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Abstract:
We give necessary and sufficient conditions for uniqueness of
the support vector solution for the problems of pattern recognition
and regression estimation, for a general class of cost functions.
We show that if the solution is not unique, all support vectors are
necessarily always at bound, and we give some simple examples of
non-unique solutions. We note that uniqueness of the primal (dual)
solution does not necessarily imply uniqueness of the dual (primal)
solution. We show how to compute the threshold $b$ when the
solution is unique, but when all support vectors are at bound, in
which case the usual method for determining $b$ does not
work.
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