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From: gal2@kimbark.uchicago.edu (Jacob Galley)
Subject: Fuzzy ARTMAP questions
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Date: Fri, 28 Apr 1995 17:32:24 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.neural-nets:23720 comp.soft-sys.matlab:13017


Hello all.  I am researching Carpenter & Grossberg's Fuzzy ARTMAP
algorithm in Matlab.  So far the results have been quite impressive.
On the circle-in-square benchmark, my routine can categorize inputs
with 97.4% accuracy after training on a set of 1000 inputs for *ONE*
epoch.  Incredible!

But I have a few questions:


1) What is the purpose of alpha, the choice parameter?  I don't
understand what effect different values of alpha have on the category
choice equation.


2) The norm of the vector x, written |x|, is defined to be the sum of
the absolute values of the elements of x.  In Matlab, this is 

	norm(x,1) = sum(abs(x));

Why is this definition of norm preferable to, say,

	norm(x,2) = sum(abs(x)^2)^(1/2);

or some other norm?  The norm used in Fuzzy ART seems to produce
hyperrectangular categories.  It seems to me that "rounder" hyper-
spherical categories might be better for at least some applications.


3) The only article I've seen specifically about Fuzzy ARTMAP is the one
by G. Carpenter, S. Grossberg, N. Markuzon, J. Reynolds & D. Rosen (1992) 
in the _IEEE Transactions on Neural Networks_ 3(5), 698-713.  Is there
a better or recently updated source worth digging up?


Thanks in advance for your advice,
Jake.

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