ddtw_distance¶

ddtw_distance(x: ndarray, y: ndarray, window: float | None = None, itakura_max_slope: float | None = None) → float[source]¶

Compute the DDTW distance between two time series.

Derivative dynamic time warping (DDTW) is an adaptation of DTW originally proposed in [1]. DDTW takes a version of the first derivatives of the series prior to performing standard DTW. The derivative function, defined in [1], is:

\[d_{i}(x) = \frac{{}(x_{i} - x_{i-1} + (x_{i+1} - x_{i-1})/2)}{2}\]

where \(x\) is the original time series and \(d_x\) is the derived time series.

Parameters:

xnp.ndarray: First time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).
ynp.ndarray: Second time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).
windowfloat, default=None: The window to use for the bounding matrix. If None, no bounding matrix is used.
itakura_max_slopefloat, default=None: Maximum slope as a proportion of the number of time points used to create Itakura parallelogram on the bounding matrix. Must be between 0. and 1.

Returns:

float: ddtw distance between x and y.

Raises:

ValueError: If x and y are not 1D or 2D arrays. If n_timepoints or m_timepoints are less than 2.

References

[1] (1,2)

Keogh, Eamonn & Pazzani, Michael. (2002). Derivative Dynamic Time Warping. First SIAM International Conference on Data Mining. 1. 10.1137/1.9781611972719.1.

Examples

>>> import numpy as np
>>> from aeon.distances import ddtw_distance
>>> x = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
>>> y = np.array([[42, 23, 21, 55, 1, 19, 33, 34, 29, 19]])
>>> round(ddtw_distance(x, y))
2180