Class ProjectedGradientNMFScikitsLearnNode

Non-Negative Matrix Factorization (NMF)

This node has been automatically generated by wrapping the ``sklearn.decomposition.nmf.ProjectedGradientNMF`` class
from the ``sklearn`` library.  The wrapped instance can be accessed
through the ``scikits_alg`` attribute.

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 :ref:`User Guide <NMF>`.

**Parameters**

n_components : int or None
    Number of components, if n_components is not set all features
    are kept.

init :  'random' | 'nndsvd' |  'nndsvda' | 'nndsvdar' | 'custom'
    Method used to initialize the procedure.
    Default: 'nndsvdar' if n_components < n_features, otherwise random.
    Valid options:


    - 'random': non-negative random matrices, scaled with:

        - sqrt(X.mean() / n_components)


    - '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)

    - 'custom': use custom matrices W and H

solver : 'pg' | 'cd'
    Numerical solver to use:

    - 'pg' is a Projected Gradient solver (deprecated).
    - 'cd' is a Coordinate Descent solver (recommended).


    .. versionadded:: 0.17
       Coordinate Descent solver.

    .. versionchanged:: 0.17
       Deprecated Projected Gradient solver.

tol : double, default: 1e-4
    Tolerance value used in stopping conditions.

max_iter : integer, default: 200
    Number of iterations to compute.

random_state : integer seed, RandomState instance, or None (default)
    Random number generator seed control.

alpha : double, default: 0.
    Constant that multiplies the regularization terms. Set it to zero to
    have no regularization.

    .. versionadded:: 0.17
       *alpha* used in the Coordinate Descent solver.

l1_ratio : double, default: 0.
    The regularization mixing parameter, with 0 <= l1_ratio <= 1.
    For l1_ratio = 0 the penalty is an elementwise L2 penalty
    (aka Frobenius Norm).
    For l1_ratio = 1 it is an elementwise L1 penalty.
    For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.

    .. versionadded:: 0.17
       Regularization parameter *l1_ratio* used in the Coordinate Descent solver.

shuffle : boolean, default: False
    If true, randomize the order of coordinates in the CD solver.

    .. versionadded:: 0.17
       *shuffle* parameter used in the Coordinate Descent solver.

nls_max_iter : integer, default: 2000
    Number of iterations in NLS subproblem.
    Used only in the deprecated 'pg' solver.

    .. versionchanged:: 0.17
       Deprecated Projected Gradient solver. Use Coordinate Descent solver
       instead.

sparseness : 'data' | 'components' | None, default: None
    Where to enforce sparsity in the model.
    Used only in the deprecated 'pg' solver.

    .. versionchanged:: 0.17
       Deprecated Projected Gradient solver. Use Coordinate Descent solver
       instead.

beta : double, default: 1
    Degree of sparseness, if sparseness is not None. Larger values mean
    more sparseness. Used only in the deprecated 'pg' solver.

    .. versionchanged:: 0.17
       Deprecated Projected Gradient solver. Use Coordinate Descent solver
       instead.

eta : double, default: 0.1
    Degree of correctness to maintain, if sparsity is not None. Smaller
    values mean larger error. Used only in the deprecated 'pg' solver.

    .. versionchanged:: 0.17
       Deprecated Projected Gradient solver. Use Coordinate Descent solver
       instead.

**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``

``n_iter_`` : int
    Actual number of iterations.

**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) #doctest: +ELLIPSIS +NORMALIZE_WHITESPACE
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_ #doctest: +ELLIPSIS
0.00115993...

**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.