Xref: utzoo alt.cyb-sys:33 comp.ai.neural-nets:979
Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!uwm.edu!uakari.primate.wisc.edu!ames!ucsd!sdcc6!sdcc13!pa1159
From: pa1159@sdcc13.ucsd.EDU (Matt Kennel)
Newsgroups: alt.cyb-sys,comp.ai.neural-nets
Subject: Re: Data Complexity
Message-ID: <1269@sdcc13.ucsd.EDU>
Date: 6 Oct 89 22:06:31 GMT
References: <517@uvaee.ee.virginia.EDU>
Reply-To: pa1159@sdcc13.ucsd.edu.UUCP (Matt Kennel)
Organization: Univ. of California, San Diego
Lines: 37

In article <517@uvaee.ee.virginia.EDU> aam9n@uvaee.ee.virginia.EDU (Ali Minai) writes:
>
>
>The question is this:
>
>Given deterministic data {(X,Y)} where X is in a finite interval of
>n-d real space and Y is in a finite interval of m-d real space,
>what *structural* measures (if any) have people suggested for
>the "complexity" of the data?
>

I don't know what other people have suggested, but I'll spout
out a suggestion of my own: crib ideas from the nonlinear dynamics
people.  For a rough-and-ready measure of the complexity of the
input space, why not use fractal dimension?  And for the output
space, what about the sum of the positive Lyapunov exponents of the
nonlinear mapping?


>4) How can such a "complexity" measure be made scale-invariant?

That's exactly what the fractal dimension does?
>
>etc.
>
>Also, what about such complexity measures for continuous functions?
>I mean measures defined structurally, not according to the type
>of the function (e.g. degree for polynomials).

I don't understand what you mean by "defined structurally."

>Ali Minai
>aam9n@uvaee.ee.virginia.edu

Matt Kennel
UCSD physics
pa1159@sdcc13.ucsd.edu