gemseo / mlearning / transform / dimension_reduction

klsvd module¶

The Karhunen-Loève SVD algorithm to reduce the dimension of a variable.

The KLSVD class wraps the KarhunenLoeveSVDAlgorithm from OpenTURNS.

class gemseo.mlearning.transform.dimension_reduction.klsvd.KLSVD(mesh, n_components=None, name='KLSVD', use_random_svd=False, n_singular_values=None, use_halko2010=True)[source]¶

Bases: DimensionReduction

The Karhunen-Loève SVD algorithm.

Based on OpenTURNS.

Warning

Under Python 3.7, GEMSEO requires openturns 1.19 which removes the non-significant components, whatever the value of n_components passed at instantiation. Under Python 3.8 and above, the number of components is equal to n_components if not None, otherwise to the mesh size.

Parameters:

mesh (ndarray) – A mesh passed as a 2D NumPy array whose rows are nodes and columns are the dimensions of the nodes.
n_components (int | None) – The number of components of the latent space. If None, use the maximum number allowed by the technique, typically min(n_samples, n_features).
name (str) –
A name for this transformer.

By default it is set to “KLSVD”.
use_random_svd (bool) –
Whether to use a stochastic algorithm to compute the SVD decomposition; if so, the number of singular values has to be fixed a priori.

By default it is set to False.
n_singular_values (int | None) – The number of singular values to compute when use_random_svd is True; if None, use the default value implemented by OpenTURNS.
use_halko2010 (bool) –
Whether to use the halko2010 algorithm or the halko2011 one.

By default it is set to True.

compute_jacobian(data)¶

Compute Jacobian of transformer.transform().

Parameters:: data (ndarray) – The data where the Jacobian is to be computed.
Returns:: The Jacobian matrix.
Return type:: NoReturn

compute_jacobian_inverse(data)¶

Compute Jacobian of the transformer.inverse_transform().

Parameters:: data (ndarray) – The data where the Jacobian is to be computed.
Returns:: The Jacobian matrix.
Return type:: NoReturn

duplicate()¶

Duplicate the current object.

Returns:: A deepcopy of the current instance.
Return type:: Transformer

fit(data, *args)¶

Fit the transformer to the data.

Parameters:

data (ndarray) – The data to be fitted.
args (Union[float, int, str]) –

Return type:

None

fit_transform(data, *args)¶

Fit the transformer to the data and transform the data.

Parameters:

data (ndarray) – The data to be transformed.
args (Union[float, int, str]) –

Returns:

The transformed data.

Return type:

ndarray

inverse_transform(data)[source]¶

Perform an inverse transform on the data.

Parameters:: data (ndarray) – The data to be inverse transformed.
Returns:: The inverse transformed data.
Return type:: ndarray

transform(data)[source]¶

Transform the data.

Parameters:: data (ndarray) – The data to be transformed.
Returns:: The transformed data.
Return type:: ndarray

CROSSED: ClassVar[bool] = False¶: Whether the fit() method requires two data arrays.

property components: ndarray¶: The principal components.

property eigenvalues: ndarray¶: The eigen values.

property is_fitted: bool¶: Whether the transformer has been fitted from some data.

property mesh: ndarray¶: The mesh.

property n_components: int¶: The number of components.

name: str¶: The name of the transformer.

property output_dimension: int¶: The dimension of the latent space.

property parameters: dict[str, Union[bool, int, float, numpy.ndarray, str, NoneType]]¶: The parameters of the transformer.

Examples using KLSVD¶

KL-SVD on Burgers equation