sklearn.decomposition
.non_negative_factorization¶

sklearn.decomposition.
non_negative_factorization
(X, W=None, H=None, n_components=None, init=’warn’, update_H=True, solver=’cd’, beta_loss=’frobenius’, tol=0.0001, max_iter=200, alpha=0.0, l1_ratio=0.0, regularization=None, random_state=None, verbose=0, shuffle=False)[source]¶ Compute Nonnegative Matrix Factorization (NMF)
Find two nonnegative 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)
For multiplicativeupdate (‘mu’) solver, the Frobenius norm (0.5 * X  WH_Fro^2) can be changed into another betadivergence loss, by changing the beta_loss parameter.
The objective function is minimized with an alternating minimization of W and H. If H is given and update_H=False, it solves for W only.
Parameters:  X : arraylike, shape (n_samples, n_features)
Constant matrix.
 W : arraylike, shape (n_samples, n_components)
If init=’custom’, it is used as initial guess for the solution.
 H : arraylike, shape (n_components, n_features)
If init=’custom’, it is used as initial guess for the solution. If update_H=False, it is used as a constant, to solve for W only.
 n_components : integer
Number of components, if n_components is not set all features are kept.
 init : None  ‘random’  ‘nndsvd’  ‘nndsvda’  ‘nndsvdar’  ‘custom’
Method used to initialize the procedure. Default: ‘random’.
The default value will change from ‘random’ to None in version 0.23 to make it consistent with decomposition.NMF.
Valid options:
 None: ‘nndsvd’ if n_components < n_features, otherwise ‘random’.
 ‘random’: nonnegative 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
 update_H : boolean, default: True
Set to True, both W and H will be estimated from initial guesses. Set to False, only W will be estimated.
 solver : ‘cd’  ‘mu’
Numerical solver to use: ‘cd’ is a Coordinate Descent solver that uses Fast Hierarchical
Alternating Least Squares (Fast HALS).
‘mu’ is a Multiplicative Update solver.
New in version 0.17: Coordinate Descent solver.
New in version 0.19: Multiplicative Update solver.
 beta_loss : float or string, default ‘frobenius’
String must be in {‘frobenius’, ‘kullbackleibler’, ‘itakurasaito’}. Beta divergence to be minimized, measuring the distance between X and the dot product WH. Note that values different from ‘frobenius’ (or 2) and ‘kullbackleibler’ (or 1) lead to significantly slower fits. Note that for beta_loss <= 0 (or ‘itakurasaito’), the input matrix X cannot contain zeros. Used only in ‘mu’ solver.
New in version 0.19.
 tol : float, default: 1e4
Tolerance of the stopping condition.
 max_iter : integer, default: 200
Maximum number of iterations before timing out.
 alpha : double, default: 0.
Constant that multiplies the regularization terms.
 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.
 regularization : ‘both’  ‘components’  ‘transformation’  None
Select whether the regularization affects the components (H), the transformation (W), both or none of them.
 random_state : int, RandomState instance or None, optional, default: None
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by
np.random
. verbose : integer, default: 0
The verbosity level.
 shuffle : boolean, default: False
If true, randomize the order of coordinates in the CD solver.
Returns:  W : arraylike, shape (n_samples, n_components)
Solution to the nonnegative least squares problem.
 H : arraylike, shape (n_components, n_features)
Solution to the nonnegative least squares problem.
 n_iter : int
Actual number of iterations.
References
Cichocki, Andrzej, and P. H. A. N. AnhHuy. “Fast local algorithms for large scale nonnegative matrix and tensor factorizations.” IEICE transactions on fundamentals of electronics, communications and computer sciences 92.3: 708721, 2009.
Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix factorization with the betadivergence. Neural Computation, 23(9).
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 non_negative_factorization >>> W, H, n_iter = non_negative_factorization(X, n_components=2, ... init='random', random_state=0)