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Assessing the Effectiveness of Intrinsic Dimension Estimators for Uncovering the Phase Space Dimensionality of Dynamical Systems from State Observations

A Comparative Analysis

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 14146)

Abstract

Devising a model of a dynamical system from raw observations of its states and evolution requires characterising its phase space, which includes identifying its dimension and state variables. Recently, Boyuan Chen and his colleagues proposed a technique that uses intrinsic dimension estimators to discover the hidden variables in experimental data. The method uses estimators of the intrinsic dimension of the manifold of observations. We present the results of a comparative empirical performance evaluation of various candidate estimators. We expand the repertoire of estimators proposed by Chen et al. and find that several estimators not initially suggested by the authors outperforms the others.

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Notes

  1. 1.

    The code to reproduce the results presented in this paper is available at: https://github.com/fchavelli/id_estimation/tree/main.

  2. 2.

    The package is available at https://scikit-dimension.readthedocs.io.

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Acknowledgements

This research is supported by Singapore Ministry of Education, grant MOE-T2EP50120-0019, and by the National Research Foundation, Prime Minister’s Office, Singapore, under its Campus for Research Excellence and Technological Enterprise (CREATE) programme as part of the programme Descartes.

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Correspondence to Félix Chavelli .

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Chavelli, F., Zi-Yu, K., Low, J.S.C., Bressan, S. (2023). Assessing the Effectiveness of Intrinsic Dimension Estimators for Uncovering the Phase Space Dimensionality of Dynamical Systems from State Observations. In: Strauss, C., Amagasa, T., Kotsis, G., Tjoa, A.M., Khalil, I. (eds) Database and Expert Systems Applications. DEXA 2023. Lecture Notes in Computer Science, vol 14146. Springer, Cham. https://doi.org/10.1007/978-3-031-39847-6_18

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  • DOI: https://doi.org/10.1007/978-3-031-39847-6_18

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