Variables obtained by experimental measurements or statistical inference typically carry uncertainties. When an algorithm uses such quantities as input variables, this uncertainty should propagate to the algorithm's output. Concretely, we consider the classic notion of principal component analysis (PCA): If it is applied to a finite data matrix containing imperfect (i.e., uncertain) multidimensional measurements, its output-a lower-dimensional representation-is itself subject to uncertainty. We demonstrate that this uncertainty can be approximated by appropriate linearization of the algorithm's nonlinear functionality, using automatic differentiation. By itself, however, this structured, uncertain output is difficult to interpret for users. We provide an animation method that effectively visualizes the uncertainty of the lower dimensional map. Implemented as an open-source software package, it allows researchers to assess the reliability of PCA embeddings.

In this paper, we present two approaches and algorithms that adapt areas of interest (AOI) or regions of interest (ROI), respectively, to the eye tracking data quality and classification task. The first approach uses feature importance in a greedy way and grows or shrinks AOIs in all directions. The second approach is an extension of the first approach, which divides the AOIs into areas and calculates a direction of growth, i.e. a gradient. Both approaches improve the classification results considerably in the case of generalized AOIs, but can also be used for qualitative analysis. In qualitative analysis, the algorithms presented allow the AOIs to be adapted to the data, which means that errors and inaccuracies in eye tracking data can be better compensated for. A good application example is abstract art, where manual AOIs annotation is hardly possible, and data-driven approaches are mainly used for initial AOIs.

In this paper, we present two approaches and algorithms that adapt areas of interest. We present a new deep neural network (DNN) that can be used to directly determine gaze position using EEG data. EEG-based eye tracking is a new and difficult research topic in the field of eye tracking, but it provides an alternative to image-based eye tracking with an input data set comparable to conventional image processing. The presented DNN exploits spatial dependencies of the EEG signal and uses convolutions similar to spatial filtering, which is used for preprocessing EEG signals. By this, we improve the direct gaze determination from the EEG signal compared to the state of the art by 3.5 cm MAE (Mean absolute error), but unfortunately still do not achieve a directly applicable system, since the inaccuracy is still significantly higher compared to image-based eye trackers.