euclidean_distance

euclidean_distance(x: ndarray, y: ndarray, **kwargs: Any) → float

Compute the Euclidean distance between two time series.

Euclidean distance is supported for 1d, 2d and 3d arrays.

The Euclidean distance between two time series of length m is the square root of the squared distance and is defined as:

\[ed(x, y) = \sqrt{\sum_{i=1}^{n} (x_i - y_i)^2}\]

Parameters:

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

First time series.

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

Second time series.

kwargs: Any

Extra kwargs. For euclidean there are none however, this is kept for consistency.

Returns:

float

Euclidean distance between x and y.

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 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 is not no_python compiled. If the metric type cannot be determined.

Examples

>>> import numpy as np
>>> from sktime.distances import euclidean_distance
>>> x_1d = np.array([1, 2, 3, 4])  # 1d array
>>> y_1d = np.array([5, 6, 7, 8])  # 1d array
>>> euclidean_distance(x_1d, y_1d)
8.0

>>> 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
>>> euclidean_distance(x_2d, y_2d)
22.627416997969522