DictionaryLearning#

class sklearn.decomposition.DictionaryLearning(n_components=None, *, alpha=1, max_iter=1000, tol=1e-08, fit_algorithm='lars', transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, n_jobs=None, code_init=None, dict_init=None, callback=None, verbose=False, split_sign=False, random_state=None, positive_code=False, positive_dict=False, transform_max_iter=1000)[source]#

Dictionary learning.

Finds a dictionary (a set of atoms) that performs well at sparsely encoding the fitted data.

Solves the optimization problem:

(U^*,V^*) = argmin 0.5 || X - U V ||_Fro^2 + alpha * || U ||_1,1
            (U,V)
            with || V_k ||_2 <= 1 for all  0 <= k < n_components

||.||_Fro stands for the Frobenius norm and ||.||_1,1 stands for the entry-wise matrix norm which is the sum of the absolute values of all the entries in the matrix.

See also

MiniBatchDictionaryLearning: A faster, less accurate, version of the dictionary learning algorithm.
MiniBatchSparsePCA: Mini-batch Sparse Principal Components Analysis.
SparseCoder: Find a sparse representation of data from a fixed, precomputed dictionary.
SparsePCA: Sparse Principal Components Analysis.

References

J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (https://www.di.ens.fr/~fbach/mairal_icml09.pdf)

Examples

>>> import numpy as np
>>> from sklearn.datasets import make_sparse_coded_signal
>>> from sklearn.decomposition import DictionaryLearning
>>> X, dictionary, code = make_sparse_coded_signal(
...     n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10,
...     random_state=42,
... )
>>> dict_learner = DictionaryLearning(
...     n_components=15, transform_algorithm='lasso_lars', transform_alpha=0.1,
...     random_state=42,
... )
>>> X_transformed = dict_learner.fit(X).transform(X)

We can check the level of sparsity of X_transformed:

>>> np.mean(X_transformed == 0)
np.float64(0.527)

We can compare the average squared euclidean norm of the reconstruction error of the sparse coded signal relative to the squared euclidean norm of the original signal:

>>> X_hat = X_transformed @ dict_learner.components_
>>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1))
np.float64(0.056)

fit(X, y=None)[source]#

Fit the model from data in X.

Parameters:

Xarray-like of shape (n_samples, n_features): Training vector, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: Returns the instance itself.

fit_transform(X, y=None)[source]#

Fit the model from data in X and return the transformed data.

Parameters:

Xarray-like of shape (n_samples, n_features): Training vector, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.

Returns:

Vndarray of shape (n_samples, n_components): Transformed data.

get_feature_names_out(input_features=None)[source]#

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

Parameters:

input_featuresarray-like of str or None, default=None: Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects: Transformed feature names.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

inverse_transform(X)[source]#

Transform data back to its original space.

Parameters:

Xarray-like of shape (n_samples, n_components): Data to be transformed back. Must have the same number of components as the data used to train the model.

Returns:

X_originalndarray of shape (n_samples, n_features): Transformed data.

set_output(*, transform=None)[source]#

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:

selfestimator instance: Estimator instance.

set_params(**params)[source]#

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:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

transform(X)[source]#

Encode the data as a sparse combination of the dictionary atoms.

Coding method is determined by the object parameter transform_algorithm.

Parameters:

Xndarray of shape (n_samples, n_features): test data to be transformed, must have the same number of features as the data used to train the model.

Returns:

X_newndarray of shape (n_samples, n_components): Transformed data.

DictionaryLearning#

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