SignatureMoments

class SignatureMoments(degree=2, use_index=True, normalize_prod=False)[source]

Signature Moments Transformer for multivariate time series.

Computes time ordered signature moments for uni- and multivariate time series.

Pipelining Differencer() * SignatureMoments() can be used to obtain the discrete path signature.

For a degree d, the columns of the transform output are strings corresponding to strings of length d over the alphabet {[0], ..., [str(n_channels - 1)]}, where n_channels is the number of variables in the time series, and the character i represents the i-th variable.

If use_index=True, the time index is included as an additional dimension, and is represented by the character [n_channels].

For a time series \(X\) with n_channels variables, the signature moment for a string \(s = i_1 i_2 ... i_d\) is the arithmetic mean of the products

\[X_{i_1}(t_1) X_{i_2}(t_2) ... X_{i_d}(t_d)\]

where \(t_1 < t_2 < ... < t_d\) are the time indices.

If normalize_prod=True, the signature moment is computed as the arithmetic mean of the geometric means instead, i.e., of

\[(X_{i_1}(t_1) X_{i_2}(t_2) ... X_{i_d}(t_d))^{1/d}\]

This ensures that all signature moments are of the same unit as the input data.

Parameters:

degree: int, default=2: The maximum length of the string-based signature elements to include. Degree can be upto 3.
use_index: bool, default=True: Whether to include the time index as an additional dimension.
normalize_prod: bool, default=False: If True, uses geometric mean instead of product for the signature moment, see above for formula. If False, uses product.

Attributes:

is_fitted: Whether fit has been called.

Examples

>>> from sktime.transformations.signature import SignatureMoments
>>> from sktime.datasets import load_airline
>>> y = load_airline()
>>> transformer = SignatureMoments(degree=2, use_index=True)
>>> Xt = transformer.fit_transform(y)

Methods

`check_is_fitted`([method_name])	Check if the estimator has been fitted.
`clone`()	Obtain a clone of the object with same hyper-parameters and config.
`clone_tags`(estimator[, tag_names])	Clone tags from another object as dynamic override.
`create_test_instance`([parameter_set])	Construct an instance of the class, using first test parameter set.
`create_test_instances_and_names`([parameter_set])	Create list of all test instances and a list of names for them.
`fit`(X[, y])	Fit transformer to X, optionally to y.
`fit_transform`(X[, y])	Fit to data, then transform it.
`get_class_tag`(tag_name[, tag_value_default])	Get class tag value from class, with tag level inheritance from parents.
`get_class_tags`()	Get class tags from class, with tag level inheritance from parent classes.
`get_config`()	Get config flags for self.
`get_fitted_params`([deep])	Get fitted parameters.
`get_param_defaults`()	Get object's parameter defaults.
`get_param_names`([sort])	Get object's parameter names.
`get_params`([deep])	Get a dict of parameters values for this object.
`get_tag`(tag_name[, tag_value_default, ...])	Get tag value from instance, with tag level inheritance and overrides.
`get_tags`()	Get tags from instance, with tag level inheritance and overrides.
`get_test_params`([parameter_set])	Return testing parameter settings for the estimator.
`inverse_transform`(X[, y])	Inverse transform X and return an inverse transformed version.
`is_composite`()	Check if the object is composed of other BaseObjects.
`load_from_path`(serial)	Load object from file location.
`load_from_serial`(serial)	Load object from serialized memory container.
`reset`()	Reset the object to a clean post-init state.
`save`([path, serialization_format])	Save serialized self to bytes-like object or to (.zip) file.
`set_config`(**config_dict)	Set config flags to given values.
`set_params`(**params)	Set the parameters of this object.
`set_random_state`([random_state, deep, ...])	Set random_state pseudo-random seed parameters for self.
`set_tags`(**tag_dict)	Set instance level tag overrides to given values.
`transform`(X[, y])	Transform X and return a transformed version.
`update`(X[, y, update_params])	Update transformer with X, optionally y.