  We consider the problem of simultaneously finding lower-dimensional subspace
structures in a given $m$-tuple of possibly corrupted, high-dimensional data
sets all of the same size. We refer to this problem as simultaneous robust
subspace recovery (SRSR) and provide a quiver invariant theoretic approach to
it. We show that SRSR is a particular case of the more general problem of
effectively deciding whether a quiver representation is semi-stable (in the
sense of Geometric Invariant Theory) and, in case it is not, finding a
subrepresentation certifying in an optimal way that the representation is not
semi-stable. In this paper, we show that SRSR and the more general quiver
semi-stability problem can be solved effectively.
