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Fusing measurements from multiple, heterogeneous, partial sources, observinga common object or process, poses challenges due to the increasing availabilityof numbers and types of sensors. In this work we propose, implement andvalidate an end-to-end computational pipeline in the form of amultiple-auto-encoder neural network architecture for this task. The inputs tothe pipeline are several sets of partial observations, and the result is aglobally consistent latent space, harmonizing (rigidifying, fusing) allmeasurements. The key enabler is the availability of multiple slightlyperturbed measurements of each instance:, local measurement, "bursts", thatallows us to estimate the local distortion induced by each instrument. Wedemonstrate the approach in a sequence of examples, starting with simpletwo-dimensional data sets and proceeding to a Wi-Fi localization problem and tothe solution of a "dynamical puzzle" arising in spatio-temporal observations ofthe solutions of Partial Differential Equations.

Gappy local conformal auto-encoders for heterogeneous data fusion: in praise of rigidity