erp_pairwise_distance

erp_pairwise_distance(X: ndarray | list[ndarray], y: ndarray | list[ndarray] | None = None, window: float | None = None, g: float = 0.0, g_arr: ndarray | None = None, itakura_max_slope: float | None = None) → ndarray

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

The optimal value of g is selected from the range [σ/5, σ], where σ is the standard deviation of the training data. When there is > 1 channel, g should be a np.ndarray where the nth value is the standard deviation of the nth channel.

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 erp pairwise distance between the instances of X is calculated.

windowfloat, default=None

The window to use for the bounding matrix. If None, no bounding matrix is used.

gfloat, default=0.0.

The reference value to penalise gaps. The default is 0.

g_arrnp.ndarray, of shape (n_channels), default=None

Numpy array that must be the length of the number of channels in x and y.

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.

Returns:

np.ndarray (n_cases, n_cases)

ERP 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 erp_pairwise_distance
>>> # Distance between each time series in a collection of time series
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> erp_pairwise_distance(X)
array([[ 0.,  9., 18.],
       [ 9.,  0.,  9.],
       [18.,  9.,  0.]])

>>> # Distance between two collections of time series
>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y = np.array([[[11, 12, 13]],[[14, 15, 16]], [[17, 18, 19]]])
>>> erp_pairwise_distance(X, y)
array([[30., 39., 48.],
       [21., 30., 39.],
       [12., 21., 30.]])

>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> erp_pairwise_distance(X, y_univariate)
array([[30.],
       [21.],
       [12.]])
>>> # 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])]
>>> erp_pairwise_distance(X)
array([[ 0., 16., 44.],
       [16.,  0., 28.],
       [44., 28.,  0.]])