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[ENH]: Add kdtw distance implementation #2827

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@SebastianSchmidl SebastianSchmidl commented May 20, 2025

Reference Issues/PRs

What does this implement/fix? Explain your changes.

Adds KDTW distance (univariate, multivariate, and variable-length support).
Original implementation is at https://people.irisa.fr/Pierre-Francois.Marteau/REDK/KDTW/kdtw.m (Matlab ⚠️ ).

Open todos:

  • current implementation is a similarity. How to convert to distance?
  • generate expected values using original Octave implementation and fix tests
  • replace kdtw kernel in KernelKMeans implementation

Does your contribution introduce a new dependency? If yes, which one?

no

@SebastianSchmidl SebastianSchmidl self-assigned this May 20, 2025
@SebastianSchmidl SebastianSchmidl added enhancement New feature, improvement request or other non-bug code enhancement distances Distances package labels May 20, 2025
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Thank you for contributing to aeon

I would have added the following labels to this PR based on the changes made: [ $\color{#5209C9}{\textsf{distances}}$, $\color{#2C2F20}{\textsf{testing}}$ ], however some package labels are already present.

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Comment on lines 193 to 196
return (
1.0
- _kdtw_cost_matrix(x, y, gamma, epsilon, normalize_input)[n, m] / norm_factor
)
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This similarity-to-distance conversion part is problematic (if no input normalization is used) because the computed similarities are very, very small for most inputs and, thus, vanish.

E.g., all the following similarities will disappear in floating-point arithmetic (first two basic motions time series with different gammas):

  • 1.0 - 2.7435e-123 == 1.0
  • 1.0 - 4.9180e-72 == 1.0
  • 1.0 - 6.5392e-53 == 1.0

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