linear separability

[ananth sankar]

Alexis says with regard to Christoph's message...

>Your analysis relies on the dividing hyperplane passing through the
>origin, a condition that you dutifully state.  But this need not be
>the case for linearly separable problems.  Consider the simple 2D case
>with the four points (1,1), (1,-1), (-1,1), (-1,-1).  Place one point
>in H1 and the rest in H2.  The problem is clearly linearly separable,
>but there is no line that passes through the origin that will serve.

Christoph also had stated that his n-dimensional input vector consisted
of n-1 inputs and a constant input of 1. Thus the search for a solution
for "a" and "b" so that a.x > b for all x is now transformed to solving
a.x - b > 0 for all x, where (a,b) is a hyperplane passing thru the origin.
Your example above has a hyperplane thru origin in 3-space solution if 
you add an additional input of 1 to each vector.


--Ananth