Research Seminar on AI: Outlier Detection for Trajectories via Flow-embeddings

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Tuesday, June 14, 2022, 4:00pm

Florian Frantzen and his team propose a method to detect outliers in empirically observed trajectories on a discrete or discretized manifold modeled by a simplicial complex. Their approach is similar to spectral embeddings such as diffusion-maps and Laplacian eigenmaps, that construct vertex embeddings from the eigenvectors of the graph Laplacian associated with low eigenvalues. Here Florian Frantzen and his team consider trajectories as edge-flow vectors defined on a simplicial complex, a higher-order generalization of graphs, and use the Hodge 1-Laplacian of the simplicial complex to derive embeddings of these edge-flows. By projecting trajectory vectors onto the eigenspace of the Hodge 1-Laplacian associated to small eigenvalues, the behavior of the trajectories relative to the homology of the complex can be characterized, which corresponds to holes in the underlying space. This enables to classify trajectories based on simply interpretable, low-dimensional statistics. Florian Frantzen and his team show how this technique can single out trajectories that behave (topologically) different compared to typical trajectories, and illustrate the performance of their approach with both synthetic and empirical data.

Florian Frantzen is a PhD student at the Computational Network Science group headed by tenure track assistant professor Michael Schaub. He received his M.Sc. and B.Sc. degrees in computer science from RWTH Aachen University. He is interested in analysing complex systems that can be abstracted as higher-order networks such as simplicial complexes or hypergraphs. His current research focuses on edge-flows on simplicial complexes, occuring for example when analysing trajectory data.

 
 

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