9.10.10. sklearn.decomposition.DictionaryLearning

class sklearn.decomposition.DictionaryLearning(n_atoms, alpha=1, max_iter=1000, tol=1e-08, fit_algorithm='lars', transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, n_jobs=1, code_init=None, dict_init=None, verbose=False, split_sign=False, random_state=None)

Dictionary learning

Finds a dictionary (a set of atoms) that can best be used to represent data using a sparse code.

Solves the optimization problem: (U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1

(U,V)

with || V_k ||_2 = 1 for all 0 <= k < n_atoms

Parameters :

n_atoms: int, :

number of dictionary elements to extract

alpha: int, :

sparsity controlling parameter

max_iter: int, :

maximum number of iterations to perform

tol: float, :

tolerance for numerical error

fit_algorithm: {‘lars’, ‘cd’} :

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.

transform_algorithm: {‘lasso_lars’, ‘lasso_cd’, ‘lars’, ‘omp’, ‘threshold’} :

Algorithm used to transform the data lars: uses the least angle regression method (linear_model.lars_path) lasso_lars: uses Lars to compute the Lasso solution lasso_cd: uses the coordinate descent method to compute the Lasso solution (linear_model.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 X.T * Y

transform_n_nonzero_coefs: int, 0.1 * n_features by default :

Number of nonzero coefficients to target in each column of the solution. This is only used by algorithm=’lars’ and algorithm=’omp’ and is overridden by alpha in the omp case.

transform_alpha: float, 1. by default :

If algorithm=’lasso_lars’ or algorithm=’lasso_cd’, alpha is the penalty applied to the L1 norm. If algorithm=’threhold’, alpha is the absolute value of the threshold below which coefficients will be squashed to zero. If algorithm=’omp’, alpha is the tolerance parameter: the value of the reconstruction error targeted. In this case, it overrides n_nonzero_coefs.

n_jobs: int, :

number of parallel jobs to run

code_init: array of shape (n_samples, n_atoms), :

initial value for the code, for warm restart

dict_init: array of shape (n_atoms, n_features), :

initial values for the dictionary, for warm restart

verbose: :

degree of verbosity of the printed output

random_state: int or RandomState :

Pseudo number generator state used for random sampling.

See also

sklearn.decomposition.SparsePCA, problem, finding

References

J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (http://www.di.ens.fr/sierra/pdfs/icml09.pdf)

Attributes

components_: array, [n_atoms, n_features]	dictionary atoms extracted from the data
error_: array	vector of errors at each iteration

Methods

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

__init__(n_atoms, alpha=1, max_iter=1000, tol=1e-08, fit_algorithm='lars', transform_algorithm='omp', transform_n_nonzero_coefs=None, transform_alpha=None, n_jobs=1, code_init=None, dict_init=None, verbose=False, split_sign=False, random_state=None)

fit(X, y=None)

Fit the model from data in X.

Parameters :

X: array-like, shape (n_samples, n_features) :

Training vector, where n_samples in the number of samples and n_features is the number of features.

Returns :

self: object :

Returns the object 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 :

X : numpy array of shape [n_samples, n_features]

Training set.

y : numpy array of shape [n_samples]

Target values.

Returns :

X_new : numpy array of shape [n_samples, n_features_new]

Transformed array.

set_params(**params)

Set the parameters of the estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :

transform(X, y=None)

Encode the data as a sparse combination of the dictionary atoms.

Coding method is determined by the object parameter transform_algorithm.

Parameters :

X: array 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_new array, shape (n_samples, n_components) :

Transformed data