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Data fusion is a natural and common approach to recovering the state of physical systems. But the dissimilar appearance of different sensors remains a fundamental obstacle. We propose a unified embedding scheme for multisensory data, based on the spectral diffusion framework, which addresses this issue. Our scheme is purely data-driven and assumes no a priori statistical or deterministic models of the data sources. To extract the underlying structure, we first embed separately each input channel; the resultant structures are then combined in diffusion coordinates. In particular, as different sensors sample similar phenomena with different sampling densities, we apply the density invariant Laplace-Beltrami embedding. This is a fundamental issue in multisensor acquisition and processing, overlooked in prior approaches. We extend previous work on group recognition and suggest a novel approach to the …