  We present a novel algorithm for (i) detecting approximate symmetries
inherently present among spatially localized molecular orbitals and (ii)
enforcing these in numerically exact manners by means of unitary optimization
techniques. The vast potential of our algorithm to compress a full set of
molecular orbitals into only a minimal set of symmetry-unique orbitals is
demonstrated, starting from localized bases of either Pipek-Mezey or
Foster-Boys orbitals. Comparisons of results based on either of these two
localization procedures indicate that Foster-Boys molecular orbitals can be
spanned by a smaller number of symmetry-unique orbitals on average, making
these outstanding candidates for the exploitation of general, (non-)Abelian
point-group symmetries in a range of local correlation methods. As an
illustration of said compressibility, our algorithm is capable of identifying a
mere 14 symmetry-unique orbitals for the buckminsterfullerene in the highly
symmetric $I_h$ molecular point group, corresponding to only $1.7\%$ of its
total 840 molecular orbitals in a standard double-$\zeta$ basis set. The
present work thus marks an important advancement in the exploitation of
point-group symmetry within local correlation methods, for which the
appropriate adaption of symmetry uniqueness among orbitals has the potential to
yield unprecedented speed-ups.
