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Topological Data Analysis in Automotive Industry

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23. Internationales Stuttgarter Symposium (ISSYM 2023)

Abstract

The automotive industry is facing the challenge of gaining knowledge from large datasets—originating for example from the research and development process, IT systems, production, or from fleet data. Problems most likely become manifest in data and result in increased costs. Examples can range from problems in the on-board electrical system to virtual validation of autonomous driving functions in R&D.

Hence, one important use case is the automatic detection of anomalous behavior in the data to forecast and identify potential problems as early as possible.

We demonstrate new mathematical methods from Topological Data Analysis (TDA) that can help to address these kinds of problems. TDA is a rather new field in mathematics that combines techniques from geometry and topology to analyze noisy datasets. Beside academia, it has been applied successfully to various fields including medicine (identification of tumor cells), finance (fraud detection), and materials science (structure analysis).

We highlight two main methods from TDA: the (ball) mapper algorithm and persistent homology and illustrate potential applications in automotive industry. We illustrate these abstract methods and show that they can produce valuable knowledge about potential problems—for example in the automotive context—giving an added value to the customer and the OEM.

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References

  1. Carlsson, G.: Topology and data. Bulletin of the American Mathematical Society 46(2), 255-308 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  2. Carlsson, G., Zomorodian, A.: The theory of multidimensional persistence. Discrete & Computational Geometry 42(1), 71-93 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. Chazal, F., Michel, B., An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists. Frontiers in AI (2021).

    Google Scholar 

  4. Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. Discrete & Computational Geometry 37(1), 103-120 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  5. Dlotko, P.: Ball mapper: a shape summary for topological data analysis. arXiv:1901.07410

  6. Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete & Computational Geometry 28(4), 511-533 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  7. Edelsbrunner, H., Harer, J.: Computational Topology: An introduction. American Mathematical Society, Providence (2010).

    MATH  Google Scholar 

  8. Edelsbrunner, H.: A short course in computational geometry and topology. Springer Brief in Applied Sciences and Technology, Springer (2014).

    Google Scholar 

  9. Fasy, B.T., Kim, J., Lecci, F., Maria, C.: Introduction to the R package TDA. arXiv:1411.1830.

  10. Ghrist, R.: Barcodes: The persistent topology of data. Bulletin of the American Mathematical Society 45(1), 61-75 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  11. Munch, E.: A User’s guide to Topological Data Analysis. Journal of Learning Analytics 4(2), 47-61 (2017).

    Article  Google Scholar 

  12. Saxena, A., Goebel, K., Simon, D., Eklund, N.: Damage Propagation Modeling for Aircraft Engine Run-to-Failure Simulation. In: Proceedings of the 1st International Conference on Prognostics and Health Management (PHM08), Denver CO (2008).

    Google Scholar 

  13. Singh, G., Memoli, F., Carlsson, G.: Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. In: Eurographics Symposium on Point Based Graphics, pp. 91–100, European Association for Computer Graphics (2007).

    Google Scholar 

  14. Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete & Computational Geometry 33(2), 249-274 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  15. Vartziotis, D., Himpel, B., Pfeil, M.: Creation of higher-energy superposition quantum states motivated by geometric transformations. arXiv:1712.07963 (2017).

  16. Lloyd, S., Garnerone, S., Zanardi, P.: Quantum algorithms for topological and geometric analysis of data. Nature Communications 7, 10138 (2016).

    Article  Google Scholar 

  17. Riegg, A., Kraus, H., Leder, M., Vaudrevange, P., Stasinou, M., Banerjee, R., Kröker, R., Dierolf, B., Rößler, T., Faessler, V., Keckeisen, M.: Quantum Computing für einen Breitensuche-Algorithmus mit Anwendung in der Fahrzeug-Routenplanung. Digital Product Forum 2022.

    Google Scholar 

  18. Bannerjee, R., Stasinou, M.-E., Vaudrevange, P., Kraus, H., Rößler, T., Keckeisen, M., V. Faessler, V.: Accelerating Simulations using Hybrid Quantum-Classical Machine Learning. SimTech2023.

    Google Scholar 

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Correspondence to P. K. S. Vaudrevange .

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© 2023 Der/die Autor(en), exklusiv lizenziert an Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature

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Beutenmüller, F., Dierolf, B., Keckeisen, M., Pausinger, F., Vaudrevange, P.K.S. (2023). Topological Data Analysis in Automotive Industry. In: Kulzer, A.C., Reuss, HC., Wagner, A. (eds) 23. Internationales Stuttgarter Symposium. ISSYM 2023. Proceedings. Springer Vieweg, Wiesbaden. https://doi.org/10.1007/978-3-658-42048-2_4

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