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Redefining embedding robustness: A Wasserstein-based analysis of delay–dimension dynamics

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  • Miyata, Tsuyoshi
  • Ichikawa, Atsushi
  • Sato, Takayuki

Abstract

Delay-coordinate embedding provides a fundamental framework for reconstructing state-space structures of dynamical systems from scalar time series. While Takens' embedding theorem guarantees the existence and robustness of valid embeddings, it does not prescribe unique optimal values for the time delay τ or embedding dimension m. In practice, these parameters are typically selected using heuristic criteria such as average mutual information (AMI) and false nearest neighbors (FNN), which often depend on implementation details and data length.

Suggested Citation

  • Miyata, Tsuyoshi & Ichikawa, Atsushi & Sato, Takayuki, 2026. "Redefining embedding robustness: A Wasserstein-based analysis of delay–dimension dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 210(P1).
    • Handle: RePEc:eee:chsofr:v:210:y:2026:i:p1:s0960077926007599
    DOI: 10.1016/j.chaos.2026.118618
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