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From: kavuri@lips.ecn.purdue.edu (Surya N Kavuri )
Newsgroups: comp.ai.neural-nets
Subject: classification using Neural Nets]
Message-ID: <1991Feb5.230509.28778@noose.ecn.purdue.edu>
Date: 5 Feb 91 23:05:09 GMT
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I posted some questions on classification.  As it is quite shabby, I am writing it again.

(Q1) If I have a set of separable classes, am I always
guaranteed proper classification using a two layered backprop ?
I am not interested in linearly separable cases which are trivial.  In particular, what if the classes share a common nonlinear boundary ?
Example:  I have a circle inside a square.  I have two classes:
Class I:  INSIDE CIRCLE
Class II: OUTSIDE CIRCLE

The domain of inputs is the square (let it be a unit square). 
Now, using two inputs (the two coordinates x1 and x2), and one
output to identify the class (1 for inside circle 0 else).
Certainly I cannot solve this.  
If I use two output nodes, one for each class, even then I am 
not sure I can classify.  We need at least three lines(hyperpl.)
to separate the circle and the two output nodes give only two
hyperplanes.  Should I expect the sigmoid to some how "bend" the
hyperplane ? 
(Q2) If I use a hidden layer, can I expect the problem to be 
solvable ? If so, is it because of the increased dimensionality
(may be more than 2 hidden nodes) at the hidden layer ? Simply, 
WHAT ?!

SURYA KAVURI
(FIAT LUX)