Path: utzoo!attcan!uunet!cs.utexas.edu!sun-barr!rutgers!njin!princeton!phoenix!mbkennel
From: mbkennel@phoenix.Princeton.EDU (Matthew B. Kennel)
Newsgroups: comp.ai.neural-nets
Subject: Re: Neural Net Applications in Chemistry
Message-ID: <8393@phoenix.Princeton.EDU>
Date: 12 May 89 19:55:05 GMT
References: <1989May10.095408.5836@gpu.utcs.utoronto.ca> <TED.89May10130744@kythera.nmsu.edu> <201@bach.nsc.com> <39817@bbn.COM> <8382@phoenix.Princeton.EDU> <14480@duke.cs.duke.edu>
Reply-To: mbkennel@phoenix.Princeton.EDU (Matthew B. Kennel)
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Organization: Princeton University, NJ
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In article <14480@duke.cs.duke.edu> hsg@romeo.UUCP (Henry Greenside) writes:
)In these discussions of Farmer et al's methods versus
)neural nets, has anyone addressed the real issue, how
)to treat high-dimensional data?
)
)In his paper, Farmer et al point out the crucial fact
)that one can learn only low dimensional chaotic systems
)(where low is rather vague, say of dimension less than
)about 5). High dimensional systems require huge amounts
)of data for learning. Presumably many interesting data
)sets (weather, stock markets, chemical patterns, etc.)
)are not low-dimensional and neither method will be
)useful.

Quite true.  This is definitely a fundamental problem.   As the
dimension gets higher and higher, the data series looks more and more
like true random noise, and so predicion becomes impossible.  Note, for
example, that the output of your favorite "random number generator" is
most likely deterministic, but probably has such a high dimension that
you can't predict with any accuracy without knowing the exact algorithm
used.

The real problem comes down to finding a representation with both
smooth mappings and low (fractal) dimensional input spaces.  This
requires plain old hard work and  clever insight.

Matt Kennel
mbkennel@phoenix.princeton.edu