shape_dtw_distance(x: ndarray, y: ndarray, window: float | None = None, descriptor: str = 'identity', reach: int = 30, itakura_max_slope: float | None = None, transformation_precomputed: bool = False, transformed_x: ndarray | None = None, transformed_y: ndarray | None = None) float[source]

Compute the ShapeDTW distance function between two series x and y.

The ShapeDTW distance measure was proposed in [1] and used for time series averaging in [2] as well.


First time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).


Second time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).

windowfloat or None, default=None

The window to use for the bounding matrix. If None, no bounding matrix is used. window is a percentage deviation, so if window = 0.1 then 10% of the series length is the max warping allowed. is used.

descriptorstr, default=None (if None then identity is used).

Defines which transformation is applied on the sub-sequences. Valid descriptors are: [‘identity’]

Identity is simply a copying mechanism of the sub-sequence, no transformations are done. For now no other descriptors are implemented.

If not specified then identity is used.

reachint, default=30.

Length of the sub-sequences to consider.

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.

transformation_precomputedbool, default = False

To choose if the transformation of the sub-sequences is pre-computed or not.

transformed_xnp.ndarray, default = None

The transformation of x, ignored if transformation_precomputed is False.

transformed_ynp.ndarray, default = None

The transformation of y, ignored if transformation_precomputed is False.


ShapeDTW distance between x and y, minimum value 0.


If x and y are not 1D or 2D arrays.


[1] Zhao, Jiaping, and Laurent Itti. “shapedtw: Shape dynamic time warping.”

Pattern Recognition 74 (2018): 171-184.

[2] Ali Ismail-Fawaz, Hassan Ismail Fawaz, François Petitjean, Maxime Devanne,

Jonathan Weber, Stefano Berretti, Geoffrey I. Webb and Germain Forestier. “ShapeDBA: Generating Effective Time Series Prototypes using ShapeDTW Barycenter Averaging” ECML/PKDD Workshop on Advanced Analytics and Learning on Temporal Data, Turin, Italy, 2023.