Fast informed nonnegative matrix factorization for mobile sensor calibration
Abstract
Air quality is usually monitored by a sparsely sampled network of authoritative and bulky sensors. Due to their high cost, only a few monitoring stations are deployed in each large city. As a consequence, considering miniaturized and mobile low-cost sensors to provide a finer spatial and temporal coverage is highly investigated. Unfortunately, these low-cost sensors tend to drift over time and thus require regular calibration, which cannot be done in-lab for obvious availability and cost considerations. To solve this issue, some data-driven techniques called “in-situ sensor calibration” were proposed. In particular, such a problem could be revisited as an informed matrix factorization problem with missing entries which jointly calibrates mobile low-cost sensors and can derive some air quality maps. Unfortunately, the proposed methods are slow to converge and cannot be applied to large-scale areas covered by hundreds of sensors. We thus propose several extensions of which will be introduced during this talk, i.e., (i) we extend the calibration model in to the case of arrays with cross-sensitive sensors, (ii) we propose several fast solvers to solve this informed problem. These solvers follow an Expectation-Maximization framework and combine the Nesterov gradient descent and accelerated structured random projections. Experiments on simulations show the relevance of the proposed methods.
