Implementation:Scikit learn Scikit learn NMF

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Dimensionality Reduction, Matrix Factorization
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for Non-Negative Matrix Factorization provided by scikit-learn.

Description

NMF (Non-Negative Matrix Factorization) finds two non-negative matrices W and H whose product approximates the non-negative input matrix X. The factorization is useful for dimensionality reduction, source separation, and topic extraction. The objective function combines a data fit term using beta-divergence (Frobenius norm by default) with L1 and L2 regularization on both the W and H matrices. The module also provides MiniBatchNMF for scalable online learning.

Usage

Use NMF when your data is non-negative and you want interpretable, parts-based representations. Common applications include topic modeling on term-frequency matrices, image feature extraction, audio source separation, and recommender systems where the non-negativity constraint leads to naturally additive and interpretable components.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/decomposition/_nmf.py

Signature

class NMF(_BaseNMF):
    def __init__(
        self,
        n_components="auto",
        *,
        init=None,
        solver="cd",
        beta_loss="frobenius",
        tol=1e-4,
        max_iter=200,
        random_state=None,
        alpha_W=0.0,
        alpha_H="same",
        l1_ratio=0.0,
        verbose=0,
        shuffle=False,
    ):

Import

from sklearn.decomposition import NMF

I/O Contract

Inputs

Name	Type	Required	Description
n_components	int or 'auto'	No	Number of components. If 'auto', inferred from W or H shapes (default='auto').
init	str	No	Initialization method: 'random', 'nndsvd', 'nndsvda', 'nndsvdar', or 'custom'.
solver	str	No	Numerical solver: 'cd' (coordinate descent) or 'mu' (multiplicative update) (default='cd').
beta_loss	str or float	No	Beta divergence loss: 'frobenius', 'kullback-leibler', 'itakura-saito', or float (default='frobenius').
tol	float	No	Stopping tolerance (default=1e-4).
max_iter	int	No	Maximum number of iterations (default=200).
random_state	int or RandomState	No	Random state for reproducibility.
alpha_W	float	No	Regularization constant for W (default=0.0).
alpha_H	float or str	No	Regularization constant for H. 'same' uses alpha_W value (default='same').
l1_ratio	float	No	Ratio of L1 vs L2 regularization, in [0, 1] (default=0.0).
shuffle	bool	No	Whether to shuffle data in coordinate descent solver (default=False).

Outputs

Name	Type	Description
components_	ndarray of shape (n_components, n_features)	Factorization matrix H (the dictionary/components).
n_components_	int	The number of components, validated against input.
reconstruction_err_	float	Frobenius norm of the difference between X and WH.
n_iter_	int	Actual number of iterations.
n_features_in_	int	Number of features seen during fit.

Usage Examples

Basic Usage

import numpy as np
from sklearn.decomposition import NMF

X = np.array([[1, 1, 2], [2, 1, 0], [0, 2, 1], [1, 0, 2]], dtype=float)
nmf = NMF(n_components=2, init='random', random_state=0)
W = nmf.fit_transform(X)
H = nmf.components_
print(W.shape)  # (4, 2)
print(H.shape)  # (2, 3)
print(nmf.reconstruction_err_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Dimensionality_Reduction