Tensor-variate Gaussian processes regression and its application to video surveillance

We present a novel framework for tensor valued Gaussian processes (GP) regression, which exploits a covariance function defined on tensor representation of data inputs. In this way, we bring together the powerful GP methods supported by Bayesian inference and higher-order tensor analysis techniques into one framework. This enables us to account for the underlying structure of data within the model, providing a powerful framework for structural data analysis, such as 3D video sequences. To this end, we propose a new kernel function with tensor arguments under the assumption of generative models, in the form of product kernels where a symmetrical Kullback-Leibler divergence measure is exploited to define the covariance function for tensorial data. A fully Bayesian treatment is employed to estimate the hyperparameters and infer the predictive distributions. Simulation results on both the synthetic data and a real world application of estimating the crowd size from 3D videos demonstrate the effectiveness of the proposed framework.