sklearn.decomposition
.dict_learning_online¶
- sklearn.decomposition.dict_learning_online(X, n_components=2, *, alpha=1, max_iter=100, return_code=True, dict_init=None, callback=None, batch_size=256, verbose=False, shuffle=True, n_jobs=None, method='lars', random_state=None, positive_dict=False, positive_code=False, method_max_iter=1000, tol=0.001, max_no_improvement=10)[source]¶
Solve a dictionary learning matrix factorization problem online.
Finds the best dictionary and the corresponding sparse code for approximating the data matrix X by solving:
(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
where V is the dictionary and U is the sparse code. ||.||_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. This is accomplished by repeatedly iterating over mini-batches by slicing the input data.
Read more in the User Guide.
- Parameters:
- Xndarray of shape (n_samples, n_features)
Data matrix.
- n_componentsint or None, default=2
Number of dictionary atoms to extract. If None, then
n_components
is set ton_features
.- alphafloat, default=1
Sparsity controlling parameter.
- max_iterint, default=100
Maximum number of iterations over the complete dataset before stopping independently of any early stopping criterion heuristics.
New in version 1.1.
Deprecated since version 1.4:
max_iter=None
is deprecated in 1.4 and will be removed in 1.6. Use the default value (i.e.100
) instead.- return_codebool, default=True
Whether to also return the code U or just the dictionary
V
.- dict_initndarray of shape (n_components, n_features), default=None
Initial values for the dictionary for warm restart scenarios. If
None
, the initial values for the dictionary are created with an SVD decomposition of the data viarandomized_svd
.- callbackcallable, default=None
A callable that gets invoked at the end of each iteration.
- batch_sizeint, default=256
The number of samples to take in each batch.
Changed in version 1.3: The default value of
batch_size
changed from 3 to 256 in version 1.3.- verbosebool, default=False
To control the verbosity of the procedure.
- shufflebool, default=True
Whether to shuffle the data before splitting it in batches.
- n_jobsint, default=None
Number of parallel jobs to run.
None
means 1 unless in ajoblib.parallel_backend
context.-1
means using all processors. See Glossary for more details.- method{‘lars’, ‘cd’}, default=’lars’
'lars'
: uses the least angle regression method to solve the lasso problem (linear_model.lars_path
);'cd'
: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso
). Lars will be faster if the estimated components are sparse.
- random_stateint, RandomState instance or None, default=None
Used for initializing the dictionary when
dict_init
is not specified, randomly shuffling the data whenshuffle
is set toTrue
, and updating the dictionary. Pass an int for reproducible results across multiple function calls. See Glossary.- positive_dictbool, default=False
Whether to enforce positivity when finding the dictionary.
New in version 0.20.
- positive_codebool, default=False
Whether to enforce positivity when finding the code.
New in version 0.20.
- method_max_iterint, default=1000
Maximum number of iterations to perform when solving the lasso problem.
New in version 0.22.
- tolfloat, default=1e-3
Control early stopping based on the norm of the differences in the dictionary between 2 steps.
To disable early stopping based on changes in the dictionary, set
tol
to 0.0.New in version 1.1.
- max_no_improvementint, default=10
Control early stopping based on the consecutive number of mini batches that does not yield an improvement on the smoothed cost function.
To disable convergence detection based on cost function, set
max_no_improvement
to None.New in version 1.1.
- Returns:
- codendarray of shape (n_samples, n_components),
The sparse code (only returned if
return_code=True
).- dictionaryndarray of shape (n_components, n_features),
The solutions to the dictionary learning problem.
- n_iterint
Number of iterations run. Returned only if
return_n_iter
is set toTrue
.
See also
dict_learning
Solve a dictionary learning matrix factorization problem.
DictionaryLearning
Find a dictionary that sparsely encodes data.
MiniBatchDictionaryLearning
A faster, less accurate, version of the dictionary learning algorithm.
SparsePCA
Sparse Principal Components Analysis.
MiniBatchSparsePCA
Mini-batch Sparse Principal Components Analysis.
Examples
>>> import numpy as np >>> from sklearn.datasets import make_sparse_coded_signal >>> from sklearn.decomposition import dict_learning_online >>> X, _, _ = make_sparse_coded_signal( ... n_samples=30, n_components=15, n_features=20, n_nonzero_coefs=10, ... random_state=42, ... ) >>> U, V = dict_learning_online( ... X, n_components=15, alpha=0.2, max_iter=20, batch_size=3, random_state=42 ... )
We can check the level of sparsity of
U
:>>> np.mean(U == 0) 0.53...
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 = U @ V >>> np.mean(np.sum((X_hat - X) ** 2, axis=1) / np.sum(X ** 2, axis=1)) 0.05...