Simplicial convolutional filters can process signals defined over levels of a simplicial complex such as nodes, edges, triangles, and so on with applications in e.g., flow prediction in transportation or financial networks. However, the underlying topology expands over time in a way that new edges and triangles form. For example, in a transportation network, a new connection between two locations is newly built, or in a currency exchange market, two currencies can be exchanged without an intermediate currency that can be understood as a new edge between them. To handle the streaming nature of data, we propose an online prediction for edge flows which generalizes to other higher-order simplicial signals. This is achieved by updating the filter coefficients via an online gradient descent with a provable sub-linear regret relative to the simplicial filter optimized over the whole sequence of edge flows. The update of the filter coefficients associated with the lower and upper Hodge Laplacians can be uncoupled in general. We test the online edge flow prediction on an expanding synthetic simplicial complex and a coauthorship complex showing a close performance to the offline counterpart.
|Title of host publication
|Proceedings of the ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
|Place of Publication
|Number of pages
|Published - 2023
|48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023 - Rhodes Island, Greece
Duration: 4 Jun 2023 → 10 Jun 2023
|ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
|Institute of Electrical and Electronics Engineers (IEEE)
|48th IEEE International Conference on Acoustics, Speech and Signal Processing 2023
|4/06/23 → 10/06/23
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