  The Self-Optimal-Transport (SOT) feature transform is designed to upgrade the
set of features of a data instance to facilitate downstream matching or
grouping related tasks. The transformed set encodes a rich representation of
high order relations between the instance features. Distances between
transformed features capture their direct original similarity and their third
party agreement regarding similarity to other features in the set. A particular
min-cost-max-flow fractional matching problem, whose entropy regularized
version can be approximated by an optimal transport (OT) optimization, results
in our transductive transform which is efficient, differentiable, equivariant,
parameterless and probabilistically interpretable. Empirically, the transform
is highly effective and flexible in its use, consistently improving networks it
is inserted into, in a variety of tasks and training schemes. We demonstrate
its merits through the problem of unsupervised clustering and its efficiency
and wide applicability for few-shot-classification, with state-of-the-art
results, and large-scale person re-identification.
