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pairwise_distance#

pairwise_distance(x: ndarray, y: ndarray = None, metric: str | Callable[[ndarray, ndarray, dict], Callable[[ndarray, ndarray], float]] | Callable[[ndarray, ndarray], float] | NumbaDistance = 'euclidean', **kwargs: Any) → ndarray[source]#

Compute the pairwise distance matrix between two time series.

First the distance metric is ‘resolved’. This means the metric that is passed is resolved to a callable. The callable is then called with x and y and the value is then returned. Then for each combination of x and y, the distance between the values are computed resulting in a 2d pairwise matrix.

Parameters:
x: np.ndarray (1d, 2d or 3d array)

First time series.

y: np.ndarray (1d, 2d or 3d array), defaults = None

Second time series. If not specified then y is set to the value of x.

metric: str or Callable, defaults = ‘euclidean’

The distance metric to use. If a string is given, the value must be one of the following strings:

‘euclidean’, ‘squared’, ‘dtw’, ‘ddtw’, ‘wdtw’, ‘wddtw’, ‘lcss’, ‘edr’, ‘erp’, ‘msm’

If callable then it has to be a distance factory or numba distance callable. If you want to pass custom kwargs to the distance at runtime, use a distance factory as it constructs the distance using the kwargs before distance computation. A distance callable takes the form (must be no_python compiled): Callable[[np.ndarray, np.ndarray], float]

A distance factory takes the form (must return a no_python callable): Callable[[np.ndarray, np.ndarray, bool, dict], Callable[[np.ndarray, np.ndarray], float]].

kwargs: Any

Extra arguments for metric. Refer to each metric documentation for a list of possible arguments.

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

Pairwise distance matrix between the two time series.

Raises:
ValueError

If the value of x or y provided is not a numpy array. If the value of x or y has more than 3 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 is not no_python compiled. If the metric type cannot be determined.

Examples

>>> import numpy as np
>>> from sktime.distances import pairwise_distance
>>> x_1d = np.array([1, 2, 3, 4])  # 1d array
>>> y_1d = np.array([5, 6, 7, 8])  # 1d array
>>> pairwise_distance(x_1d, y_1d, metric='dtw')
array([[16., 25., 36., 49.],
       [ 9., 16., 25., 36.],
       [ 4.,  9., 16., 25.],
       [ 1.,  4.,  9., 16.]])

>>> 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
>>> pairwise_distance(x_2d, y_2d, metric='dtw')
array([[256., 576.],
       [ 58., 256.]])

>>> x_3d = np.array([[[1], [2], [3], [4]], [[5], [6], [7], [8]]])  # 3d array
>>> y_3d = np.array([[[9], [10], [11], [12]], [[13], [14], [15], [16]]])  # 3d array
>>> pairwise_distance(x_3d, y_3d, metric='dtw')
array([[256., 576.],
       [ 64., 256.]])

>>> 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
>>> pairwise_distance(x_2d, y_2d, metric='dtw', window=0.5)
array([[256., 576.],
       [ 58., 256.]])
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