In this paper, we consider the problem of blindly calibrating a mobile sensor network i.e., determining the gain and the offset of each sensor from heterogeneous observations on a defined spatial area over time. For that purpose, we propose to revisit blind sensor calibration as an informed Nonnegative Matrix Factorization (NMF) problem with missing entries. In the considered framework, one matrix factor contains the calibration structure of the sensors and especially the values of the sensed phenomenon while the other one contains the calibration parameters of the whole sensor network. The available information is taken into account by using a specific parameterization of the NMF problem. Moreover, we also consider additional NMF constraints which can be independently taken into account, i.e., an approximate constraint over the mean calibration parameters and a sparse approximation of the sensed phenomenon over a known dictionary. The enhancement of our proposed approaches is investigated through more than 5000 simulations and is shown to be accurate for the considered application and to outperform a multi-hop micro-calibration technique as well as a method based on low-rank matrix completion and nonnegative least squares.

Video-based insect tracking provides vital insights into insect behavior and ecology, enhancing our understanding of their movements and interactions. Therefore, examining trends in this field over the last few years is essential. This study aims to conduct a bibliometric analysis to unveil the growing interest in video-based insect tracking with a short review based on documents used for bibliometric analysis. To achieve this, 453 documents were extracted from Scopus on 12 June 2023. Only documents in English published between 2010 and 2023, resulting in a dataset of 318 documents, were analyzed. The findings illustrate a consistent growth in video-based insect research over the last years, with a significant peak in 2021, comprising 32 documents. The journal PLOS ONE stands out as the most productive source. The USA exhibited the most significant interest in video-based insect tracking over the last years. Keyword analysis reflects the multidisciplinary nature of insect tracking research. The review demonstrated that video-based insect tracking serves two primary objectives: pose estimation and trajectory information. However, the main challenge in video-based insect tracking is to preserve the identity of multiple individuals in situations involving occlusions or complex interactions.

In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an $\alpha \beta$ -divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row sum-to-one property of one matrix factor. In this contribution, we extend our previous work which partly involved some of these aspects to $\alpha \beta$ -divergence cost functions. We derive new update rules which are extendthe previous ones and take into account the available information. Experiments conducted for several operating conditions on realistic simulated mixtures of particulate matter sources show the relevance of these approaches. Results from a real dataset campaign are also presented and validated with expert knowledge.

In this paper, we propose two weighted Non-negative Matrix Factorization (NMF) methods using a β-divergence cost function. This divergence is used as a dissimilarity measure which can be tuned by the parameter β. The weights allow to deal with the uncertainty associated to each data sample. Our first approach consists of generalizing weighted NMF methods proposed with specific divergences or norms to the β-divergence. In our second approach, we assume that some components of the factorization are known and we use them to inform our NMF algorithm. We thus consider a specific parameterization which involves these constraints. In particular, we propose specific multiplicative update rules for the minimization of this parameterization with a weighted divergence. Lastly, some experiments on simulated mixtures of particulate matter sources show the relevance of these approaches.