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From: saswss@hotellng.unx.sas.com (Warren Sarle)
Subject: Re: Question: Unsupervised ANN in Astrophysics Application?
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Date: Sat, 5 Nov 1994 21:31:01 GMT
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Keywords: astrophysics, unsupervised, regression
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In article <39dkge$jcl@news.ycc.yale.edu>, sdyson@minerva.cis.yale.edu (Samuel E Dyson) writes:
|>      I am an undergraduate physics major investigating the use of
|> unsupervised ANNs as a means of discovering dependences among the
|> properties of 1000 gamma ray bursts.  Each burst represents one
|> observation and has about 15 measurable properties.  I wish to find
|> classifications of bursts according to functional relationships between
|> the columns of a matrix whose 1000 rows are the gamma ray bursts and the
|> 15 or so columns are the properties of those bursts.  The specific
|> functional relationships that might exist are not known and therefore
|> cannot be 'taught' to a supervised NN.  We do not know what truth is and
|> would like to let an unsupervised NN discover the dependences between
|> properties through regression or other means.  Statistical packages (SAS
|> and SPLUS) have been investigated but require interactive searches for
|> dependences among all columns which would be highly inefficient.
|> Suggestions? Reply to Sam Dyson at: sdyson@minerva.cis.yale.edu or (203)
|> 436-1684.

You are mistaken about the "interactive searches". 

First do a principal component analysis. Small eigenvalues indicate
linear relationships. The size of the eigenvalue gives the accuracy
of the relationship. The corresponding eigenvector gives the linear
coefficients.

If that doesn't produce satisfactory results, try a nonlinear variant
of principal components such as PRINQUAL in SAS. S-Plus probably has
something similar. You can get similar results by including various
nonlinear transformations of your 15 properties, such as polynomials,
splines, or trigonometric functions, in a standard principal component
analysis.

There may exist some form of neural network that identifies nonlinear
functional relationships, but the usual unsupervised networks identify
the large eigenvalues, whereas your application requires the small
eigenvalues.

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.
