8.5.3. sklearn.decomposition.ProjectedGradientNMF

class sklearn.decomposition.ProjectedGradientNMF(n_components=None, init='nndsvdar', sparseness=None, beta=1, eta=0.1, tol=0.0001, max_iter=200, nls_max_iter=2000)

Non-Negative matrix factorization by Projected Gradient (NMF)

Parameters :

X: {array-like, sparse matrix}, shape = [n_samples, n_features] :

Data the model will be fit to.

n_components: int or None :

Number of components, if n_components is not set all components are kept

init: ‘nndsvd’ | ‘nndsvda’ | ‘nndsvdar’ | int | RandomState :

Method used to initialize the procedure. Default: ‘nndsvdar’ Valid options:

'nndsvd': Nonnegative Double Singular Value Decomposition (NNDSVD)
    initialization (better for sparseness)
'nndsvda': NNDSVD with zeros filled with the average of X
    (better when sparsity is not desired)
'nndsvdar': NNDSVD with zeros filled with small random values
    (generally faster, less accurate alternative to NNDSVDa
    for when sparsity is not desired)
int seed or RandomState: non-negative random matrices

sparseness: ‘data’ | ‘components’ | None, default: None :

Where to enforce sparsity in the model.

beta: double, default: 1 :

Degree of sparseness, if sparseness is not None. Larger values mean more sparseness.

eta: double, default: 0.1 :

Degree of correctness to mantain, if sparsity is not None. Smaller values mean larger error.

tol: double, default: 1e-4 :

Tolerance value used in stopping conditions.

max_iter: int, default: 200 :

Number of iterations to compute.

nls_max_iter: int, default: 2000 :

Number of iterations in NLS subproblem.

Notes

This implements

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/

P. Hoyer. Non-negative Matrix Factorization with Sparseness Constraints. Journal of Machine Learning Research 2004.

NNDSVD is introduced in

C. Boutsidis, E. Gallopoulos: SVD based initialization: A head start for nonnegative matrix factorization - Pattern Recognition, 2008 http://www.cs.rpi.edu/~boutsc/files/nndsvd.pdf

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 ProjectedGradientNMF
>>> model = ProjectedGradientNMF(n_components=2, init=0)
>>> model.fit(X) 
ProjectedGradientNMF(beta=1, eta=0.1, init=0, max_iter=200, n_components=2,
                     nls_max_iter=2000, sparseness=None, tol=0.0001)
>>> model.components_
array([[ 0.77032744,  0.11118662],
       [ 0.38526873,  0.38228063]])
>>> model.reconstruction_err_ 
0.00746...
>>> model = ProjectedGradientNMF(n_components=2, init=0,
...                              sparseness='components')
>>> model.fit(X) 
ProjectedGradientNMF(beta=1, eta=0.1, init=0, max_iter=200, n_components=2,
           nls_max_iter=2000, sparseness='components', tol=0.0001)
>>> model.components_
array([[ 1.67481991,  0.29614922],
       [-0.        ,  0.4681982 ]])
>>> model.reconstruction_err_ 
0.513...

Attributes

components_	array, [n_components, n_features]	Non-negative components of the data
reconstruction_err_	number	Frobenius norm of the matrix difference between the training data and the reconstructed data from the fit produced by the model. || X - WH ||_2 Not computed for sparse input matrices because it is too expensive in terms of memory.

Methods

fit(X[, y])	Learn a NMF model for the data X.
fit_transform(X[, y])	Learn a NMF model for the data X and returns the transformed data.
set_params(**params)	Set the parameters of the estimator.
transform(X)	Transform the data X according to the fitted NMF model

__init__(n_components=None, init='nndsvdar', sparseness=None, beta=1, eta=0.1, tol=0.0001, max_iter=200, nls_max_iter=2000)

fit(X, y=None, **params)

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)

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

Returns :

data: array, [n_samples, n_components] :

Transformed data

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)

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 :

data: array, [n_samples, n_components] :

Transformed data