sklearn.decomposition.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, 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.

New 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'.

New 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.

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.

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.

New in version 0.20.

positive_dictbool, default=False

Whether to enforce positivity when finding the dictionary.

New in version 0.20.

transform_max_iterint, default=1000

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

New 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.

New 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.

New 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=100, n_components=15, n_features=20, n_nonzero_coefs=10,
...     random_state=42,
... )
>>> dict_learner = DictionaryLearning(
...     n_components=15, transform_algorithm='lasso_lars', random_state=42,
... )
>>> X_transformed = dict_learner.fit_transform(X)

We can check the level of sparsity of X_transformed:

>>> np.mean(X_transformed == 0)
0.87...

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))
0.08...

Methods

fit(X[, y])	Fit the model from data in X.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.
transform(X)	Encode the data as a sparse combination of the dictionary atoms.

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_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

Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

Additional fit parameters.

Returns

X_newndarray array of shape (n_samples, n_features_new)

Transformed array.

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_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.