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.

Good public transport occupancy predictions are important for both passengers (to avoid crowded vehicles) and operating companies (to intervene with dispositive actions, hereby increasing the service quality). In this paper, we present a novel approach to improve the real-time prediction of passenger numbers. It combines a day-ahead prediction made using SARIMA with a real-time detection of characteristic deviation profiles. In our experiments with data from Germany, the proposed model outperforms artificial neural networks when only little data is available or the prediction happens with larger lead times than 90 minutes. It also has the inherent advantage of being faster to train and explainable in all steps.