Choice of the basis functions

[GOLDFARB%unb.ca@UNBMVS1.csd.unb.ca]

On  Fri, 06 Sep 91 02:09:17 ADT  	"Thomas H. Hildebrandt  "
<thildebr at athos.csee.lehigh.edu> writes:

>                                I could not agree with you more in
> thinking that the search for an appropriate basis set is one of the
> important open problems in connectionist research.
>
> If nothing is known about the process to be modelled, is there any
> more efficient way to select a basis than trial-and-error?
>
> Are some sets of basis functions more likely to efficiently describe a
> randomly selected process?  Aside from compactness, what other
> properties can be ascribed to a desirable basis?
>
> Given a particular set of basis functions, what criteria must be met
> by the underlying process in order for the bases to generalize well?
> Can these criteria be tested easily?
>
> These are just a few of the questions that come to mind.  I'll be
> interested in any thoughts you have in this area.
>
>                Thomas H. Hildebrandt

Within the metric model proposed in
    L.Goldfarb, A New Approach to Pattern Recognition, in Progress in
    Pattern Recognition 2, L.N.Kanal and A.Rosenfeld, eds., North-
    Holland, Amsterdam,1985
the question of choice of the "right" basis can be resolved quite
naturally: the finite training metric set is first isometrically
embedded in the "appropriate" Minkowski vector space, and then a
subset best representing the principal axes of the constructed
vector representation is chosen as the basis.

-- Lev Goldfarb