squared_pairwise_distance¶

squared_pairwise_distance(X: ndarray | List[ndarray], y: ndarray | List[ndarray] | None = None) → ndarray[source]¶

Compute the squared pairwise distance between a set of time series.

Parameters:

Xnp.ndarray or List of np.ndarray: A collection of time series instances of shape (n_cases, n_timepoints) or (n_cases, n_channels, n_timepoints).
ynp.ndarray or List of np.ndarray or None, default=None: A single series or a collection of time series of shape (m_timepoints,) or (m_cases, m_timepoints) or (m_cases, m_channels, m_timepoints). If None, then the squared pairwise distance between the instances of X is calculated.

Returns:

np.ndarray (n_cases, n_cases): squared pairwise matrix between the instances of X.

Raises:

ValueError: If X is not 2D or 3D array when only passing X. If X and y are not 1D, 2D or 3D arrays when passing both X and y.

Examples

>>> import numpy as np
>>> from aeon.distances import squared_pairwise_distance
>>> X = np.array([[[1, 2, 3, 4]],[[4, 5, 6, 3]], [[7, 8, 9, 3]]])
>>> squared_pairwise_distance(X)
array([[  0.,  28., 109.],
       [ 28.,   0.,  27.],
       [109.,  27.,   0.]])

>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y = np.array([[[11, 12, 13]],[[14, 15, 16]], [[17, 18, 19]]])
>>> squared_pairwise_distance(X, y)
array([[300., 507., 768.],
       [147., 300., 507.],
       [ 48., 147., 300.]])

>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> squared_pairwise_distance(X, y_univariate)
array([[300.],
       [147.],
       [ 48.]])

>>> # Distance between each TS in a collection of unequal-length time series
>>> X = [np.array([1, 2, 3]), np.array([4, 5, 6, 7]), np.array([8, 9, 10, 11, 12])]
>>> squared_pairwise_distance(X)
array([[  0.,  27., 147.],
       [ 27.,   0.,  64.],
       [147.,  64.,   0.]])