pykoop.KoopmanPipeline

class KoopmanPipeline(lifting_functions=None, regressor=None)

Bases: _BaseComposition, KoopmanLiftingFn

Meta-estimator for chaining lifting functions with an estimator.

Parameters:

lifting_functions (List[Tuple[str, KoopmanLiftingFn]] | None)
regressor (KoopmanRegressor | None)

liting_functions_

Fit lifting functions (and their names).

Type:: List[Tuple[str, KoopmanLiftingFn]]

regressor_

Fit regressor.

Type:: KoopmanRegressor

transformers_fit_

True if lifting functions have been fit.

Type:: bool

regressor_fit_

True if regressor has been fit.

Type:: bool

n_features_in_

Number of features before transformation, including episode feature.

Type:: int

n_states_in_

Number of states before transformation.

Type:: int

n_inputs_in_

Number of inputs before transformation.

Type:: int

n_features_out_

Number of features after transformation, including episode feature.

Type:: int

n_states_out_

Number of states after transformation.

Type:: int

n_inputs_out_

Number of inputs after transformation.

Type:: int

min_samples_

Minimum number of samples needed to use the transformer.

Type:: int

episode_feature_

Indicates if episode feature was present during fit().

Type:: bool

feature_names_in_

Array of input feature name strings.

Type:: np.ndarray

Examples

Apply a basic Koopman pipeline to mass-spring-damper data

>>> kp = pykoop.KoopmanPipeline(
...     lifting_functions=[('pl', pykoop.PolynomialLiftingFn(order=2))],
...     regressor=pykoop.Edmd(),
... )
>>> kp.fit(X_msd, n_inputs=1, episode_feature=True)
KoopmanPipeline(lifting_functions=[('pl', PolynomialLiftingFn(order=2))],
regressor=Edmd())
>>> kp.get_feature_names_in().tolist()
['ep', 'x0', 'x1', 'u0']
>>> kp.get_feature_names_out().tolist()
['ep', 'x0', 'x1', 'x0^2', 'x0*x1', 'x1^2', 'u0', 'x0*u0', 'x1*u0', 'u0^2']

Apply more sophisticated Koopman pipeline to mass-spring-damper data

>>> kp = KoopmanPipeline(
...     lifting_functions=[
...         ('ma', pykoop.SkLearnLiftingFn(
...                    sklearn.preprocessing.MaxAbsScaler())),
...         ('pl', pykoop.PolynomialLiftingFn(order=2)),
...         ('ss', pykoop.SkLearnLiftingFn(
...                    sklearn.preprocessing.StandardScaler())),
...     ],
...     regressor=pykoop.Edmd(),
... )
>>> kp.fit(X_msd, n_inputs=1, episode_feature=True)
KoopmanPipeline(lifting_functions=[('ma',
SkLearnLiftingFn(transformer=MaxAbsScaler())),
('pl', PolynomialLiftingFn(order=2)),
('ss', SkLearnLiftingFn(transformer=StandardScaler()))],
regressor=Edmd())
>>> Xt_msd = kp.transform(X_msd[:2, :])

Apply bilinear Koopman pipeline to mass-spring-damper data

>>> kp = KoopmanPipeline(
...     lifting_functions=[
...         ('ma', pykoop.SkLearnLiftingFn(
...                    sklearn.preprocessing.MaxAbsScaler())),
...         ('sp', pykoop.SplitPipeline(
...             lifting_functions_state=[
...                 ('pl', pykoop.PolynomialLiftingFn(order=2)),
...             ],
...             lifting_functions_input=None,
...         )),
...         ('bi', pykoop.BilinearInputLiftingFn()),
...         ('ss', pykoop.SkLearnLiftingFn(
...                    sklearn.preprocessing.StandardScaler())),
...     ],
...     regressor=pykoop.Edmd(),
... )
>>> kp.fit(X_msd, n_inputs=1, episode_feature=True)
KoopmanPipeline(lifting_functions=[('ma',
SkLearnLiftingFn(transformer=MaxAbsScaler())),
('sp', SplitPipeline(lifting_functions_state=[('pl',
PolynomialLiftingFn(order=2))])),
('bi', BilinearInputLiftingFn()),
('ss', SkLearnLiftingFn(transformer=StandardScaler()))],
regressor=Edmd())

__init__(lifting_functions=None, regressor=None)

Instantiate for KoopmanPipeline.

Parameters:

lifting_functions (Optional[List[Tuple[str, KoopmanLiftingFn]]]) – List of names and lifting function objects.
regressor (Optional[KoopmanRegressor]) – Koopman regressor.

Return type:

None

Methods

`__init__`([lifting_functions, regressor])	Instantiate for `KoopmanPipeline`.
`fit`(X[, y, n_inputs, episode_feature])	Fit the Koopman pipeline.
`fit_transform`(X[, y])	Fit to data, then transform it.
`fit_transformers`(X[, y, n_inputs, ...])	Fit only the lifting functions in the pipeline.
`frequency_response`(t_step[, f_min, f_max, ...])	Compute frequency response of Koopman system.
`get_feature_names_in`([format, episode_feature])	Automatically generate input feature names.
`get_feature_names_out`([input_features, ...])	Get output feature names.
`get_metadata_routing`()	Get metadata routing of this object.
`get_params`([deep])	Get parameters for this estimator.
`inverse_transform`(X)	Invert transformed data.
`lift`(X[, episode_feature])	Lift state and input.
`lift_input`(X[, episode_feature])	Lift input only.
`lift_state`(X[, episode_feature])	Lift state only.
`make_scorer`([n_steps, discount_factor, ...])	Make a Koopman pipeline scorer.
`n_samples_in`([n_samples_out])	Calculate number of input samples required for given output length.
`plot_bode`(t_step[, f_min, f_max, n_points, ...])	Plot frequency response of Koopman system.
`plot_eigenvalues`([unit_circle, figure_kw, ...])	Plot eigenvalues of Koopman `A` matrix.
`plot_koopman_matrix`([subplots_kw, plot_kw])	Plot heatmap of Koopman matrices.
`plot_lifted_trajectory`(X[, episode_feature, ...])	Plot lifted data matrix.
`plot_predicted_trajectory`(X0_or_X[, U, ...])	Plot predicted trajectory.
`plot_svd`([subplots_kw, plot_kw])	Plot singular values of Koopman matrices.
`predict`(X)	Perform a single-step prediction for each state in each episode.
`predict_trajectory`(X0_or_X[, U, ...])	Predict state trajectory given input for each episode.
`retract`(X[, episode_feature])	Retract lifted state and input.
`retract_input`(X[, episode_feature])	Retract lifted input only.
`retract_state`(X[, episode_feature])	Retract lifted state only.
`score`(X[, y])	Calculate prediction score.
`set_fit_request`(*[, episode_feature, n_inputs])	Request metadata passed to the `fit` method.
`set_output`(*[, transform])	Set output container.
`set_params`(**kwargs)	Set the parameters of this estimator.
`transform`(X)	Transform data.

static make_scorer(n_steps=None, discount_factor=1, regression_metric='neg_mean_squared_error', regression_metric_kw=None, error_score=nan, multistep=True, relift_state=True)

Make a Koopman pipeline scorer.

A scikit-learn scorer accepts the parameters (estimator, X, y) and returns a float representing the prediction quality of estimator on X with reference to y. Uses existing scikit-learn regression metrics [1]. Higher numbers are better. Metrics corresponding to losses are negated.

Technically, the scorer will predict the entire episode, regardless of how n_steps is set. It will then assign a zero weight to all errors beyond n_steps.

Parameters:

n_steps (Optional[int]) – Number of steps ahead to predict. If None or longer than the episode, will score the entire episode.
discount_factor (float) – Discount factor used to weight the error timeseries. Should be positive, with magnitude 1 or slightly less. The error at each timestep is weighted by discount_factor**k, where k is the timestep.
regression_metric (Union[str, Callable]) –
Regression metric to use. One of
- 'explained_variance',
- 'neg_mean_absolute_error',
- 'neg_mean_squared_error',
- 'neg_mean_squared_log_error',
- 'neg_median_absolute_error',
- 'r2', or
- 'neg_mean_absolute_percentage_error',
which are existing scikit-learn regression metrics [1]. Can also directly specify a function with the same keyword arguments as the scikit-learn ones. That is, at least y_true, y_pred, sample_weight, and multioutput.
regression_metric_kw (Optional[Dict[str, Any]]) – Keyword arguments for regression_method. If sample_weight keyword argument is specified, discount_factor is ignored.
error_score (Union[str, float]) – Value to assign to the score if X_predicted has diverged or if an error has occured in estimator fitting. If set to 'raise', a ValueError is raised. If a numerical value is given, a sklearn.exceptions.FitFailedWarning warning is raised and the specified score is returned. The error score defines the worst possible score. If a score is finite but lower than the error score, the error score will be returned instead.
multistep (bool) – If true, predict using predict_trajectory(). Otherwise, predict using predict() (one-step-ahead prediction). Multistep prediction is highly recommended unless debugging. If one-step-ahead prediciton is used, n_steps and discount_factor are ignored.
relift_state (bool) – If true, retract and re-lift state between prediction steps (default). Otherwise, only retract the state after all predictions are made. Correspond to the local and global error definitions of [MAM22]. Ignored if multistep is false.

Returns:

Scorer compatible with scikit-learn.

Return type:

Callable[[KoopmanPipeline, np.ndarray, Optional[np.ndarray]], float]

Raises:

ValueError – If discount_factor is negative or greater than one or if error_score='raise' and an error occurs in scoring.

References

fit(X, y=None, n_inputs=0, episode_feature=False)

Fit the Koopman pipeline.

Parameters:

X (np.ndarray) – Data matrix.
y (Optional[np.ndarray]) – Ignored.
n_inputs (int) – Number of input features at the end of X.
episode_feature (bool) – True if first feature indicates which episode a timestep is from.

Returns:

Instance of itself.

Return type:

KoopmanPipeline

Raises:

ValueError – If constructor or fit parameters are incorrect.

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters:

X (array-like of shape (n_samples, n_features)) – Input samples.
y (array-like of shape (n_samples,) or (n_samples, n_outputs), default=None) – Target values (None for unsupervised transformations).
**fit_params (dict) – Additional fit parameters.

Returns:

X_new – Transformed array.

Return type:

ndarray array of shape (n_samples, n_features_new)

fit_transformers(X, y=None, n_inputs=0, episode_feature=False)

Fit only the lifting functions in the pipeline.

Parameters:

X (np.ndarray) – Data matrix.
y (Optional[np.ndarray]) – Ignored.
n_inputs (int) – Number of input features at the end of X.
episode_feature (bool) – True if first feature indicates which episode a timestep is from.

Returns:

Instance of itself.

Return type:

KoopmanPipeline

Raises:

ValueError – If constructor or fit parameters are incorrect.

frequency_response(t_step, f_min=0, f_max=None, n_points=1000, decibels=True)

Compute frequency response of Koopman system.

Parameters:

t_step (float) – Sampling timestep.
f_min (float) – Minimum frequency to plot.
f_max (float) – Maximum frequency to plot. If None, uses the Nyquist frequency.
n_points (int) – Number of frequecy points to plot.
decibels (bool) – Plot gain in dB (default is true).

Returns:

Frequency (Hz) and frequency response (gain or dB).

Return type:

Tuple[np.ndarray, np.ndarray]

Raises:

ValueError – If f_min is less than zero or f_max is greater than the Nyquist frequency.

get_feature_names_in(format=None, episode_feature=None)

Automatically generate input feature names.

Parameters:

format (Optional[str]) – Feature name formatting method. Possible values are 'plaintext' (default if None) or 'latex'.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Automatically generated input feaure names.

Return type:

np.ndarray

get_feature_names_out(input_features=None, symbols_only=False, format=None, episode_feature=None)

Get output feature names.

Parameters:

input_features (Optional[np.ndarray]) – Array of string input feature names. If provided, they are checked against feature_names_in_. If None, ignored.
symbols_only (bool) – If true, only return symbols (theta_0, upsilon_0, etc.). Otherwise, returns the full equations (default).
format (Optional[str]) – Feature name formatting method. Possible values are 'plaintext' (default if None) or 'latex'.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Output feature names.

Return type:

np.ndarray

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:: routing – A MetadataRequest encapsulating routing information.
Return type:: MetadataRequest

get_params(deep=True)

Get parameters for this estimator.

Parameters:: deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:: params – Parameter names mapped to their values.
Return type:: dict

inverse_transform(X)

Invert transformed data.

Parameters:: X (np.ndarray) – Transformed data matrix.
Returns:: Inverted transformed data matrix.
Return type:: np.ndarray

lift(X, episode_feature=None)

Lift state and input.

Potentially more convenient alternative to calling transform().

Parameters:

X (np.ndarray) – State and input.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Lifted state and input.

Return type:

np.ndarray

lift_input(X, episode_feature=None)

Lift input only.

More convenient alternative to calling transform(), then stripping the unwanted lifted states.

Parameters:

X (np.ndarray) – State and input.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Lifted input.

Return type:

np.ndarray

lift_state(X, episode_feature=None)

Lift state only.

More convenient alternative to padding the state with dummy inputs, calling transform(), then stripping the unwanted lifted inputs.

Parameters:

X (np.ndarray) – State.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Lifted state.

Return type:

np.ndarray

n_samples_in(n_samples_out=1)

Calculate number of input samples required for given output length.

Parameters:: n_samples_out (int) – Number of samples needed at the output.
Returns:: Number of samples needed at the input.
Return type:: int

plot_bode(t_step, f_min=0, f_max=None, n_points=1000, decibels=True, subplots_kw=None, plot_kw=None)

Plot frequency response of Koopman system.

Parameters:

t_step (float) – Sampling timestep.
f_min (float) – Minimum frequency to plot.
f_max (Optional[float]) – Maximum frequency to plot. If None, uses the Nyquist frequency.
n_points (int) – Number of frequecy points to plot.
decibels (bool) – Plot gain in dB (default is true).
subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplots().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().

Returns:

Matplotlib plt.Figure and plt.Axes objects.

Return type:

Tuple[plt.Figure, plt.Axes]

Raises:

ValueError – If f_min is less than zero or f_max is greater than the Nyquist frequency.

plot_eigenvalues(unit_circle=True, figure_kw=None, subplot_kw=None, plot_kw=None)

Plot eigenvalues of Koopman A matrix.

Parameters:

figure_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.figure().
subplot_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplot().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().
unit_circle (bool)

Returns:

Matplotlib plt.Figure and plt.Axes objects.

Return type:

Tuple[plt.Figure, plt.Axes]

plot_koopman_matrix(subplots_kw=None, plot_kw=None)

Plot heatmap of Koopman matrices.

Parameters:

subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplots().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().

Returns:

Matplotlib plt.Figure and plt.Axes objects.

Return type:

Tuple[plt.Figure, plt.Axes]

plot_lifted_trajectory(X, episode_feature=None, episode_style=None, subplots_kw=None, plot_kw=None)

Plot lifted data matrix.

Parameters:

X (np.ndarray) – Data matrix.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.
episode_style (Optional[str]) – If 'columns', each episode is a column (default). If 'overlay', states from each episode are plotted overtop of each other in different colors.
subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplots().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().

Returns:

Matplotlib plt.Figure object and two-dimensional array of plt.Axes objects.

Return type:

Tuple[plt.Figure, np.ndarray]

plot_predicted_trajectory(X0_or_X, U=None, relift_state=True, plot_lifted=False, plot_input=False, plot_error=False, episode_feature=None, plot_ground_truth=True, episode_style=None, subplots_kw=None, plot_kw=None)

Plot predicted trajectory.

Parameters:

X0_or_X (np.ndarray) – Initial state if U is specified. If U is None, then treated as the ground truth trajectory from which the initial state and full input are extracted.
U (Optional[np.ndarray]) – Input. Length of prediction is governed by length of input. If None, input is taken from last features of X0_or_X.
relift_state (bool) – If true, retract and re-lift state between prediction steps (default). Otherwise, only retract the state after all predictions are made. Correspond to the local and global error definitions of [MAM22].
plot_lifted (bool) – If true, plot the lifted state. If false, plot the original state (default).
plot_input (bool) – If true, plot the input as well as the state. If false, plot only the original state (default).
plot_error (bool) – If true, plot the prediction error instead of the state. If false, plot the predicted state and ground truth (default).
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.
plot_ground_truth (bool) – Plot contents of X0_or_X as ground truth if U is None. Ignored if U is not None.
episode_style (Optional[str]) – If 'columns', each episode is a column (default). If 'overlay', states from each episode are plotted overtop of each other in different colors.
subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplots().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().

Returns:

Matplotlib plt.Figure object and two-dimensional array of plt.Axes objects.

Return type:

Tuple[plt.Figure, np.ndarray]

plot_svd(subplots_kw=None, plot_kw=None)

Plot singular values of Koopman matrices.

Parameters:

subplots_kw (Optional[Dict[str, Any]]) – Keyword arguments for plt.subplots().
plot_kw (Optional[Dict[str, Any]]) – Keyword arguments for Matplotlib plt.Axes.plot().

Returns:

Matplotlib plt.Figure and plt.Axes objects.

Return type:

Tuple[plt.Figure, plt.Axes]

predict(X)

Perform a single-step prediction for each state in each episode.

Lifts the state, preforms a single-step prediction in the lifted space, then retracts to the original state space.

Parameters:: X (np.ndarray) – Data matrix.
Returns:: Predicted data matrix.
Return type:: np.ndarray

predict_trajectory(X0_or_X, U=None, relift_state=True, return_lifted=False, return_input=False, episode_feature=None)

Predict state trajectory given input for each episode.

Parameters:

X0_or_X (np.ndarray) – Initial state if U is specified. If U is None, then treated as the initial state and full input in one matrix, where the remaining states are ignored.
U (Optional[np.ndarray]) – Input. Length of prediction is governed by length of input. If None, input is taken from last features of X0_or_X.
relift_state (bool) – If true, retract and re-lift state between prediction steps (default). Otherwise, only retract the state after all predictions are made. Correspond to the local and global error definitions of [MAM22].
return_lifted (bool) – If true, return the lifted state. If false, return the original state (default).
return_input (bool) – If true, return the input as well as the state. If false, return only the original state (default).
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Predicted state. If return_input, input is appended to the array. If return_lifted, the predicted state (and input) are returned in the lifted space.

Return type:

np.ndarray

Raises:

ValueError – If an episode is shorter than min_samples_.

Examples

Predict trajectory with one argument

>>> kp = pykoop.KoopmanPipeline(
...     lifting_functions=[
...         ('pl', pykoop.PolynomialLiftingFn(order=2)),
...     ],
...     regressor=pykoop.Edmd(),
... )
>>> kp.fit(X_msd, n_inputs=1, episode_feature=True)
KoopmanPipeline(lifting_functions=[('pl',
PolynomialLiftingFn(order=2))], regressor=Edmd())
>>> X_pred = kp.predict_trajectory(X_msd)

Predict trajectory with two arguments >>> x0 = pykoop.extract_initial_conditions( … X_msd, … min_samples=kp.min_samples_, … n_inputs=1, … episode_feature=True, … ) >>> u = pykoop.extract_input( … X_msd, … n_inputs=1, … episode_feature=True, … ) >>> X_pred = kp.predict_trajectory(x0, u)

retract(X, episode_feature=None)

Retract lifted state and input.

Potentially more convenient alternative to calling inverse_transform().

Parameters:

X (np.ndarray) – Lifted state and input.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

State and input.

Return type:

np.ndarray

retract_input(X, episode_feature=None)

Retract lifted input only.

More convenient alternative to padding the lifted state with dummy lifted states, calling inverse_transform(), then stripping the unwanted states.

Parameters:

X (np.ndarray) – Lifted input.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

Input.

Return type:

np.ndarray

retract_state(X, episode_feature=None)

Retract lifted state only.

More convenient alternative to padding the lifted state with dummy lifted inputs, calling inverse_transform().

Parameters:

X (np.ndarray) – Lifted state.
episode_feature (Optional[bool]) – True if first feature indicates which episode a timestep is from. If None, self.episode_feature_ is used.

Returns:

State.

Return type:

np.ndarray

score(X, y=None)

Calculate prediction score.

For more flexible scoring, see make_scorer().

Parameters:

X (np.ndarray) – Data matrix.
y (Optional[np.ndarray]) – Ignored.

Returns:

Mean squared error prediction score.

Return type:

float

set_fit_request(*, episode_feature='$UNCHANGED$', n_inputs='$UNCHANGED$')

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

episode_feature (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for episode_feature parameter in fit.
n_inputs (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for n_inputs parameter in fit.
self (KoopmanPipeline)

Returns:

self – The updated object.

Return type:

object

set_output(*, transform=None)

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:

transform ({"default", "pandas", "polars"}, default=None) –

Configure output of transform and fit_transform.

”default”: Default output format of a transformer
”pandas”: DataFrame output
”polars”: Polars output
None: Transform configuration is unchanged

Added in version 1.4: “polars” option was added.

Returns:

self – Estimator instance.

Return type:

estimator instance

set_params(**kwargs)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:: **params (dict) – Estimator parameters.
Returns:: self – Estimator instance.
Return type:: estimator instance

transform(X)

Transform data.

Parameters:: X (np.ndarray) – Data matrix.
Returns:: Transformed data matrix.
Return type:: np.ndarray