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PhD Student

Computational Network Science
RWTH Aachen University

hoppe@cs.rwth-aachen.de

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Bio

I am currently a PhD Student in Michael T. Schaub’s Group at RWTH Aachen University.

Previously, I also obtained my Bachelor’s and Master’s in Computer Science at RWTH University. My master’s thesis led to my first (joint) publication on passenger prediction in public transport, but my focus has since shifted toward graph signal processing and algebraic topology. In that area, I am proud to report that our paper Representing Edge Flows on Graphs via Sparse Cell Complexes received the Best Paper award at the 2023 Learning on Graphs Conference. I am also interested in higher-order networks more generally; here, I have been contributing to TopoX.

In my free time, I am active in the german-language debating scene, more specifically, the debating club Aachen.

Publications

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Representing Edge Flows on Graphs via Sparse Cell Complexes
In The Second Learning on Graphs Conference, 2023.
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.
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Improving the Prediction of Passenger Numbers in Public Transit Networks by Combining Short-Term Forecasts With Real-Time Occupancy Data
In IEEE Open Journal of Intelligent Transportation Systems, 2023.
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.