Blind Source Separation in Time and Space

There is nowadays an abundance of measurements which are taken at specific locations and / or repeatedly over time. In the project ``Blind Source Separation in Time and Space`` the aim is to filter the signals out of these often high-dimensional observations which makes interpreting and modelling the data much easier. For this purpose new statistical methodology will be developed to estimate the signal space dimension as well as the actual signals in a supervised and unsupervised dimension reduction context. Due to the complexity of the spatial, temporal and spatio-temporal data, the choice of the method for the data at hand might have a big impact on the results as well as the tuning parameter selection for the given method. To optimize method selection and parameter tuning a novel visual analytics approach will be developed for these methods to guide the user interactively to an optimal analysis of the data. Especially the combination and interaction of state of the art statistical methodology with visual analytics methods will improve the insight of the data analysts when analysing such complex data.

In today`s world, many measurements are taken at specific locations and/or repeatedly over time. The "Blind Source Separation in Time and Space" project posited that by representing data using latent variableshidden or unobserved variablesdimension reduction could be achieved with minimal information loss, facilitating more straightforward interpretation and modeling. Within a framework of mild statistical assumptions, the project developed a variety of estimators to extract these latent variables from temporal, spatial, and spatio-temporal data. The statistical properties of these estimators were meticulously derived, together with efficient algorithms to compute them. Furthermore, the project explored and refined different approaches for determining the number of significant latent variables. The efficacy of all developed methods was thoroughly evaluated in simulation studies, and their practicality was validated through applications in diverse fields such as geochemistry, climate and micro- climate data, neuroscience, and geological engineering. Applying blind source separation methods to multivariate temporal, spatial, and spatio-temporal data proved complex. Analysts face the challenge of selecting the most appropriate method and fine-tuning a myriad of parameters to optimize outcomes. Innovative visual analytic tools were developed to assist analysts in this endeavor. These tools guide choosing optimal parameter settings and facilitate the comparison of different estimators. Multiple studies with experts validated that these visual analytic tools simplify using blind source separation methods and can lead to profound insights when analyzing complex data sets. The project resulted in numerous scientific methodological publications across fields such as statistics, computer science, and signal processing and some publications in applied journals. Furthermore, nearly all implemented methods and the associated code are freely available to the public.