msm_cost_matrix¶

msm_cost_matrix(x: ndarray, y: ndarray, window: float | None = None, independent: bool = True, c: float = 1.0, itakura_max_slope: float | None = None) → ndarray[source]¶

Compute the MSM cost matrix between two time series.

By default, this takes a collection of \(n\) time series \(X\) and returns a matrix \(D\) where \(D_{i,j}\) is the MSM 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: First time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).
ynp.ndarray: Second time series, either univariate, shape (n_timepoints,), or multivariate, shape (n_channels, n_timepoints).
windowfloat, default=None: The window size to use for the bounding matrix. If None, the bounding matrix is not used.
independentbool, default=True: Whether to use the independent or dependent MSM distance. The default is True (to use independent).
cfloat, default=1.: Cost for split or merge operation. Default is 1.
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_timepoints_x, n_timepoints_y): MSM cost matrix between x and y.

Raises:

ValueError: If x and y are not 1D or 2D arrays.

Examples

>>> import numpy as np
>>> from aeon.distances import msm_cost_matrix
>>> x = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
>>> y = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]])
>>> msm_cost_matrix(x, y)
array([[ 0.,  2.,  4.,  6.,  8., 10., 12., 14., 16., 18.],
       [ 2.,  0.,  2.,  4.,  6.,  8., 10., 12., 14., 16.],
       [ 4.,  2.,  0.,  2.,  4.,  6.,  8., 10., 12., 14.],
       [ 6.,  4.,  2.,  0.,  2.,  4.,  6.,  8., 10., 12.],
       [ 8.,  6.,  4.,  2.,  0.,  2.,  4.,  6.,  8., 10.],
       [10.,  8.,  6.,  4.,  2.,  0.,  2.,  4.,  6.,  8.],
       [12., 10.,  8.,  6.,  4.,  2.,  0.,  2.,  4.,  6.],
       [14., 12., 10.,  8.,  6.,  4.,  2.,  0.,  2.,  4.],
       [16., 14., 12., 10.,  8.,  6.,  4.,  2.,  0.,  2.],
       [18., 16., 14., 12., 10.,  8.,  6.,  4.,  2.,  0.]])