frechet_path

tslearn.metrics.frechet_path(s1, s2, global_constraint=None, sakoe_chiba_radius=None, itakura_max_slope=None, be=None)

Compute Frechet similarity measure [1] between (possibly multidimensional) time series and an optimal alignment path.

Frechet distance is computed as the maximium distance between aligned time series, i.e., if \(\pi\) is the optimal alignment path:

\[Frechet(X, Y) = \max_{(i, j) \in \pi} \|X_{i} - Y_{j}\|\]

It is not required that both time series share the same size, but they must be the same dimension.

Parameters:

s1array-like, shape=(sz1, d) or (sz1,)

A time series. If shape is (sz1,), the time series is assumed to be univariate.

s2array-like, shape=(sz2, d) or (sz2,)

Another time series. If shape is (sz2,), the time series is assumed to be univariate.

global_constraint{“itakura”, “sakoe_chiba”} or None (default: None)

Global constraint to restrict admissible paths for Frechet distance.

sakoe_chiba_radiusint or None (default: None)

Radius to be used for Sakoe-Chiba band global constraint. The Sakoe-Chiba radius corresponds to the parameter \(\delta\) mentioned in [2], it controls how far in time we can go in order to match a given point from one time series to a point in another time series. If None and global_constraint is set to “sakoe_chiba”, a radius of 1 is used. If both sakoe_chiba_radius and itakura_max_slope are set, global_constraint is used to infer which constraint to use among the two. In this case, if global_constraint corresponds to no global constraint, a RuntimeWarning is raised and no global constraint is used.

itakura_max_slopefloat or None (default: None)

Maximum slope for the Itakura parallelogram constraint. If None and global_constraint is set to “itakura”, a maximum slope of 2. is used. If both sakoe_chiba_radius and itakura_max_slope are set, global_constraint is used to infer which constraint to use among the two. In this case, if global_constraint corresponds to no global constraint, a RuntimeWarning is raised and no global constraint is used.

beBackend object or string or None

Backend. If be is an instance of the class NumPyBackend or the string “numpy”, the NumPy backend is used. If be is an instance of the class PyTorchBackend or the string “pytorch”, the PyTorch backend is used. If be is None, the backend is determined by the input arrays. See our dedicated user-guide page for more information.

Returns:

list of integer pairs

Matching path represented as a list of index pairs. In each pair, the first index corresponds to s1 and the second one corresponds to s2.

float

Similarity score

See also

frechet

Get only the similarity score

frechet_path_from_metric

Compute similarity score and path using a user-defined distance metric

cdist_frechet

Cross similarity matrix between time series datasets

References

[1]

FRÉCHET, M. “Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Mathematico di Palermo”, 22, 1–74, 1906.

[2]

H. Sakoe, S. Chiba, “Dynamic programming algorithm optimization for spoken word recognition,” IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 26(1), pp. 43–49, 1978.

Examples

>>> path, dist = frechet_path([1, 2, 3], [1., 2., 2., 3.])
>>> path
[(0, 0), (1, 1), (1, 2), (2, 3)]
>>> float(dist)
0.0
>>> float(frechet_path([1, 2, 3], [1., 2., 2., 3., 4.])[1])
1.0

Examples using tslearn.metrics.frechet_path

Frechet

Frechet