Gappy local conformal auto-encoders for heterogeneous data fusion: in
  praise of rigidity
Erez Peterfreund Iryna Burak Ofir Lindenbaum Jim Gimlett Felix Dietrich Ronald R. Coifman Ioannis G. Kevrekidis
Fusing measurements from multiple, heterogeneous, partial sources, observing
a common object or process, poses challenges due to the increasing availability
of numbers and types of sensors. In this work we propose, implement and
validate an end-to-end computational pipeline in the form of a
multiple-auto-encoder neural network architecture for this task. The inputs to
the pipeline are several sets of partial observations, and the result is a
globally consistent latent space, harmonizing (rigidifying, fusing) all
measurements. The key enabler is the availability of multiple slightly
perturbed measurements of each instance:, local measurement, "bursts", that
allows us to estimate the local distortion induced by each instrument. We
demonstrate the approach in a sequence of examples, starting with simple
two-dimensional data sets and proceeding to a Wi-Fi localization problem and to
the solution of a "dynamical puzzle" arising in spatio-temporal observations of
the solutions of Partial Differential Equations.