  Many robotics applications require alignment and fusion of observations
obtained at multiple views to form a global model of the environment. Multi-way
data association methods provide a mechanism to improve alignment accuracy of
pairwise associations and ensure their consistency. However, existing methods
that solve this computationally challenging problem are often too slow for
real-time applications. Furthermore, some of the existing techniques can
violate the cycle consistency principle, thus drastically reducing the fusion
accuracy. This work presents the CLEAR (Consistent Lifting, Embedding, and
Alignment Rectification) algorithm to address these issues. By leveraging
insights from the multi-way matching and spectral graph clustering literature,
CLEAR provides cycle consistent and accurate solutions in a computationally
efficient manner. Numerical experiments on both synthetic and real datasets are
carried out to demonstrate the scalability and superior performance of our
algorithm in real-world problems. This algorithmic framework can provide
significant improvement in the accuracy and efficiency of existing discrete
assignment problems, which traditionally use pairwise (but potentially
inconsistent) correspondences. An implementation of CLEAR is made publicly
available online.
