lcss_distance

lcss_distance(x: ndarray, y: ndarray, window: float | None = None, itakura_max_slope: float | None = None, bounding_matrix: ndarray | None = None, epsilon: float = 1.0, **kwargs: Any) → float

Compute the longest common subsequence (LCSS) score between two time series.

LCSS attempts to find the longest common sequence between two time series and returns a value that is the percentage that longest common sequence assumes. Originally present in [1], LCSS is computed by matching indexes that are similar up until a defined threshold (epsilon).

The value returned will be between 0.0 and 1.0, where 0.0 means the two time series are exactly the same and 1.0 means they are complete opposites.

Parameters:

x: np.ndarray (1d or 2d array)

First time series.

y: np.ndarray (1d or 2d array)

Second time series.

window: float, defaults = None

Float that is the radius of the sakoe chiba window (if using Sakoe-Chiba lower bounding). Value must be between 0. and 1.

itakura_max_slope: float, defaults = None

Gradient of the slope for itakura parallelogram (if using Itakura Parallelogram lower bounding). Value must be between 0. and 1.

bounding_matrix: np.ndarray (2d of size mxn where m is len(x) and n is len(y)),

defaults = None

Custom bounding matrix to use. If defined then other lower_bounding params are ignored. The matrix should be structure so that indexes considered in bound should be the value 0. and indexes outside the bounding matrix should be infinity.

epsilonfloat, defaults = 1.

Matching threshold to determine if two subsequences are considered close enough to be considered ‘common’.

kwargs: Any

Extra kwargs.

Returns:

float

Lcss distance between x and y. The value returned will be between 0.0 and 1.0, where 0.0 means the two time series are exactly the same and 1.0 means they are complete opposites.

Raises:

ValueError

If the sakoe_chiba_window_radius is not a float. If the itakura_max_slope is not a float. If the value of x or y provided is not a numpy array. If the value of x or y has more than 2 dimensions. If a metric string provided, and is not a defined valid string. If a metric object (instance of class) is provided and doesn’t inherit from NumbaDistance. If the metric type cannot be determined If both window and itakura_max_slope are set

References

[1]

M. Vlachos, D. Gunopoulos, and G. Kollios. 2002. “Discovering Similar Multidimensional Trajectories”, In Proceedings of the 18th International Conference on Data Engineering (ICDE ‘02). IEEE Computer Society, USA, 673.