`sklearn.decomposition`.NMF¶

class sklearn.decomposition.NMF(n_components=None, *, init=None, solver='cd', beta_loss='frobenius', tol=0.0001, max_iter=200, random_state=None, alpha='deprecated', alpha_W=0.0, alpha_H='same', l1_ratio=0.0, verbose=0, shuffle=False, regularization='deprecated')[source]¶

Non-Negative Matrix Factorization (NMF).

Find two non-negative matrices, i.e. matrices with all non-negative elements, (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:

\[ \begin{align}\begin{aligned}L(W, H) &= 0.5 * ||X - WH||_{loss}^2\\&+ alpha\_W * l1\_ratio * n\_features * ||vec(W)||_1\\&+ alpha\_H * l1\_ratio * n\_samples * ||vec(H)||_1\\&+ 0.5 * alpha\_W * (1 - l1\_ratio) * n\_features * ||W||_{Fro}^2\\&+ 0.5 * alpha\_H * (1 - l1\_ratio) * n\_samples * ||H||_{Fro}^2\end{aligned}\end{align} \]

Where:

\(||A||_{Fro}^2 = \sum_{i,j} A_{ij}^2\) (Frobenius norm)

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

The generic norm \(||X - WH||_{loss}\) may represent the Frobenius norm or another supported beta-divergence loss. The choice between options is controlled by the beta_loss parameter.

The regularization terms are scaled by n_features for W and by n_samples for H to keep their impact balanced with respect to one another and to the data fit term as independent as possible of the size n_samples of the training set.

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

Note that the transformed data is named W and the components matrix is named H. In the NMF literature, the naming convention is usually the opposite since the data matrix X is transposed.

See also

DictionaryLearning: Find a dictionary that sparsely encodes data.
MiniBatchSparsePCA: Mini-batch Sparse Principal Components Analysis.
PCA: Principal component analysis.
SparseCoder: Find a sparse representation of data from a fixed, precomputed dictionary.
SparsePCA: Sparse Principal Components Analysis.
TruncatedSVD: Dimensionality reduction using truncated SVD.

References

[1]

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

[2]

“Algorithms for nonnegative matrix factorization with the beta-divergence” Fevotte, C., & Idier, J. (2011). 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_feature_names_out`([input_features])	Get output feature names for transformation.
`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): Training vector, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.
**paramskwargs: Parameters (keyword arguments) and values passed to the fit_transform instance.

Returns:

selfobject: Returns the instance itself.

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): Training vector, where n_samples is the number of samples and n_features is the number of features.
yIgnored: Not used, present for API consistency by convention.
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_feature_names_out(input_features=None)[source]¶

Get output feature names for transformation.

Parameters:

input_featuresarray-like of str or None, default=None: Only used to validate feature names with the names seen in fit.

Returns:

feature_names_outndarray of str objects: Transformed feature names.

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.

New in version 0.18.

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): Returns a data matrix of the original shape.

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): Training vector, where n_samples is the number of samples and n_features is the number of features.

Returns:

Wndarray of shape (n_samples, n_components): Transformed data.

Examples using `sklearn.decomposition.NMF`¶

Beta-divergence loss functions

Faces dataset decompositions

Topic extraction with Non-negative Matrix Factorization and Latent Dirichlet Allocation

Selecting dimensionality reduction with Pipeline and GridSearchCV

sklearn.decomposition.NMF¶

Examples using sklearn.decomposition.NMF¶

`sklearn.decomposition`.NMF¶

Examples using `sklearn.decomposition.NMF`¶