8.5.11. 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 dictionary * X'

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=’threshold’, 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.

split_sign : bool, False by default

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.

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

SparseCoder, MiniBatchDictionaryLearning, SparsePCA, MiniBatchSparsePCA

Notes

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.

Notes

This method just calls fit and transform consecutively, i.e., it is not an optimized implementation of fit_transform, unlike other transformers such as PCA.

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