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 forapproximating the data matrix X by solving:

(U^*,V^*)=argmin0.5||X-UV||_Fro^2+alpha*||U||_1,1(U,V)with||V_k||_2=1forall0<=k<n_components

where V is the dictionary and U is the sparse code. ||.||_Fro stands forthe Frobenius norm and ||.||_1,1 stands for the entry-wise matrix normwhich is the sum of the absolute values of all the entries in the matrix.This is accomplished by repeatedly iterating over mini-batches by slicingthe input data.

Read more in theUser Guide.

Parameters:
Xarray-like of shape (n_samples, n_features)

Data matrix.

n_componentsint or None, default=2

Number of dictionary atoms to extract. If None, thenn_componentsis set ton_features.

alphafloat, default=1

Sparsity controlling parameter.

max_iterint, default=100

Maximum number of iterations over the complete dataset beforestopping independently of any early stopping criterion heuristics.

Added in version 1.1.

return_codebool, default=True

Whether to also return the code U or just the dictionaryV.

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

Initial values for the dictionary for warm restart scenarios.IfNone, the initial values for the dictionary are createdwith 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 ofbatch_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. SeeGlossaryfor more details.

method{‘lars’, ‘cd’}, default=’lars’

  • 'lars': uses the least angle regression method to solve the lassoproblem (linear_model.lars_path);

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

random_stateint, RandomState instance or None, default=None

Used for initializing the dictionary whendict_init is notspecified, randomly shuffling the data whenshuffle is set toTrue, and updating the dictionary. Pass an int for reproducibleresults across multiple function calls.SeeGlossary.

positive_dictbool, default=False

Whether to enforce positivity when finding the dictionary.

Added in version 0.20.

positive_codebool, default=False

Whether to enforce positivity when finding the code.

Added in version 0.20.

method_max_iterint, default=1000

Maximum number of iterations to perform when solving the lasso problem.

Added in version 0.22.

tolfloat, default=1e-3

Control early stopping based on the norm of the differences in thedictionary between 2 steps.

To disable early stopping based on changes in the dictionary, settol to 0.0.

Added in version 1.1.

max_no_improvementint, default=10

Control early stopping based on the consecutive number of mini batchesthat does not yield an improvement on the smoothed cost function.

To disable convergence detection based on cost function, setmax_no_improvement to None.

Added in version 1.1.

Returns:
codendarray of shape (n_samples, n_components),

The sparse code (only returned ifreturn_code=True).

dictionaryndarray of shape (n_components, n_features),

The solutions to the dictionary learning problem.

n_iterint

Number of iterations run. Returned only ifreturn_n_iter isset 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

>>>importnumpyasnp>>>fromsklearn.datasetsimportmake_sparse_coded_signal>>>fromsklearn.decompositionimportdict_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 ofU:

>>>np.mean(U==0)np.float64(0.53)

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

>>>X_hat=U@V>>>np.mean(np.sum((X_hat-X)**2,axis=1)/np.sum(X**2,axis=1))np.float64(0.053)

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