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The problem of information fusion from multiple data-sets acquired bymultimodal sensors has drawn significant research attention over the years. Inthis paper, we focus on a particular problem setting consisting of a physicalphenomenon or a system of interest observed by multiple sensors. We assume thatall sensors measure some aspects of the system of interest with additionalsensor-specific and irrelevant components. Our goal is to recover the variablesrelevant to the observed system and to filter out the nuisance effects of thesensor-specific variables. We propose an approach based on manifold learning,which is particularly suitable for problems with multiple modalities, since itaims to capture the intrinsic structure of the data and relies on minimal priormodel knowledge. Specifically, we propose a nonlinear filtering scheme, whichextracts the hidden sources of variability captured by two or more sensors,that are independent of the sensor-specific components. In addition topresenting a theoretical analysis, we demonstrate our technique on realmeasured data for the purpose of sleep stage assessment based on multiple,multimodal sensor measurements. We show that without prior knowledge on thedifferent modalities and on the measured system, our method gives rise to adata-driven representation that is well correlated with the underlying sleepprocess and is robust to noise and sensor-specific effects.

Diffusion-based nonlinear filtering for multimodal data fusion with application to sleep stage assessment