decomposition.ProjectedGradientNMF()

Non-Negative Matrix Factorization (NMF)

Find two non-negative matrices (W, H) whose product approximates the non- negative matrix X. This factorization can be used for example for dimensionality reduction, source separation or topic extraction.

The objective function is:

0.5 * ||X - WH||_Fro^2
+ alpha * l1_ratio * ||vec(W)||_1
+ alpha * l1_ratio * ||vec(H)||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2

Where:

||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)

The objective function is minimized with an alternating minimization of W and H.

Read more in the User Guide.

References

C.-J. Lin. Projected gradient methods for non-negative matrix factorization. Neural Computation, 19(2007), 2756-2779. http://www.csie.ntu.edu.tw/~cjlin/nmf/

Cichocki, Andrzej, and P. H. A. N. Anh-Huy. ?Fast local algorithms for large scale nonnegative matrix and tensor factorizations.? IEICE transactions on fundamentals of electronics, communications and computer sciences 92.3: 708-721, 2009.

Examples

>>> import numpy as np
>>> X = np.array([[1,1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
>>> from sklearn.decomposition import NMF
>>> model = NMF(n_components=2, init='random', random_state=0)
>>> model.fit(X) 
NMF(alpha=0.0, beta=1, eta=0.1, init='random', l1_ratio=0.0, max_iter=200,
  n_components=2, nls_max_iter=2000, random_state=0, shuffle=False,
  solver='cd', sparseness=None, tol=0.0001, verbose=0)

>>> model.components_
array([[ 2.09783018,  0.30560234],
       [ 2.13443044,  2.13171694]])
>>> model.reconstruction_err_ 
0.00115993...

Methods

__init__(*args, **kwargs) [source]

DEPRECATED: It will be removed in release 0.19. Use NMF instead.?pg? solver is still available until release 0.19.

fit(X, y=None, **params) [source]

Learn a NMF model for the data X.

Parameters:	X: {array-like, sparse matrix}, shape (n_samples, n_features) : Data matrix to be decomposed
Returns:	self :

fit_transform(X, y=None, W=None, H=None) [source]

Learn a NMF model for the data X and returns the transformed data.

This is more efficient than calling fit followed by transform.

Parameters:	X: {array-like, sparse matrix}, shape (n_samples, n_features) : Data matrix to be decomposed W : array-like, shape (n_samples, n_components) If init=?custom?, it is used as initial guess for the solution. H : array-like, shape (n_components, n_features) If init=?custom?, it is used as initial guess for the solution.
Returns:	W: array, shape (n_samples, n_components) : Transformed data.

get_params(deep=True) [source]

Get parameters for this estimator.

Parameters:	deep : boolean, optional If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params : mapping of string to any Parameter names mapped to their values.

inverse_transform(W) [source]

Transform data back to its original space.

Parameters:	W: {array-like, sparse matrix}, shape (n_samples, n_components) : Transformed data matrix
Returns:	X: {array-like, sparse matrix}, shape (n_samples, n_features) : Data matrix of original shape .. versionadded:: 0.18 :

set_params(**params) [source]

Set the parameters of this estimator.

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

Returns:	self :

transform(X) [source]

Transform the data X according to the fitted NMF model

Parameters:	X: {array-like, sparse matrix}, shape (n_samples, n_features) : Data matrix to be transformed by the model
Returns:	W: array, shape (n_samples, n_components) : Transformed data