dtw_pairwise_distance¶

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

By default, this takes a collection of \(n\) time series \(X\) and returns a matrix \(D\) where \(D_{i,j}\) is the DTW distance between the \(i^{th}\) and the \(j^{th}\) series in \(X\). If \(X\) is 2 dimensional, it is assumed to be a collection of univariate series with shape (n_cases, n_timepoints). If it is 3 dimensional, it is assumed to be shape (n_cases, n_channels, n_timepoints).

This function has an optional argument, \(y\), to allow calculation of the distance matrix between \(X\) and one or more series stored in \(y\). If \(y\) is 1 dimensional, we assume it is a single univariate series and the distance matrix returned is shape (n_cases,1). If it is 2D, we assume it is a collection of univariate series with shape (m_cases, m_timepoints) and the distance (n_cases,m_cases). If it is 3 dimensional, it is assumed to be shape (m_cases, m_channels, m_timepoints).

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 dtw pairwise distance between the instances of X is calculated.
windowfloat or None, default=None: The window to use for the bounding matrix. If None, no bounding matrix is used.
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: DTW pairwise matrix between the instances of X of shape (n_cases, n_cases) or between X and y of shape (n_cases, n_cases).

Raises:

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

Examples

>>> import numpy as np
>>> from aeon.distances import dtw_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]]])
>>> dtw_pairwise_distance(X)
array([[  0.,  26., 108.],
       [ 26.,   0.,  26.],
       [108.,  26.,   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]]])
>>> dtw_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])
>>> dtw_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])]
>>> dtw_pairwise_distance(X)
array([[  0.,  42., 292.],
       [ 42.,   0.,  83.],
       [292.,  83.,   0.]])