[comp.ai.neural-nets] classification using NNs

kavuri@cb.ecn.purdue.edu (Surya N Kavuri ) (02/06/91)

 If I have a set of linearly separable classes, am I 
always guaranteed proper classification using a two 
layered backprop ? In particular, what if the classes
are adjacent sharing the boundary ?
Example: I have a circle inside a square.  I have two classes:
class I: inside circle
class II: outside circle 
The square a unit square and let us assume that constitutes
the domain of inputs.  Now, using two inputs(x1 and x2 coords)
and one output to identify the class, I cannot classify. 
If I use two output nodes, one for each class, even then I am 
not sure I can classify.  We need atleast three lines 
(hyperplanes) to separate the circle and the two output nodes
give two hyperplanes.  Should I expect the sigmoid to some how
"bend" the hyperplane (its linear summation input) ? Why ?

SURYA KAVURI
(FIAT LUX)