dict_learning#

sklearn.decomposition.dict_learning(X,n_components,*,alpha,max_iter=100,tol=1e-08,method='lars',n_jobs=None,dict_init=None,code_init=None,callback=None,verbose=False,random_state=None,return_n_iter=False,positive_dict=False,positive_code=False,method_max_iter=1000)[source]#

Solve a dictionary learning matrix factorization problem.

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.

Read more in theUser Guide.

Parameters:

Xarray-like of shape (n_samples, n_features)

Data matrix.

n_componentsint

Number of dictionary atoms to extract.

alphaint or float

Sparsity controlling parameter.

max_iterint, default=100

Maximum number of iterations to perform.

tolfloat, default=1e-8

Tolerance for the stopping condition.

method{‘lars’, ‘cd’}, default=’lars’

The method used:

• 'lars': uses the least angle regression method to solve the lasso

  problem (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.

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.

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

Initial value for the dictionary for warm restart scenarios. Only usedifcode_init anddict_init are not None.

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

Initial value for the sparse code for warm restart scenarios. Only usedifcode_init anddict_init are not None.

callbackcallable, default=None

Callable that gets invoked every five iterations.

verbosebool, default=False

To control the verbosity of the procedure.

random_stateint, RandomState instance or None, default=None

Used for randomly initializing the dictionary. Pass an int forreproducible results across multiple function calls.SeeGlossary.

return_n_iterbool, default=False

Whether or not to return the number of iterations.

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.

Added in version 0.22.

Returns:

codendarray of shape (n_samples, n_components)

The sparse code factor in the matrix factorization.

dictionaryndarray of shape (n_components, n_features),

The dictionary factor in the matrix factorization.

errorsarray

Vector of errors at each iteration.

n_iterint

Number of iterations run. Returned only ifreturn_n_iter isset to True.

See also

dict_learning_online

Solve a dictionary learning matrix factorization problem online.

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>>>X,_,_=make_sparse_coded_signal(...n_samples=30,n_components=15,n_features=20,n_nonzero_coefs=10,...random_state=42,...)>>>U,V,errors=dict_learning(X,n_components=15,alpha=0.1,random_state=42)

We can check the level of sparsity ofU:

>>>np.mean(U==0)np.float64(0.62)

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(0.0192)