Josef Hoppe

Obtaining sparse, interpretable representations of observable data is crucial in many machine learning and signal processing tasks. For data representing flows along the edges of a graph, an intuitively interpretable way to obtain such representations is to lift the graph structure to a simplicial complex: The eigenvectors of the associated Hodge-Laplacian, respectively the incidence matrices of the corresponding simplicial complex then induce a Hodge decomposition, which can be used to represent the observed data in terms of gradient, curl, and harmonic flows. In this paper, we generalize this approach to cellular complexes and introduce the cell inference optimization problem, i.e., the problem of augmenting the observed graph by a set of cells, such that the eigenvectors of the associated Hodge Laplacian provide a sparse, interpretable representation of the observed edge flows on the graph. We show that this problem is NP-hard and introduce an efficient approximation algorithm for its solution. Experiments on real-world and synthetic data demonstrate that our algorithm outperforms current state-of-the-art methods while being computationally efficient.

Passengers of public transportation nowadays expect reliable and accurate travel information. The need for occupancy information is becoming more prevalent in intelligent public transport systems as people started avoiding overcrowded vehicles during the COVID-19 pandemic. Furthermore, public transportation companies require accurate occupancy forecasts to improve service quality. We present a novel approach to improve the prediction of passenger numbers that enhances a day-ahead prediction with real-time data. We first train a baseline predictor on historical automatic passenger counting data. Next, we train a real-time model on the deviations between baseline prediction and observed values, thus capturing events not addressed by the baseline. For the forecast, we attempt to detect emerging patterns in real time and adjust the baseline prediction with deviations from the patterns. Our experiments with data from Germany show that the proposed model improves the forecast of the baseline model and is only outperformed by artificial neural networks in some instances. If the training sets only cover a limited period of up to four months, our approach outperforms competing methods. For larger training sets, there are mixed results in the sense that for some test cases, certain types of neural networks yield slightly better results, but our method still performs well with less training effort, is explainable along the whole prediction process and can be applied to existing prediction methods.