ddtw_distance

ddtw_distance(x: ndarray, y: ndarray, window: float | None = None, itakura_max_slope: float | None = None, bounding_matrix: ndarray = None, compute_derivative=None, **kwargs: Any) → float

Compute the derivative dynamic time warping (DDTW) distance between time series.

DDTW is an adaptation of DTW originally proposed in [1]. DDTW attempts to improve on dtw by better account for the ‘shape’ of the time series. This is done by considering y axis data points as higher level features of ‘shape’. To do this the first derivative of the sequence is taken, and then using this derived sequence a dtw computation is done.

The default derivative used is:

\[D_{x}[q] = \frac{{}(q_{i} - q_{i-1} + ((q_{i+1} - q_{i-1}/2)}{2}\]

Where q is the original time series and d_q is the derived time series.

Parameters:

x: np.ndarray (1d or 2d array)

First time series.

y: np.ndarray (1d or 2d array)

Second time series.

window: float, defaults = None

Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba lower bounding). Value must be between 0. and 1.

itakura_max_slope: float, defaults = None

Gradient of the slope for itakura parallelogram (if using Itakura Parallelogram lower bounding). Value must be between 0. and 1.

bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),

defaults = None

Custom bounding matrix to use. If defined then other lower_bounding params are ignored. The matrix should be structure so that indexes considered in bound should be the value 0. and indexes outside the bounding matrix should be infinity.

compute_derivative: Callable[[np.ndarray], np.ndarray],

defaults = average slope difference

Callable that computes the derivative. If none is provided the average of the slope between two points used.

kwargs: Any

Extra kwargs.

Returns:

float

Ddtw distance between the x and y.

Raises:

ValueError

If the sakoe_chiba_window_radius is not a float. If the itakura_max_slope is not a float. If the value of x or y provided is not a numpy array. If the value of x or y has more than 2 dimensions. If a metric string provided, and is not a defined valid string. If a metric object (instance of class) is provided and doesn’t inherit from NumbaDistance. If a resolved metric or compute derivative callable is not no_python compiled. If the metric type cannot be determined If the compute derivative callable is not no_python compiled. If both window and itakura_max_slope are set

References

[1]

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 sktime.distances import ddtw_distance
>>> x_1d = np.array([1, 2, 3, 4])  # 1d array
>>> y_1d = np.array([5, 6, 7, 8])  # 1d array
>>> ddtw_distance(x_1d, y_1d) 
0.0

>>> x_2d = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])  # 2d array
>>> y_2d = np.array([[9, 10, 11, 12], [13, 14, 15, 16]])  # 2d array
>>> ddtw_distance(x_2d, y_2d) 
0.0