Multimodal Data Fusion in Sensor Networks via Copula Processes

We develop an efficient data fusion algorithm for field reconstruction of multiple physical phenomena, which exhibit multiple modalities each with complex dependence behavior. In particular, we design a novel spatial model where multiple latent processes are modelled as Multi-Output Gaussian Process. We encode a linear dependency structure through a specified covariance function in both space and between different modalities of the spatial processes monitored. To account for different data modalities, we model the spatial dependence between each process via Copula dependence structures [1], thus allowing to choose any marginal distribution or process (possibly different) for each of the physical phenomena. We formulate the field reconstruction problem and develop a low complexity algorithm to approximate the intractable predictive posterior distribution. We show that our model significantly outperforms the model which treats the different physical phenomena independently in terms of prediction meansquared-errors (MSE). This provides the motivation to use our model for multimodal data fusion.