  This paper studies loss functions for finite sets. For a given finite set
$S$, we give sum-of-square type loss functions of minimum degree. When $S$ is
the vertex set of a standard simplex, we show such loss functions have no
spurious minimizers (i.e., every local minimizer is a global one). Up to
transformations, we give similar loss functions without spurious minimizers for
general finite sets. When $S$ is approximately given by a sample set $T$, we
show how to get loss functions by solving a quadratic optimization problem.
Numerical experiments and applications are given to show the efficiency of
these loss functions.
