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)

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.

Read more in the User Guide.

Parameters:

n_componentsint, default=None

Number of dictionary elements to extract. If None, then n_components is set to n_features.

alphafloat, default=1.0

Sparsity controlling parameter.

max_iterint, default=1000

Maximum number of iterations to perform.

tolfloat, default=1e-8

Tolerance for numerical error.

fit_algorithm{‘lars’, ‘cd’}, default=’lars’

• 'lars': uses the least angle regression method to solve the lasso problem (lars_path);

• 'cd': uses the coordinate descent method to compute the Lasso solution (Lasso). Lars will be faster if the estimated components are sparse.

Added in version 0.17: cd coordinate descent method to improve speed.

transform_algorithm{‘lasso_lars’, ‘lasso_cd’, ‘lars’, ‘omp’, ‘threshold’}, default=’omp’

Algorithm used to transform the data:

• 'lars': uses the least angle regression method (lars_path);

• 'lasso_lars': uses Lars to compute the Lasso solution.

• 'lasso_cd': uses the coordinate descent method to compute the Lasso solution (Lasso). 'lasso_lars' will be faster if the estimated components are sparse.

• 'omp': uses orthogonal matching pursuit to estimate the sparse solution.

• 'threshold': squashes to zero all coefficients less than alpha from the projection dictionary * X'.

Added in version 0.17: lasso_cd coordinate descent method to improve speed.

transform_n_nonzero_coefsint, default=None

Number of nonzero coefficients to target in each column of the solution. This is only used by algorithm='lars' and algorithm='omp'. If None, then transform_n_nonzero_coefs=int(n_features / 10).

transform_alphafloat, default=None

If algorithm='lasso_lars' or algorithm='lasso_cd', alpha is the penalty applied to the L1 norm. If algorithm='threshold', alpha is the absolute value of the threshold below which coefficients will be squashed to zero. If None, defaults to alpha.

Changed in version 1.2: When None, default value changed from 1.0 to alpha.

n_jobsint or None, default=None

Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

code_initndarray of shape (n_samples, n_components), default=None

Initial value for the code, for warm restart. Only used if code_init and dict_init are not None.

dict_initndarray of shape (n_components, n_features), default=None

Initial values for the dictionary, for warm restart. Only used if code_init and dict_init are not None.

callbackcallable, default=None

Callable that gets invoked every five iterations.

Added in version 1.3.

verbosebool, default=False

To control the verbosity of the procedure.

split_signbool, default=False

Whether to split the sparse feature vector into the concatenation of its negative part and its positive part. This can improve the performance of downstream classifiers.

random_stateint, RandomState instance or None, default=None

Used for initializing the dictionary when dict_init is not specified, randomly shuffling the data when shuffle is set to True, and updating the dictionary. Pass an int for reproducible results across multiple function calls. See Glossary.

positive_codebool, default=False

Whether to enforce positivity when finding the code.

Added in version 0.20.

positive_dictbool, default=False

Whether to enforce positivity when finding the dictionary.

Added in version 0.20.

transform_max_iterint, default=1000

Maximum number of iterations to perform if algorithm='lasso_cd' or 'lasso_lars'.

Added in version 0.22.

Attributes:

components_ndarray of shape (n_components, n_features)

dictionary atoms extracted from the data

error_array

vector of errors at each iteration

n_features_in_int

Number of features seen during fit.

Added in version 0.24.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

Added in version 1.0.

n_iter_int

Number of iterations run.

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/sierra/pdfs/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)
0.52...

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))
0.05...

fit(X, y=None)

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)

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)

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()

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)

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.

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:

selfestimator instance

Estimator instance.

set_params(**params)

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)

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.