# lcss_pairwise_distance¶

lcss_pairwise_distance(X: , y: = None, window: = None, epsilon: float = 1.0, itakura_max_slope: = None) [source]

Compute the LCSS 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 lcss 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.

epsilonfloat, default=1.

Matching threshold to determine if two subsequences are considered close enough to be considered ‘common’. The 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_cases, n_cases)

LCSS 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 lcss_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]]])
>>> lcss_pairwise_distance(X)
array([[0.        , 0.66666667, 1.        ],
[0.66666667, 0.        , 0.66666667],
[1.        , 0.66666667, 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]]])
>>> lcss_pairwise_distance(X, y)
array([[1., 1., 1.],
[1., 1., 1.],
[1., 1., 1.]])
```
```>>> X = np.array([[[1, 2, 3]],[[4, 5, 6]], [[7, 8, 9]]])
>>> y_univariate = np.array([11, 12, 13])
>>> lcss_pairwise_distance(X, y_univariate)
array([[1.],
[1.],
[1.]])
```
```>>> # 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])]
>>> lcss_pairwise_distance(X)
array([[0.        , 0.66666667, 1.        ],
[0.66666667, 0.        , 0.75      ],
[1.        , 0.75      , 0.        ]])
```