class sklearn.decomposition.NMF(n_components=None, *, init='warn', solver='cd', beta_loss='frobenius', tol=0.0001, max_iter=200, random_state=None, alpha=0.0, l1_ratio=0.0, verbose=0, shuffle=False, regularization='both') [source]
 
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:  \[ \begin{align}\begin{aligned}0.5 * ||X - WH||_{Fro}^2 + alpha * l1_{ratio} * ||vec(W)||_1\\+ alpha * l1_{ratio} * ||vec(H)||_1\\+ 0.5 * alpha * (1 - l1_{ratio}) * ||W||_{Fro}^2\\+ 0.5 * alpha * (1 - l1_{ratio}) * ||H||_{Fro}^2\end{aligned}\end{align} \] 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 multiplicative-update (‘mu’) solver, the Frobenius norm (\(0.5 * ||X - WH||_{Fro}^2\)) can be changed into another beta-divergence loss, by changing the beta_loss parameter. The objective function is minimized with an alternating minimization of W and H. Read more in the User Guide.  Parameters 
 
n_componentsint, default=None 

Number of components, if n_components is not set all features are kept.  
init{‘random’, ‘nndsvd’, ‘nndsvda’, ‘nndsvdar’, ‘custom’}, default=None 

Method used to initialize the procedure. Default: None. Valid options:  
None: ‘nndsvd’ if n_components <= min(n_samples, n_features), otherwise random. 
'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{‘cd’, ‘mu’}, default=’cd’ 

Numerical solver to use: ‘cd’ is a Coordinate Descent solver. ‘mu’ is a Multiplicative Update solver.  New in version 0.17: Coordinate Descent solver.   New in version 0.19: Multiplicative Update solver.   
beta_lossfloat or {‘frobenius’, ‘kullback-leibler’, ‘itakura-saito’}, default=’frobenius’ 

Beta divergence to be minimized, measuring the distance between X and the dot product WH. Note that values different from ‘frobenius’ (or 2) and ‘kullback-leibler’ (or 1) lead to significantly slower fits. Note that for beta_loss <= 0 (or ‘itakura-saito’), the input matrix X cannot contain zeros. Used only in ‘mu’ solver.  New in version 0.19.   
tolfloat, default=1e-4 

Tolerance of the stopping condition.  
max_iterint, default=200 

Maximum number of iterations before timing out.  
random_stateint, RandomState instance or None, default=None 

Used for initialisation (when init == ‘nndsvdar’ or ‘random’), and in Coordinate Descent. Pass an int for reproducible results across multiple function calls. See Glossary.  
alphafloat, default=0. 

Constant that multiplies the regularization terms. Set it to zero to have no regularization.  New in version 0.17: alpha used in the Coordinate Descent solver.   
l1_ratiofloat, 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.  New in version 0.17: Regularization parameter l1_ratio used in the Coordinate Descent solver.   
verboseint, default=0 

Whether to be verbose.  
shufflebool, default=False 

If true, randomize the order of coordinates in the CD solver.  New in version 0.17: shuffle parameter used in the Coordinate Descent solver.   
regularization{‘both’, ‘components’, ‘transformation’, None}, default=’both’ 

Select whether the regularization affects the components (H), the transformation (W), both or none of them.  New in version 0.24.     Attributes 
 
components_ndarray of shape (n_components, n_features) 

Factorization matrix, sometimes called ‘dictionary’.  
n_components_int 

The number of components. It is same as the n_components parameter if it was given. Otherwise, it will be same as the number of features.  
reconstruction_err_float 

Frobenius norm of the matrix difference, or beta-divergence, between the training data X and the reconstructed data WH from the fitted model.  
n_iter_int 

Actual number of iterations.     References 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. Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix factorization with the beta-divergence. 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 NMF
>>> model = NMF(n_components=2, init='random', random_state=0)
>>> W = model.fit_transform(X)
>>> H = model.components_
 Methods  
fit(X[, y]) Learn a NMF model for the data X.  
fit_transform(X[, y, W, H]) Learn a NMF model for the data X and returns the transformed data.  
get_params([deep]) Get parameters for this estimator.  
inverse_transform(W) Transform data back to its original space.  
set_params(**params) Set the parameters of this estimator.  
transform(X) Transform the data X according to the fitted NMF model.    
fit(X, y=None, **params) [source]
 
Learn a NMF model for the data X.  Parameters 
 
X{array-like, sparse matrix} of shape (n_samples, n_features) 

Data matrix to be decomposed  
yIgnored 
  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} of shape (n_samples, n_features) 

Data matrix to be decomposed  
yIgnored 

Warray-like of shape (n_samples, n_components) 

If init=’custom’, it is used as initial guess for the solution.  
Harray-like of shape (n_components, n_features) 

If init=’custom’, it is used as initial guess for the solution.    Returns 
 
Wndarray of shape (n_samples, n_components) 

Transformed data.     
  
get_params(deep=True) [source]
 
Get parameters for this estimator.  Parameters 
 
deepbool, default=True 

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns 
 
paramsdict 

Parameter names mapped to their values.     
  
inverse_transform(W) [source]
 
Transform data back to its original space.  Parameters 
 
W{ndarray, sparse matrix} of shape (n_samples, n_components) 

Transformed data matrix.    Returns 
 
X{ndarray, sparse matrix} of shape (n_samples, n_features) 

Data matrix of original shape.    New in version 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 Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters 
 
**paramsdict 

Estimator parameters.    Returns 
 
selfestimator instance 

Estimator instance.     
  
transform(X) [source]
 
Transform the data X according to the fitted NMF model.  Parameters 
 
X{array-like, sparse matrix} of shape (n_samples, n_features) 

Data matrix to be transformed by the model.    Returns 
 
Wndarray of shape (n_samples, n_components) 

Transformed data.