Kalman Filtering for Simplicial Processes

Conference Paper (2024)
Author(s)

R.T. Money (Simula Metropolitan Center for Digital Engineering, TU Delft - Multimedia Computing)

M. Sabbaqi (TU Delft - Multimedia Computing)

Joshin Krishnan (Simula Metropolitan Center for Digital Engineering)

Baltasar Beferull-Lozano (Simula Metropolitan Center for Digital Engineering)

E. Isufi (TU Delft - Multimedia Computing)

Multimedia Computing
DOI related publication
https://doi.org/10.1109/IEEECONF60004.2024.10942943
More Info
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Publication Year
2024
Language
English
Multimedia Computing
Bibliographical Note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.@en
Pages (from-to)
49-53
ISBN (electronic)
9798350354058
Reuse Rights

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Abstract

In this paper, we propose a topology-aware Kalman filter for hidden dynamics over simplicial complex. Specifically, we consider that the hidden dynamics of a system can be expressed as a simplicial process that respects the structure of the underlying network. And these dynamics are observed through an observation matrix, which can be represented using simplicial convolution filters. This combination allows us to model effectively a broader spectrum of network dynamics than graph-based alternatives, such as edge flow evolution. Additionally, we propose a parametric, structure-aware noise covariance model for the system dynamics. We alternate between estimating the process state using the Kalman filter and updating the parameters through maximum likelihood estimation. The efficacy of the proposed approach is demonstrated through experiments on both real-world and synthetic datasets.

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