  We present a multiway fusion algorithm capable of directly processing
uncertain pairwise affinities. In contrast to existing works that require
initial pairwise associations, our MIXER algorithm improves accuracy by
leveraging the additional information provided by pairwise affinities. Our main
contribution is a multiway fusion formulation that is particularly suited to
processing non-binary affinities and a novel continuous relaxation whose
solutions are guaranteed to be binary, thus avoiding the typical, but
potentially problematic, solution binarization steps that may cause
infeasibility. A crucial insight of our formulation is that it allows for three
modes of association, ranging from non-match, undecided, and match. Exploiting
this insight allows fusion to be delayed for some data pairs until more
information is available, which is an effective feature for fusion of data with
multiple attributes/information sources. We evaluate MIXER on typical synthetic
data and benchmark datasets and show increased accuracy against the state of
the art in multiway matching, especially in noisy regimes with low observation
redundancy. Additionally, we collect RGB data of cars in a parking lot to
demonstrate MIXER's ability to fuse data having multiple attributes (color,
visual appearance, and bounding box). On this challenging dataset, MIXER
achieves 74% F1 accuracy and is 49x faster than the next best algorithm, which
has 42% accuracy. Open source code is available at
https://github.com/mit-acl/mixer.
