth.