Repository: scikit-learn/scikit-learn
Issue category: Feature Request

Online implementation of Non-negative Matrix Factorizarion (NMF)
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#### Description
<!-- Example: Joblib Error thrown when calling fit on LatentDirichletAllocation with evaluate_every > 0-->
@GaelVaroquaux Maybe an online version of the NMF could be useful in big data settings.

#### Steps/Code to Reproduce
<!--
Example:
```python
from sklearn.feature_extraction.text import CountVectorizer
from sklearn.decomposition import LatentDirichletAllocation

docs = ["Help I have a bug" for i in range(1000)]

vectorizer = CountVectorizer(input=docs, analyzer='word')
lda_features = vectorizer.fit_transform(docs)

lda_model = LatentDirichletAllocation(
    n_topics=10,
    learning_method='online',
    evaluate_every=10,
    n_jobs=4,
)
model = lda_model.fit(lda_features)
```
If the code is too long, feel free to put it in a public gist and link
it in the issue: https://gist.github.com
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#### Expected Results
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#### Actual Results
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Here I show the results for an sparse matrix as input of size 1M x 2.8k
The factorization has `n_components = 10` and each point is an entire pass on the data.
The current online implementation only supports the kullback-leibler divergence, but in practice
can be generalized to any beta divergence.

![batch_vs_online_nmf](https://user-images.githubusercontent.com/11759948/53494592-69748b00-3a9e-11e9-8cc8-ce53ce3fe7f2.png)

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<!-- Thanks for contributing! -->

Draft implementation of MiniBatchNMF
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#### What does this implement/fix? Explain your changes.

Implementation of a mini-batch NMF with multiplicative updates.
#13308 
#### Any other comments?


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Functions to edit:
sklearn/decomposition/_nmf.py:norm
sklearn/decomposition/_nmf.py:_beta_divergence
sklearn/decomposition/_nmf.py:_fit_coordinate_descent
sklearn/decomposition/_nmf.py:_multiplicative_update_w
sklearn/decomposition/_nmf.py:_multiplicative_update_h
sklearn/decomposition/_nmf.py:_fit_multiplicative_update
sklearn/decomposition/_nmf.py:non_negative_factorization
sklearn/decomposition/_nmf.py:NMF._fit_transform
sklearn/utils/estimator_checks.py:_set_checking_parameters
Functions added: sklearn/decomposition/_nmf.py:MiniBatchNMF
sklearn/decomposition/_nmf.py:MiniBatchNMF.__init__
sklearn/decomposition/_nmf.py:MiniBatchNMF._check_params
sklearn/decomposition/_nmf.py:MiniBatchNMF._solve_W
sklearn/decomposition/_nmf.py:MiniBatchNMF._minibatch_step
sklearn/decomposition/_nmf.py:MiniBatchNMF._minibatch_convergence
sklearn/decomposition/_nmf.py:MiniBatchNMF.fit_transform
sklearn/decomposition/_nmf.py:MiniBatchNMF._fit_transform
sklearn/decomposition/_nmf.py:MiniBatchNMF.transform
sklearn/decomposition/_nmf.py:MiniBatchNMF.partial_fit

Patch:
diff --git a/doc/computing/scaling_strategies.rst b/doc/computing/scaling_strategies.rst
index 5eee5728e4b9a..277d499f4cc13 100644
--- a/doc/computing/scaling_strategies.rst
+++ b/doc/computing/scaling_strategies.rst
@@ -80,6 +80,7 @@ Here is a list of incremental estimators for different tasks:
       + :class:`sklearn.decomposition.MiniBatchDictionaryLearning`
       + :class:`sklearn.decomposition.IncrementalPCA`
       + :class:`sklearn.decomposition.LatentDirichletAllocation`
+      + :class:`sklearn.decomposition.MiniBatchNMF`
   - Preprocessing
       + :class:`sklearn.preprocessing.StandardScaler`
       + :class:`sklearn.preprocessing.MinMaxScaler`
diff --git a/doc/modules/classes.rst b/doc/modules/classes.rst
index 9640f176925c5..a4217ad44cd76 100644
--- a/doc/modules/classes.rst
+++ b/doc/modules/classes.rst
@@ -319,6 +319,7 @@ Samples generator
    decomposition.MiniBatchDictionaryLearning
    decomposition.MiniBatchSparsePCA
    decomposition.NMF
+   decomposition.MiniBatchNMF
    decomposition.PCA
    decomposition.SparsePCA
    decomposition.SparseCoder
diff --git a/doc/modules/decomposition.rst b/doc/modules/decomposition.rst
index dd8fac301ceed..4f6a889473f13 100644
--- a/doc/modules/decomposition.rst
+++ b/doc/modules/decomposition.rst
@@ -921,6 +921,29 @@ stored components::
     * :ref:`sphx_glr_auto_examples_applications_plot_topics_extraction_with_nmf_lda.py`
     * :ref:`sphx_glr_auto_examples_decomposition_plot_beta_divergence.py`
 
+.. _MiniBatchNMF:
+
+Mini-batch Non Negative Matrix Factorization
+--------------------------------------------
+
+:class:`MiniBatchNMF` [7]_ implements a faster, but less accurate version of the
+non negative matrix factorization (i.e. :class:`~sklearn.decomposition.NMF`),
+better suited for large datasets.
+
+By default, :class:`MiniBatchNMF` divides the data into mini-batches and
+optimizes the NMF model in an online manner by cycling over the mini-batches
+for the specified number of iterations. The ``batch_size`` parameter controls
+the size of the batches.
+
+In order to speed up the mini-batch algorithm it is also possible to scale
+past batches, giving them less importance than newer batches. This is done
+introducing a so-called forgetting factor controlled by the ``forget_factor``
+parameter.
+
+The estimator also implements ``partial_fit``, which updates ``H`` by iterating
+only once over a mini-batch. This can be used for online learning when the data
+is not readily available from the start, or when the data does not fit into memory.
+
 .. topic:: References:
 
     .. [1] `"Learning the parts of objects by non-negative matrix factorization"
@@ -945,6 +968,9 @@ stored components::
            the beta-divergence" <1010.1763>`
            C. Fevotte, J. Idier, 2011
 
+    .. [7] :arxiv:`"Online algorithms for nonnegative matrix factorization with the
+       Itakura-Saito divergence" <1106.4198>`
+       A. Lefevre, F. Bach, C. Fevotte, 2011
 
 .. _LatentDirichletAllocation:
 
diff --git a/doc/whats_new/v1.1.rst b/doc/whats_new/v1.1.rst
index 3dc5799c228ad..0acd0612dd0c7 100644
--- a/doc/whats_new/v1.1.rst
+++ b/doc/whats_new/v1.1.rst
@@ -288,6 +288,11 @@ Changelog
 :mod:`sklearn.decomposition`
 ............................
 
+- |MajorFeature| Added a new estimator :class:`decomposition.MiniBatchNMF`. It is a
+  faster but less accurate version of non-negative matrix factorization, better suited
+  for large datasets. :pr:`16948` by :user:`Chiara Marmo <cmarmo>`,
+  :user:`Patricio Cerda <pcerda>` and :user:`Jérémie du Boisberranger <jeremiedbb>`. 
+
 - |Enhancement| :class:`decomposition.PCA` exposes a parameter `n_oversamples` to tune
   :func:`sklearn.decomposition.randomized_svd` and
   get accurate results when the number of features is large.
diff --git a/examples/applications/plot_topics_extraction_with_nmf_lda.py b/examples/applications/plot_topics_extraction_with_nmf_lda.py
index 48b69d710226b..38945241ab68b 100644
--- a/examples/applications/plot_topics_extraction_with_nmf_lda.py
+++ b/examples/applications/plot_topics_extraction_with_nmf_lda.py
@@ -30,13 +30,15 @@
 import matplotlib.pyplot as plt
 
 from sklearn.feature_extraction.text import TfidfVectorizer, CountVectorizer
-from sklearn.decomposition import NMF, LatentDirichletAllocation
+from sklearn.decomposition import NMF, MiniBatchNMF, LatentDirichletAllocation
 from sklearn.datasets import fetch_20newsgroups
 
 n_samples = 2000
 n_features = 1000
 n_components = 10
 n_top_words = 20
+batch_size = 128
+init = "nndsvda"
 
 
 def plot_top_words(model, feature_names, n_top_words, title):
@@ -101,7 +103,15 @@ def plot_top_words(model, feature_names, n_top_words, title):
     "n_samples=%d and n_features=%d..." % (n_samples, n_features)
 )
 t0 = time()
-nmf = NMF(n_components=n_components, random_state=1, alpha=0.1, l1_ratio=0.5).fit(tfidf)
+nmf = NMF(
+    n_components=n_components,
+    random_state=1,
+    init=init,
+    beta_loss="frobenius",
+    alpha_W=0.00005,
+    alpha_H=0.00005,
+    l1_ratio=1,
+).fit(tfidf)
 print("done in %0.3fs." % (time() - t0))
 
 
@@ -121,10 +131,12 @@ def plot_top_words(model, feature_names, n_top_words, title):
 nmf = NMF(
     n_components=n_components,
     random_state=1,
+    init=init,
     beta_loss="kullback-leibler",
     solver="mu",
     max_iter=1000,
-    alpha=0.1,
+    alpha_W=0.00005,
+    alpha_H=0.00005,
     l1_ratio=0.5,
 ).fit(tfidf)
 print("done in %0.3fs." % (time() - t0))
@@ -137,6 +149,63 @@ def plot_top_words(model, feature_names, n_top_words, title):
     "Topics in NMF model (generalized Kullback-Leibler divergence)",
 )
 
+# Fit the MiniBatchNMF model
+print(
+    "\n" * 2,
+    "Fitting the MiniBatchNMF model (Frobenius norm) with tf-idf "
+    "features, n_samples=%d and n_features=%d, batch_size=%d..."
+    % (n_samples, n_features, batch_size),
+)
+t0 = time()
+mbnmf = MiniBatchNMF(
+    n_components=n_components,
+    random_state=1,
+    batch_size=batch_size,
+    init=init,
+    beta_loss="frobenius",
+    alpha_W=0.00005,
+    alpha_H=0.00005,
+    l1_ratio=0.5,
+).fit(tfidf)
+print("done in %0.3fs." % (time() - t0))
+
+
+tfidf_feature_names = tfidf_vectorizer.get_feature_names_out()
+plot_top_words(
+    mbnmf,
+    tfidf_feature_names,
+    n_top_words,
+    "Topics in MiniBatchNMF model (Frobenius norm)",
+)
+
+# Fit the MiniBatchNMF model
+print(
+    "\n" * 2,
+    "Fitting the MiniBatchNMF model (generalized Kullback-Leibler "
+    "divergence) with tf-idf features, n_samples=%d and n_features=%d, "
+    "batch_size=%d..." % (n_samples, n_features, batch_size),
+)
+t0 = time()
+mbnmf = MiniBatchNMF(
+    n_components=n_components,
+    random_state=1,
+    batch_size=batch_size,
+    init=init,
+    beta_loss="kullback-leibler",
+    alpha_W=0.00005,
+    alpha_H=0.00005,
+    l1_ratio=0.5,
+).fit(tfidf)
+print("done in %0.3fs." % (time() - t0))
+
+tfidf_feature_names = tfidf_vectorizer.get_feature_names_out()
+plot_top_words(
+    mbnmf,
+    tfidf_feature_names,
+    n_top_words,
+    "Topics in MiniBatchNMF model (generalized Kullback-Leibler divergence)",
+)
+
 print(
     "\n" * 2,
     "Fitting LDA models with tf features, n_samples=%d and n_features=%d..."
diff --git a/sklearn/decomposition/__init__.py b/sklearn/decomposition/__init__.py
index c280aeb2cf71d..c5f323d3c5d72 100644
--- a/sklearn/decomposition/__init__.py
+++ b/sklearn/decomposition/__init__.py
@@ -5,7 +5,11 @@
 """
 
 
-from ._nmf import NMF, non_negative_factorization
+from ._nmf import (
+    NMF,
+    MiniBatchNMF,
+    non_negative_factorization,
+)
 from ._pca import PCA
 from ._incremental_pca import IncrementalPCA
 from ._kernel_pca import KernelPCA
@@ -31,6 +35,7 @@
     "IncrementalPCA",
     "KernelPCA",
     "MiniBatchDictionaryLearning",
+    "MiniBatchNMF",
     "MiniBatchSparsePCA",
     "NMF",
     "PCA",
diff --git a/sklearn/decomposition/_nmf.py b/sklearn/decomposition/_nmf.py
index 443f9c4be1649..7623822ba5912 100644
--- a/sklearn/decomposition/_nmf.py
+++ b/sklearn/decomposition/_nmf.py
@@ -10,14 +10,16 @@
 import numpy as np
 import scipy.sparse as sp
 import time
+import itertools
 import warnings
 from math import sqrt
+from scipy import linalg
 
 from ._cdnmf_fast import _update_cdnmf_fast
 from .._config import config_context
 from ..base import BaseEstimator, TransformerMixin, _ClassNamePrefixFeaturesOutMixin
 from ..exceptions import ConvergenceWarning
-from ..utils import check_random_state, check_array
+from ..utils import check_random_state, check_array, gen_batches
 from ..utils.extmath import randomized_svd, safe_sparse_dot, squared_norm
 from ..utils.validation import (
     check_is_fitted,
@@ -30,7 +32,7 @@
 def norm(x):
     """Dot product-based Euclidean norm implementation.
 
-    See: http://fseoane.net/blog/2011/computing-the-vector-norm/
+    See: http://fa.bianp.net/blog/2011/computing-the-vector-norm/
 
     Parameters
     ----------
@@ -166,6 +168,7 @@ def _beta_divergence(X, W, H, beta, square_root=False):
         res /= beta * (beta - 1)
 
     if square_root:
+        res = max(res, 0)  # avoid negative number due to rounding errors
         return np.sqrt(2 * res)
     else:
         return res
@@ -493,10 +496,10 @@ def _fit_coordinate_descent(
 
     References
     ----------
-    Cichocki, Andrzej, and Phan, 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.
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. IEICE transactions on fundamentals
+       of electronics, communications and computer sciences 92.3: 708-721, 2009.
     """
     # so W and Ht are both in C order in memory
     Ht = check_array(H.T, order="C")
@@ -637,11 +640,15 @@ def _multiplicative_update_w(
     if gamma != 1:
         delta_W **= gamma
 
-    return delta_W, H_sum, HHt, XHt
+    W *= delta_W
 
+    return W, H_sum, HHt, XHt
 
-def _multiplicative_update_h(X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma):
-    """Update H in Multiplicative Update NMF."""
+
+def _multiplicative_update_h(
+    X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma, A=None, B=None, rho=None
+):
+    """update H in Multiplicative Update NMF."""
     if beta_loss == 2:
         numerator = safe_sparse_dot(W.T, X)
         denominator = np.linalg.multi_dot([W.T, W, H])
@@ -712,14 +719,27 @@ def _multiplicative_update_h(X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma):
         denominator = denominator + l2_reg_H * H
     denominator[denominator == 0] = EPSILON
 
-    numerator /= denominator
-    delta_H = numerator
-
-    # gamma is in ]0, 1]
-    if gamma != 1:
-        delta_H **= gamma
+    if A is not None and B is not None:
+        # Updates for the online nmf
+        if gamma != 1:
+            H **= 1 / gamma
+        numerator *= H
+        A *= rho
+        B *= rho
+        A += numerator
+        B += denominator
+        H = A / B
+
+        if gamma != 1:
+            H **= gamma
+    else:
+        delta_H = numerator
+        delta_H /= denominator
+        if gamma != 1:
+            delta_H **= gamma
+        H *= delta_H
 
-    return delta_H
+    return H
 
 
 def _fit_multiplicative_update(
@@ -800,6 +820,8 @@ def _fit_multiplicative_update(
 
     References
     ----------
+    Lee, D. D., & Seung, H., S. (2001). Algorithms for Non-negative Matrix
+    Factorization. Adv. Neural Inform. Process. Syst.. 13.
     Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix
     factorization with the beta-divergence. Neural Computation, 23(9).
     """
@@ -823,21 +845,35 @@ def _fit_multiplicative_update(
     for n_iter in range(1, max_iter + 1):
         # update W
         # H_sum, HHt and XHt are saved and reused if not update_H
-        delta_W, H_sum, HHt, XHt = _multiplicative_update_w(
-            X, W, H, beta_loss, l1_reg_W, l2_reg_W, gamma, H_sum, HHt, XHt, update_H
+        W, H_sum, HHt, XHt = _multiplicative_update_w(
+            X,
+            W,
+            H,
+            beta_loss=beta_loss,
+            l1_reg_W=l1_reg_W,
+            l2_reg_W=l2_reg_W,
+            gamma=gamma,
+            H_sum=H_sum,
+            HHt=HHt,
+            XHt=XHt,
+            update_H=update_H,
         )
-        W *= delta_W
 
         # necessary for stability with beta_loss < 1
         if beta_loss < 1:
             W[W < np.finfo(np.float64).eps] = 0.0
 
-        # update H
+        # update H (only at fit or fit_transform)
         if update_H:
-            delta_H = _multiplicative_update_h(
-                X, W, H, beta_loss, l1_reg_H, l2_reg_H, gamma
+            H = _multiplicative_update_h(
+                X,
+                W,
+                H,
+                beta_loss=beta_loss,
+                l1_reg_H=l1_reg_H,
+                l2_reg_H=l2_reg_H,
+                gamma=gamma,
             )
-            H *= delta_H
 
             # These values will be recomputed since H changed
             H_sum, HHt, XHt = None, None, None
@@ -902,15 +938,16 @@ def non_negative_factorization(
 
         .. math::
 
-            0.5 * ||X - WH||_{loss}^2
+            L(W, H) &= 0.5 * ||X - WH||_{loss}^2
+
+            &+ alpha\\_W * l1\\_ratio * n\\_features * ||vec(W)||_1
 
-            + alpha\\_W * l1_{ratio} * n\\_features * ||vec(W)||_1
+            &+ alpha\\_H * l1\\_ratio * n\\_samples * ||vec(H)||_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\\_W * (1 - l1_{ratio}) * n\\_features * ||W||_{Fro}^2
+            &+ 0.5 * alpha\\_H * (1 - l1\\_ratio) * n\\_samples * ||H||_{Fro}^2
 
-            + 0.5 * alpha\\_H * (1 - l1_{ratio}) * n\\_samples * ||H||_{Fro}^2
 
     Where:
 
@@ -1084,13 +1121,14 @@ def non_negative_factorization(
 
     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).
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       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] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
     """
     X = check_array(X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32])
 
@@ -1120,23 +1158,23 @@ def non_negative_factorization(
 class NMF(_ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
     """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.
+    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:
 
         .. math::
 
-            0.5 * ||X - WH||_{loss}^2
+            L(W, H) &= 0.5 * ||X - WH||_{loss}^2
 
-            + alpha\\_W * l1_{ratio} * n\\_features * ||vec(W)||_1
+            &+ alpha\\_W * l1\\_ratio * n\\_features * ||vec(W)||_1
 
-            + alpha\\_H * l1_{ratio} * n\\_samples * ||vec(H)||_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\\_W * (1 - l1\\_ratio) * n\\_features * ||W||_{Fro}^2
 
-            + 0.5 * alpha\\_H * (1 - l1_{ratio}) * n\\_samples * ||H||_{Fro}^2
+            &+ 0.5 * alpha\\_H * (1 - l1\\_ratio) * n\\_samples * ||H||_{Fro}^2
 
     Where:
 
@@ -1325,13 +1363,14 @@ class NMF(_ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
 
     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.
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       Cichocki, Andrzej, and P. H. A. N. Anh-Huy. 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).
+    .. [2] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
 
     Examples
     --------
@@ -1632,7 +1671,7 @@ def _fit_transform(self, X, y=None, W=None, H=None, update_H=True):
                 random_state=self.random_state,
             )
         elif self.solver == "mu":
-            W, H, n_iter = _fit_multiplicative_update(
+            W, H, n_iter, *_ = _fit_multiplicative_update(
                 X,
                 W,
                 H,
@@ -1643,8 +1682,8 @@ def _fit_transform(self, X, y=None, W=None, H=None, update_H=True):
                 l1_reg_H,
                 l2_reg_W,
                 l2_reg_H,
-                update_H=update_H,
-                verbose=self.verbose,
+                update_H,
+                self.verbose,
             )
         else:
             raise ValueError("Invalid solver parameter '%s'." % self.solver)
@@ -1729,3 +1768,628 @@ def inverse_transform(self, W):
     def _n_features_out(self):
         """Number of transformed output features."""
         return self.components_.shape[0]
+
+
+class MiniBatchNMF(NMF):
+    """Mini-Batch Non-Negative Matrix Factorization (NMF).
+
+    .. versionadded:: 1.1
+
+    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:
+
+        .. math::
+
+            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
+
+    Where:
+
+    :math:`||A||_{Fro}^2 = \\sum_{i,j} A_{ij}^2` (Frobenius norm)
+
+    :math:`||vec(A)||_1 = \\sum_{i,j} abs(A_{ij})` (Elementwise L1 norm)
+
+    The generic norm :math:`||X - WH||_{loss}^2` may represent
+    the Frobenius norm or another supported beta-divergence loss.
+    The choice between options is controlled by the `beta_loss` parameter.
+
+    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.
+
+    Read more in the :ref:`User Guide <MiniBatchNMF>`.
+
+    Parameters
+    ----------
+    n_components : int, 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.
+        Valid options:
+
+        - `None`: 'nndsvda' 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`
+
+    batch_size : int, default=1024
+        Number of samples in each mini-batch. Large batch sizes
+        give better long-term convergence at the cost of a slower start.
+
+    beta_loss : float 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.
+
+    tol : float, default=1e-4
+        Control early stopping based on the norm of the differences in `H`
+        between 2 steps. To disable early stopping based on changes in `H`, set
+        `tol` to 0.0.
+
+    max_no_improvement : int, default=10
+        Control early stopping based on the consecutive number of mini batches
+        that does not yield an improvement on the smoothed cost function.
+        To disable convergence detection based on cost function, set
+        `max_no_improvement` to None.
+
+    max_iter : int, default=200
+        Maximum number of iterations over the complete dataset before
+        timing out.
+
+    alpha_W : float, default=0.0
+        Constant that multiplies the regularization terms of `W`. Set it to zero
+        (default) to have no regularization on `W`.
+
+    alpha_H : float or "same", default="same"
+        Constant that multiplies the regularization terms of `H`. Set it to zero to
+        have no regularization on `H`. If "same" (default), it takes the same value as
+        `alpha_W`.
+
+    l1_ratio : float, default=0.0
+        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.
+
+    forget_factor : float, default=0.7
+        Amount of rescaling of past information. Its value could be 1 with
+        finite datasets. Choosing values < 1 is recommended with online
+        learning as more recent batches will weight more than past batches.
+
+    fresh_restarts : bool, default=False
+        Whether to completely solve for W at each step. Doing fresh restarts will likely
+        lead to a better solution for a same number of iterations but it is much slower.
+
+    fresh_restarts_max_iter : int, default=30
+        Maximum number of iterations when solving for W at each step. Only used when
+        doing fresh restarts. These iterations may be stopped early based on a small
+        change of W controlled by `tol`.
+
+    transform_max_iter : int, default=None
+        Maximum number of iterations when solving for W at transform time.
+        If None, it defaults to `max_iter`.
+
+    random_state : int, 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 :term:`Glossary <random_state>`.
+
+    verbose : bool, default=False
+        Whether to be verbose.
+
+    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 started iterations over the whole dataset.
+
+    n_steps_ : int
+        Number of mini-batches processed.
+
+    n_features_in_ : int
+        Number of features seen during :term:`fit`.
+
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Defined only when `X`
+        has feature names that are all strings.
+
+    See Also
+    --------
+    NMF : Non-negative matrix factorization.
+    MiniBatchDictionaryLearning : Finds a dictionary that can best be used to represent
+        data using a sparse code.
+
+    References
+    ----------
+    .. [1] :doi:`"Fast local algorithms for large scale nonnegative matrix and tensor
+       factorizations" <10.1587/transfun.E92.A.708>`
+       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] :doi:`"Algorithms for nonnegative matrix factorization with the
+       beta-divergence" <10.1162/NECO_a_00168>`
+       Fevotte, C., & Idier, J. (2011). Neural Computation, 23(9).
+
+    .. [3] :doi:`"Online algorithms for nonnegative matrix factorization with the
+       Itakura-Saito divergence" <10.1109/ASPAA.2011.6082314>`
+       Lefevre, A., Bach, F., Fevotte, C. (2011). WASPA.
+
+    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 MiniBatchNMF
+    >>> model = MiniBatchNMF(n_components=2, init='random', random_state=0)
+    >>> W = model.fit_transform(X)
+    >>> H = model.components_
+    """
+
+    def __init__(
+        self,
+        n_components=None,
+        *,
+        init=None,
+        batch_size=1024,
+        beta_loss="frobenius",
+        tol=1e-4,
+        max_no_improvement=10,
+        max_iter=200,
+        alpha_W=0.0,
+        alpha_H="same",
+        l1_ratio=0.0,
+        forget_factor=0.7,
+        fresh_restarts=False,
+        fresh_restarts_max_iter=30,
+        transform_max_iter=None,
+        random_state=None,
+        verbose=0,
+    ):
+
+        super().__init__(
+            n_components=n_components,
+            init=init,
+            solver="mu",
+            beta_loss=beta_loss,
+            tol=tol,
+            max_iter=max_iter,
+            random_state=random_state,
+            alpha_W=alpha_W,
+            alpha_H=alpha_H,
+            l1_ratio=l1_ratio,
+            verbose=verbose,
+        )
+
+        self.max_no_improvement = max_no_improvement
+        self.batch_size = batch_size
+        self.forget_factor = forget_factor
+        self.fresh_restarts = fresh_restarts
+        self.fresh_restarts_max_iter = fresh_restarts_max_iter
+        self.transform_max_iter = transform_max_iter
+
+    def _check_params(self, X):
+        super()._check_params(X)
+
+        # batch_size
+        self._batch_size = self.batch_size
+        if not isinstance(self._batch_size, numbers.Integral) or self._batch_size <= 0:
+            raise ValueError(
+                "batch_size must be a positive integer, got "
+                f"{self._batch_size!r} instead."
+            )
+        self._batch_size = min(self._batch_size, X.shape[0])
+
+        # forget_factor
+        self._rho = self.forget_factor ** (self._batch_size / X.shape[0])
+
+        # gamma for Maximization-Minimization (MM) algorithm [Fevotte 2011]
+        if self._beta_loss < 1:
+            self._gamma = 1.0 / (2.0 - self._beta_loss)
+        elif self._beta_loss > 2:
+            self._gamma = 1.0 / (self._beta_loss - 1.0)
+        else:
+            self._gamma = 1.0
+
+        # transform_max_iter
+        self._transform_max_iter = (
+            self.max_iter
+            if self.transform_max_iter is None
+            else self.transform_max_iter
+        )
+
+        return self
+
+    def _solve_W(self, X, H, max_iter):
+        """Minimize the objective function w.r.t W.
+
+        Update W with H being fixed, until convergence. This is the heart
+        of `transform` but it's also used during `fit` when doing fresh restarts.
+        """
+        avg = np.sqrt(X.mean() / self._n_components)
+        W = np.full((X.shape[0], self._n_components), avg, dtype=X.dtype)
+        W_buffer = W.copy()
+
+        # Get scaled regularization terms. Done for each minibatch to take into account
+        # variable sizes of minibatches.
+        l1_reg_W, _, l2_reg_W, _ = self._scale_regularization(X)
+
+        for _ in range(max_iter):
+            W, *_ = _multiplicative_update_w(
+                X, W, H, self._beta_loss, l1_reg_W, l2_reg_W, self._gamma
+            )
+
+            W_diff = linalg.norm(W - W_buffer) / linalg.norm(W)
+            if self.tol > 0 and W_diff <= self.tol:
+                break
+
+            W_buffer[:] = W
+
+        return W
+
+    def _minibatch_step(self, X, W, H, update_H):
+        """Perform the update of W and H for one minibatch."""
+        batch_size = X.shape[0]
+
+        # get scaled regularization terms. Done for each minibatch to take into account
+        # variable sizes of minibatches.
+        l1_reg_W, l1_reg_H, l2_reg_W, l2_reg_H = self._scale_regularization(X)
+
+        # update W
+        if self.fresh_restarts or W is None:
+            W = self._solve_W(X, H, self.fresh_restarts_max_iter)
+        else:
+            W, *_ = _multiplicative_update_w(
+                X, W, H, self._beta_loss, l1_reg_W, l2_reg_W, self._gamma
+            )
+
+        # necessary for stability with beta_loss < 1
+        if self._beta_loss < 1:
+            W[W < np.finfo(np.float64).eps] = 0.0
+
+        batch_cost = (
+            _beta_divergence(X, W, H, self._beta_loss)
+            + l1_reg_W * W.sum()
+            + l1_reg_H * H.sum()
+            + l2_reg_W * (W**2).sum()
+            + l2_reg_H * (H**2).sum()
+        ) / batch_size
+
+        # update H (only at fit or fit_transform)
+        if update_H:
+            H[:] = _multiplicative_update_h(
+                X,
+                W,
+                H,
+                beta_loss=self._beta_loss,
+                l1_reg_H=l1_reg_H,
+                l2_reg_H=l2_reg_H,
+                gamma=self._gamma,
+                A=self._components_numerator,
+                B=self._components_denominator,
+                rho=self._rho,
+            )
+
+            # necessary for stability with beta_loss < 1
+            if self._beta_loss <= 1:
+                H[H < np.finfo(np.float64).eps] = 0.0
+
+        return batch_cost
+
+    def _minibatch_convergence(
+        self, X, batch_cost, H, H_buffer, n_samples, step, n_steps
+    ):
+        """Helper function to encapsulate the early stopping logic"""
+        batch_size = X.shape[0]
+
+        # counts steps starting from 1 for user friendly verbose mode.
+        step = step + 1
+
+        # Ignore first iteration because H is not updated yet.
+        if step == 1:
+            if self.verbose:
+                print(f"Minibatch step {step}/{n_steps}: mean batch cost: {batch_cost}")
+            return False
+
+        # Compute an Exponentially Weighted Average of the cost function to
+        # monitor the convergence while discarding minibatch-local stochastic
+        # variability: https://en.wikipedia.org/wiki/Moving_average
+        if self._ewa_cost is None:
+            self._ewa_cost = batch_cost
+        else:
+            alpha = batch_size / (n_samples + 1)
+            alpha = min(alpha, 1)
+            self._ewa_cost = self._ewa_cost * (1 - alpha) + batch_cost * alpha
+
+        # Log progress to be able to monitor convergence
+        if self.verbose:
+            print(
+                f"Minibatch step {step}/{n_steps}: mean batch cost: "
+                f"{batch_cost}, ewa cost: {self._ewa_cost}"
+            )
+
+        # Early stopping based on change of H
+        H_diff = linalg.norm(H - H_buffer) / linalg.norm(H)
+        if self.tol > 0 and H_diff <= self.tol:
+            if self.verbose:
+                print(f"Converged (small H change) at step {step}/{n_steps}")
+            return True
+
+        # Early stopping heuristic due to lack of improvement on smoothed
+        # cost function
+        if self._ewa_cost_min is None or self._ewa_cost < self._ewa_cost_min:
+            self._no_improvement = 0
+            self._ewa_cost_min = self._ewa_cost
+        else:
+            self._no_improvement += 1
+
+        if (
+            self.max_no_improvement is not None
+            and self._no_improvement >= self.max_no_improvement
+        ):
+            if self.verbose:
+                print(
+                    "Converged (lack of improvement in objective function) "
+                    f"at step {step}/{n_steps}"
+                )
+            return True
+
+        return False
+
+    def fit_transform(self, X, y=None, W=None, H=None):
+        """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.
+
+        y : Ignored
+            Not used, present here for API consistency by convention.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32]
+        )
+
+        with config_context(assume_finite=True):
+            W, H, n_iter, n_steps = self._fit_transform(X, W=W, H=H)
+
+        self.reconstruction_err_ = _beta_divergence(
+            X, W, H, self._beta_loss, square_root=True
+        )
+
+        self.n_components_ = H.shape[0]
+        self.components_ = H
+        self.n_iter_ = n_iter
+        self.n_steps_ = n_steps
+
+        return W
+
+    def _fit_transform(self, X, W=None, H=None, update_H=True):
+        """Learn a NMF model for the data X and returns the transformed data.
+
+        Parameters
+        ----------
+        X : {ndarray, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If init='custom', it is used as initial guess for the solution.
+
+        H : array-like of shape (n_components, n_features), default=None
+            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.
+
+        update_H : bool, default=True
+            If True, both W and H will be estimated from initial guesses,
+            this corresponds to a call to the `fit_transform` method.
+            If False, only W will be estimated, this corresponds to a call
+            to the `transform` method.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+
+        H : ndarray of shape (n_components, n_features)
+            Factorization matrix, sometimes called 'dictionary'.
+
+        n_iter : int
+            Actual number of started iterations over the whole dataset.
+
+        n_steps : int
+            Number of mini-batches processed.
+        """
+        check_non_negative(X, "NMF (input X)")
+        self._check_params(X)
+
+        if X.min() == 0 and self._beta_loss <= 0:
+            raise ValueError(
+                "When beta_loss <= 0 and X contains zeros, "
+                "the solver may diverge. Please add small values "
+                "to X, or use a positive beta_loss."
+            )
+
+        n_samples = X.shape[0]
+
+        # initialize or check W and H
+        W, H = self._check_w_h(X, W, H, update_H)
+        H_buffer = H.copy()
+
+        # Initialize auxiliary matrices
+        self._components_numerator = H.copy()
+        self._components_denominator = np.ones(H.shape, dtype=H.dtype)
+
+        # Attributes to monitor the convergence
+        self._ewa_cost = None
+        self._ewa_cost_min = None
+        self._no_improvement = 0
+
+        batches = gen_batches(n_samples, self._batch_size)
+        batches = itertools.cycle(batches)
+        n_steps_per_iter = int(np.ceil(n_samples / self._batch_size))
+        n_steps = self.max_iter * n_steps_per_iter
+
+        for i, batch in zip(range(n_steps), batches):
+
+            batch_cost = self._minibatch_step(X[batch], W[batch], H, update_H)
+
+            if update_H and self._minibatch_convergence(
+                X[batch], batch_cost, H, H_buffer, n_samples, i, n_steps
+            ):
+                break
+
+            H_buffer[:] = H
+
+        if self.fresh_restarts:
+            W = self._solve_W(X, H, self._transform_max_iter)
+
+        n_steps = i + 1
+        n_iter = int(np.ceil(n_steps / n_steps_per_iter))
+
+        if n_iter == self.max_iter and self.tol > 0:
+            warnings.warn(
+                f"Maximum number of iterations {self.max_iter} reached. "
+                "Increase it to improve convergence.",
+                ConvergenceWarning,
+            )
+
+        return W, H, n_iter, n_steps
+
+    def transform(self, X):
+        """Transform the data X according to the fitted MiniBatchNMF model.
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be transformed by the model.
+
+        Returns
+        -------
+        W : ndarray of shape (n_samples, n_components)
+            Transformed data.
+        """
+        check_is_fitted(self)
+        X = self._validate_data(
+            X, accept_sparse=("csr", "csc"), dtype=[np.float64, np.float32], reset=False
+        )
+
+        W = self._solve_W(X, self.components_, self._transform_max_iter)
+
+        return W
+
+    def partial_fit(self, X, y=None, W=None, H=None):
+        """Update the model using the data in `X` as a mini-batch.
+
+        This method is expected to be called several times consecutively
+        on different chunks of a dataset so as to implement out-of-core
+        or online learning.
+
+        This is especially useful when the whole dataset is too big to fit in
+        memory at once (see :ref:`scaling_strategies`).
+
+        Parameters
+        ----------
+        X : {array-like, sparse matrix} of shape (n_samples, n_features)
+            Data matrix to be decomposed.
+
+        y : Ignored
+            Not used, present here for API consistency by convention.
+
+        W : array-like of shape (n_samples, n_components), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            Only used for the first call to `partial_fit`.
+
+        H : array-like of shape (n_components, n_features), default=None
+            If `init='custom'`, it is used as initial guess for the solution.
+            Only used for the first call to `partial_fit`.
+
+        Returns
+        -------
+        self
+            Returns the instance itself.
+        """
+        has_components = hasattr(self, "components_")
+
+        X = self._validate_data(
+            X,
+            accept_sparse=("csr", "csc"),
+            dtype=[np.float64, np.float32],
+            reset=not has_components,
+        )
+
+        if not has_components:
+            # This instance has not been fitted yet (fit or partial_fit)
+            self._check_params(X)
+            _, H = self._check_w_h(X, W=W, H=H, update_H=True)
+
+            self._components_numerator = H.copy()
+            self._components_denominator = np.ones(H.shape, dtype=H.dtype)
+            self.n_steps_ = 0
+        else:
+            H = self.components_
+
+        self._minibatch_step(X, None, H, update_H=True)
+
+        self.n_components_ = H.shape[0]
+        self.components_ = H
+        self.n_steps_ += 1
+
+        return self
diff --git a/sklearn/utils/estimator_checks.py b/sklearn/utils/estimator_checks.py
index 5e9601ae220a6..cc51507f90d49 100644
--- a/sklearn/utils/estimator_checks.py
+++ b/sklearn/utils/estimator_checks.py
@@ -652,6 +652,9 @@ def _set_checking_parameters(estimator):
         # NMF
         if name == "NMF":
             estimator.set_params(max_iter=500)
+        # MiniBatchNMF
+        if estimator.__class__.__name__ == "MiniBatchNMF":
+            estimator.set_params(max_iter=20, fresh_restarts=True)
         # MLP
         if name in ["MLPClassifier", "MLPRegressor"]:
             estimator.set_params(max_iter=100)

Test patch: diff --git a/sklearn/decomposition/tests/test_nmf.py b/sklearn/decomposition/tests/test_nmf.py
index cca0fad114ae5..9f3df5b64a803 100644
--- a/sklearn/decomposition/tests/test_nmf.py
+++ b/sklearn/decomposition/tests/test_nmf.py
@@ -1,10 +1,13 @@
 import re
+import sys
+from io import StringIO
 
 import numpy as np
 import scipy.sparse as sp
 
 from scipy import linalg
-from sklearn.decomposition import NMF, non_negative_factorization
+from sklearn.decomposition import NMF, MiniBatchNMF
+from sklearn.decomposition import non_negative_factorization
 from sklearn.decomposition import _nmf as nmf  # For testing internals
 from scipy.sparse import csc_matrix
 
@@ -20,14 +23,17 @@
 from sklearn.exceptions import ConvergenceWarning
 
 
-@pytest.mark.parametrize("solver", ["cd", "mu"])
-def test_convergence_warning(solver):
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_convergence_warning(Estimator, solver):
     convergence_warning = (
         "Maximum number of iterations 1 reached. Increase it to improve convergence."
     )
     A = np.ones((2, 2))
     with pytest.warns(ConvergenceWarning, match=convergence_warning):
-        NMF(solver=solver, max_iter=1).fit(A)
+        Estimator(max_iter=1, **solver).fit(A)
 
 
 def test_initialize_nn_output():
@@ -39,15 +45,13 @@ def test_initialize_nn_output():
         assert not ((W < 0).any() or (H < 0).any())
 
 
+@pytest.mark.filterwarnings(
+    r"ignore:The multiplicative update \('mu'\) solver cannot update zeros present in"
+    r" the initialization"
+)
 def test_parameter_checking():
     A = np.ones((2, 2))
     name = "spam"
-    msg = "Invalid solver parameter: got 'spam' instead of one of"
-    with pytest.raises(ValueError, match=msg):
-        NMF(solver=name).fit(A)
-    msg = "Invalid init parameter: got 'spam' instead of one of"
-    with pytest.raises(ValueError, match=msg):
-        NMF(init=name).fit(A)
 
     with ignore_warnings(category=FutureWarning):
         # TODO remove in 1.2
@@ -55,21 +59,17 @@ def test_parameter_checking():
         with pytest.raises(ValueError, match=msg):
             NMF(regularization=name).fit(A)
 
-    msg = "Invalid beta_loss parameter: got 'spam' instead of one"
-    with pytest.raises(ValueError, match=msg):
-        NMF(solver="mu", beta_loss=name).fit(A)
     msg = "Invalid beta_loss parameter: solver 'cd' does not handle beta_loss = 1.0"
     with pytest.raises(ValueError, match=msg):
         NMF(solver="cd", beta_loss=1.0).fit(A)
-
     msg = "Negative values in data passed to"
     with pytest.raises(ValueError, match=msg):
         NMF().fit(-A)
-    with pytest.raises(ValueError, match=msg):
-        nmf._initialize_nmf(-A, 2, "nndsvd")
     clf = NMF(2, tol=0.1).fit(A)
     with pytest.raises(ValueError, match=msg):
         clf.transform(-A)
+    with pytest.raises(ValueError, match=msg):
+        nmf._initialize_nmf(-A, 2, "nndsvd")
 
     for init in ["nndsvd", "nndsvda", "nndsvdar"]:
         msg = re.escape(
@@ -78,10 +78,59 @@ def test_parameter_checking():
         )
         with pytest.raises(ValueError, match=msg):
             NMF(3, init=init).fit(A)
+        with pytest.raises(ValueError, match=msg):
+            MiniBatchNMF(3, init=init).fit(A)
         with pytest.raises(ValueError, match=msg):
             nmf._initialize_nmf(A, 3, init)
 
 
+@pytest.mark.parametrize(
+    "param, match",
+    [
+        ({"n_components": 0}, "Number of components must be a positive integer"),
+        ({"max_iter": -1}, "Maximum number of iterations must be a positive integer"),
+        ({"tol": -1}, "Tolerance for stopping criteria must be positive"),
+        ({"init": "wrong"}, "Invalid init parameter"),
+        ({"beta_loss": "wrong"}, "Invalid beta_loss parameter"),
+    ],
+)
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_nmf_common_wrong_params(Estimator, param, match):
+    # Check that appropriate errors are raised for invalid values of parameters common
+    # to NMF and MiniBatchNMF.
+    A = np.ones((2, 2))
+    with pytest.raises(ValueError, match=match):
+        Estimator(**param).fit(A)
+
+
+@pytest.mark.parametrize(
+    "param, match",
+    [
+        ({"solver": "wrong"}, "Invalid solver parameter"),
+    ],
+)
+def test_nmf_wrong_params(param, match):
+    # Check that appropriate errors are raised for invalid values specific to NMF
+    # parameters
+    A = np.ones((2, 2))
+    with pytest.raises(ValueError, match=match):
+        NMF(**param).fit(A)
+
+
+@pytest.mark.parametrize(
+    "param, match",
+    [
+        ({"batch_size": 0}, "batch_size must be a positive integer"),
+    ],
+)
+def test_minibatch_nmf_wrong_params(param, match):
+    # Check that appropriate errors are raised for invalid values specific to
+    # MiniBatchNMF parameters
+    A = np.ones((2, 2))
+    with pytest.raises(ValueError, match=match):
+        MiniBatchNMF(**param).fit(A)
+
+
 def test_initialize_close():
     # Test NNDSVD error
     # Test that _initialize_nmf error is less than the standard deviation of
@@ -110,42 +159,97 @@ def test_initialize_variants():
 
 # ignore UserWarning raised when both solver='mu' and init='nndsvd'
 @ignore_warnings(category=UserWarning)
-@pytest.mark.parametrize("solver", ("cd", "mu"))
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
 @pytest.mark.parametrize("init", (None, "nndsvd", "nndsvda", "nndsvdar", "random"))
 @pytest.mark.parametrize("alpha_W", (0.0, 1.0))
 @pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
-def test_nmf_fit_nn_output(solver, init, alpha_W, alpha_H):
+def test_nmf_fit_nn_output(Estimator, solver, init, alpha_W, alpha_H):
     # Test that the decomposition does not contain negative values
     A = np.c_[5.0 - np.arange(1, 6), 5.0 + np.arange(1, 6)]
-    model = NMF(
+    model = Estimator(
         n_components=2,
-        solver=solver,
         init=init,
         alpha_W=alpha_W,
         alpha_H=alpha_H,
         random_state=0,
+        **solver,
     )
     transf = model.fit_transform(A)
     assert not ((model.components_ < 0).any() or (transf < 0).any())
 
 
-@pytest.mark.parametrize("solver", ("cd", "mu"))
-def test_nmf_fit_close(solver):
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_fit_close(Estimator, solver):
     rng = np.random.mtrand.RandomState(42)
     # Test that the fit is not too far away
-    pnmf = NMF(
+    pnmf = Estimator(
         5,
-        solver=solver,
         init="nndsvdar",
         random_state=0,
         max_iter=600,
+        **solver,
     )
     X = np.abs(rng.randn(6, 5))
     assert pnmf.fit(X).reconstruction_err_ < 0.1
 
 
-@pytest.mark.parametrize("solver", ("cd", "mu"))
+def test_nmf_true_reconstruction():
+    # Test that the fit is not too far away from an exact solution
+    # (by construction)
+    n_samples = 15
+    n_features = 10
+    n_components = 5
+    beta_loss = 1
+    batch_size = 3
+    max_iter = 1000
+
+    rng = np.random.mtrand.RandomState(42)
+    W_true = np.zeros([n_samples, n_components])
+    W_array = np.abs(rng.randn(n_samples))
+    for j in range(n_components):
+        W_true[j % n_samples, j] = W_array[j % n_samples]
+    H_true = np.zeros([n_components, n_features])
+    H_array = np.abs(rng.randn(n_components))
+    for j in range(n_features):
+        H_true[j % n_components, j] = H_array[j % n_components]
+    X = np.dot(W_true, H_true)
+
+    model = NMF(
+        n_components=n_components,
+        solver="mu",
+        beta_loss=beta_loss,
+        max_iter=max_iter,
+        random_state=0,
+    )
+    transf = model.fit_transform(X)
+    X_calc = np.dot(transf, model.components_)
+
+    assert model.reconstruction_err_ < 0.1
+    assert_allclose(X, X_calc)
+
+    mbmodel = MiniBatchNMF(
+        n_components=n_components,
+        beta_loss=beta_loss,
+        batch_size=batch_size,
+        random_state=0,
+        max_iter=max_iter,
+    )
+    transf = mbmodel.fit_transform(X)
+    X_calc = np.dot(transf, mbmodel.components_)
+
+    assert mbmodel.reconstruction_err_ < 0.1
+    assert_allclose(X, X_calc, atol=1)
+
+
+@pytest.mark.parametrize("solver", ["cd", "mu"])
 def test_nmf_transform(solver):
+    # Test that fit_transform is equivalent to fit.transform for NMF
     # Test that NMF.transform returns close values
     rng = np.random.mtrand.RandomState(42)
     A = np.abs(rng.randn(6, 5))
@@ -154,14 +258,34 @@ def test_nmf_transform(solver):
         n_components=3,
         init="random",
         random_state=0,
-        tol=1e-5,
+        tol=1e-6,
+    )
+    ft = m.fit_transform(A)
+    t = m.transform(A)
+    assert_allclose(ft, t, atol=1e-1)
+
+
+def test_minibatch_nmf_transform():
+    # Test that fit_transform is equivalent to fit.transform for MiniBatchNMF
+    # Only guaranteed with fresh restarts
+    rng = np.random.mtrand.RandomState(42)
+    A = np.abs(rng.randn(6, 5))
+    m = MiniBatchNMF(
+        n_components=3,
+        random_state=0,
+        tol=1e-3,
+        fresh_restarts=True,
     )
     ft = m.fit_transform(A)
     t = m.transform(A)
-    assert_array_almost_equal(ft, t, decimal=2)
+    assert_allclose(ft, t)
 
 
-def test_nmf_transform_custom_init():
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_transform_custom_init(Estimator, solver):
     # Smoke test that checks if NMF.transform works with custom initialization
     random_state = np.random.RandomState(0)
     A = np.abs(random_state.randn(6, 5))
@@ -170,7 +294,9 @@ def test_nmf_transform_custom_init():
     H_init = np.abs(avg * random_state.randn(n_components, 5))
     W_init = np.abs(avg * random_state.randn(6, n_components))
 
-    m = NMF(solver="cd", n_components=n_components, init="custom", random_state=0)
+    m = Estimator(
+        n_components=n_components, init="custom", random_state=0, tol=1e-3, **solver
+    )
     m.fit_transform(A, W=W_init, H=H_init)
     m.transform(A)
 
@@ -192,17 +318,37 @@ def test_nmf_inverse_transform(solver):
     assert_array_almost_equal(A, A_new, decimal=2)
 
 
-def test_n_components_greater_n_features():
+def test_mbnmf_inverse_transform():
+    # Test that MiniBatchNMF.transform followed by MiniBatchNMF.inverse_transform
+    # is close to the identity
+    rng = np.random.RandomState(0)
+    A = np.abs(rng.randn(6, 4))
+    nmf = MiniBatchNMF(
+        random_state=rng,
+        max_iter=500,
+        init="nndsvdar",
+        fresh_restarts=True,
+    )
+    ft = nmf.fit_transform(A)
+    A_new = nmf.inverse_transform(ft)
+    assert_allclose(A, A_new, rtol=1e-3, atol=1e-2)
+
+
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_n_components_greater_n_features(Estimator):
     # Smoke test for the case of more components than features.
     rng = np.random.mtrand.RandomState(42)
     A = np.abs(rng.randn(30, 10))
-    NMF(n_components=15, random_state=0, tol=1e-2).fit(A)
+    Estimator(n_components=15, random_state=0, tol=1e-2).fit(A)
 
 
-@pytest.mark.parametrize("solver", ["cd", "mu"])
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
 @pytest.mark.parametrize("alpha_W", (0.0, 1.0))
 @pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
-def test_nmf_sparse_input(solver, alpha_W, alpha_H):
+def test_nmf_sparse_input(Estimator, solver, alpha_W, alpha_H):
     # Test that sparse matrices are accepted as input
     from scipy.sparse import csc_matrix
 
@@ -211,14 +357,15 @@ def test_nmf_sparse_input(solver, alpha_W, alpha_H):
     A[:, 2 * np.arange(5)] = 0
     A_sparse = csc_matrix(A)
 
-    est1 = NMF(
-        solver=solver,
+    est1 = Estimator(
         n_components=5,
         init="random",
         alpha_W=alpha_W,
         alpha_H=alpha_H,
         random_state=0,
-        tol=1e-2,
+        tol=0,
+        max_iter=100,
+        **solver,
     )
     est2 = clone(est1)
 
@@ -227,24 +374,25 @@ def test_nmf_sparse_input(solver, alpha_W, alpha_H):
     H1 = est1.components_
     H2 = est2.components_
 
-    assert_array_almost_equal(W1, W2)
-    assert_array_almost_equal(H1, H2)
+    assert_allclose(W1, W2)
+    assert_allclose(H1, H2)
 
 
-def test_nmf_sparse_transform():
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_sparse_transform(Estimator, solver):
     # Test that transform works on sparse data.  Issue #2124
     rng = np.random.mtrand.RandomState(42)
     A = np.abs(rng.randn(3, 2))
     A[1, 1] = 0
     A = csc_matrix(A)
 
-    for solver in ("cd", "mu"):
-        model = NMF(
-            solver=solver, random_state=0, n_components=2, max_iter=400, init="nndsvd"
-        )
-        A_fit_tr = model.fit_transform(A)
-        A_tr = model.transform(A)
-        assert_array_almost_equal(A_fit_tr, A_tr, decimal=1)
+    model = Estimator(random_state=0, n_components=2, max_iter=400, **solver)
+    A_fit_tr = model.fit_transform(A)
+    A_tr = model.transform(A)
+    assert_allclose(A_fit_tr, A_tr, atol=1e-1)
 
 
 @pytest.mark.parametrize("init", ["random", "nndsvd"])
@@ -254,6 +402,7 @@ def test_nmf_sparse_transform():
 def test_non_negative_factorization_consistency(init, solver, alpha_W, alpha_H):
     # Test that the function is called in the same way, either directly
     # or through the NMF class
+    max_iter = 500
     rng = np.random.mtrand.RandomState(42)
     A = np.abs(rng.randn(10, 10))
     A[:, 2 * np.arange(5)] = 0
@@ -262,17 +411,19 @@ def test_non_negative_factorization_consistency(init, solver, alpha_W, alpha_H):
         A,
         init=init,
         solver=solver,
+        max_iter=max_iter,
         alpha_W=alpha_W,
         alpha_H=alpha_H,
         random_state=1,
         tol=1e-2,
     )
-    W_nmf_2, _, _ = non_negative_factorization(
+    W_nmf_2, H, _ = non_negative_factorization(
         A,
         H=H,
         update_H=False,
         init=init,
         solver=solver,
+        max_iter=max_iter,
         alpha_W=alpha_W,
         alpha_H=alpha_H,
         random_state=1,
@@ -282,6 +433,7 @@ def test_non_negative_factorization_consistency(init, solver, alpha_W, alpha_H):
     model_class = NMF(
         init=init,
         solver=solver,
+        max_iter=max_iter,
         alpha_W=alpha_W,
         alpha_H=alpha_H,
         random_state=1,
@@ -290,8 +442,8 @@ def test_non_negative_factorization_consistency(init, solver, alpha_W, alpha_H):
     W_cls = model_class.fit_transform(A)
     W_cls_2 = model_class.transform(A)
 
-    assert_array_almost_equal(W_nmf, W_cls, decimal=10)
-    assert_array_almost_equal(W_nmf_2, W_cls_2, decimal=10)
+    assert_allclose(W_nmf, W_cls)
+    assert_allclose(W_nmf_2, W_cls_2)
 
 
 def test_non_negative_factorization_checking():
@@ -360,7 +512,7 @@ def test_beta_divergence():
     n_samples = 20
     n_features = 10
     n_components = 5
-    beta_losses = [0.0, 0.5, 1.0, 1.5, 2.0]
+    beta_losses = [0.0, 0.5, 1.0, 1.5, 2.0, 3.0]
 
     # initialization
     rng = np.random.mtrand.RandomState(42)
@@ -458,8 +610,8 @@ def test_nmf_multiplicative_update_sparse():
             random_state=42,
         )
 
-        assert_array_almost_equal(W1, W2, decimal=7)
-        assert_array_almost_equal(H1, H2, decimal=7)
+        assert_allclose(W1, W2, atol=1e-7)
+        assert_allclose(H1, H2, atol=1e-7)
 
         # Compare with almost same beta_loss, since some values have a specific
         # behavior, but the results should be continuous w.r.t beta_loss
@@ -480,8 +632,8 @@ def test_nmf_multiplicative_update_sparse():
             random_state=42,
         )
 
-        assert_array_almost_equal(W1, W3, decimal=4)
-        assert_array_almost_equal(H1, H3, decimal=4)
+        assert_allclose(W1, W3, atol=1e-4)
+        assert_allclose(H1, H3, atol=1e-4)
 
 
 def test_nmf_negative_beta_loss():
@@ -520,8 +672,25 @@ def _assert_nmf_no_nan(X, beta_loss):
         _assert_nmf_no_nan(X_csr, beta_loss)
 
 
-@pytest.mark.parametrize("solver", ("cd", "mu"))
-def test_nmf_regularization(solver):
+@pytest.mark.parametrize("beta_loss", [-0.5, 0.0])
+def test_minibatch_nmf_negative_beta_loss(beta_loss):
+    """Check that an error is raised if beta_loss < 0 and X contains zeros."""
+    rng = np.random.RandomState(0)
+    X = rng.normal(size=(6, 5))
+    X[X < 0] = 0
+
+    nmf = MiniBatchNMF(beta_loss=beta_loss, random_state=0)
+
+    msg = "When beta_loss <= 0 and X contains zeros, the solver may diverge."
+    with pytest.raises(ValueError, match=msg):
+        nmf.fit(X)
+
+
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_regularization(Estimator, solver):
     # Test the effect of L1 and L2 regularizations
     n_samples = 6
     n_features = 5
@@ -531,20 +700,19 @@ def test_nmf_regularization(solver):
 
     # L1 regularization should increase the number of zeros
     l1_ratio = 1.0
-
-    regul = nmf.NMF(
+    regul = Estimator(
         n_components=n_components,
-        solver=solver,
         alpha_W=0.5,
         l1_ratio=l1_ratio,
         random_state=42,
+        **solver,
     )
-    model = nmf.NMF(
+    model = Estimator(
         n_components=n_components,
-        solver=solver,
         alpha_W=0.0,
         l1_ratio=l1_ratio,
         random_state=42,
+        **solver,
     )
 
     W_regul = regul.fit_transform(X)
@@ -553,30 +721,31 @@ def test_nmf_regularization(solver):
     H_regul = regul.components_
     H_model = model.components_
 
-    W_regul_n_zeros = W_regul[W_regul == 0].size
-    W_model_n_zeros = W_model[W_model == 0].size
-    H_regul_n_zeros = H_regul[H_regul == 0].size
-    H_model_n_zeros = H_model[H_model == 0].size
+    eps = np.finfo(np.float64).eps
+    W_regul_n_zeros = W_regul[W_regul <= eps].size
+    W_model_n_zeros = W_model[W_model <= eps].size
+    H_regul_n_zeros = H_regul[H_regul <= eps].size
+    H_model_n_zeros = H_model[H_model <= eps].size
 
     assert W_regul_n_zeros > W_model_n_zeros
     assert H_regul_n_zeros > H_model_n_zeros
 
-    # L2 regularization should decrease the mean of the coefficients
+    # L2 regularization should decrease the sum of the squared norm
+    # of the matrices W and H
     l1_ratio = 0.0
-
-    regul = nmf.NMF(
+    regul = Estimator(
         n_components=n_components,
-        solver=solver,
         alpha_W=0.5,
         l1_ratio=l1_ratio,
         random_state=42,
+        **solver,
     )
-    model = nmf.NMF(
+    model = Estimator(
         n_components=n_components,
-        solver=solver,
         alpha_W=0.0,
         l1_ratio=l1_ratio,
         random_state=42,
+        **solver,
     )
 
     W_regul = regul.fit_transform(X)
@@ -668,35 +837,40 @@ def test_nmf_underflow():
         (np.int64, np.float64),
     ],
 )
-@pytest.mark.parametrize("solver", ["cd", "mu"])
-@pytest.mark.parametrize("alpha_W", (0.0, 1.0))
-@pytest.mark.parametrize("alpha_H", (0.0, 1.0, "same"))
-def test_nmf_dtype_match(dtype_in, dtype_out, solver, alpha_W, alpha_H):
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_dtype_match(Estimator, solver, dtype_in, dtype_out):
     # Check that NMF preserves dtype (float32 and float64)
     X = np.random.RandomState(0).randn(20, 15).astype(dtype_in, copy=False)
     np.abs(X, out=X)
-    nmf = NMF(solver=solver, alpha_W=alpha_W, alpha_H=alpha_H)
+
+    nmf = Estimator(alpha_W=1.0, alpha_H=1.0, tol=1e-2, random_state=0, **solver)
 
     assert nmf.fit(X).transform(X).dtype == dtype_out
     assert nmf.fit_transform(X).dtype == dtype_out
     assert nmf.components_.dtype == dtype_out
 
 
-@pytest.mark.parametrize("solver", ["cd", "mu"])
-def test_nmf_float32_float64_consistency(solver):
+@pytest.mark.parametrize(
+    ["Estimator", "solver"],
+    [[NMF, {"solver": "cd"}], [NMF, {"solver": "mu"}], [MiniBatchNMF, {}]],
+)
+def test_nmf_float32_float64_consistency(Estimator, solver):
     # Check that the result of NMF is the same between float32 and float64
     X = np.random.RandomState(0).randn(50, 7)
     np.abs(X, out=X)
-
-    nmf32 = NMF(solver=solver, random_state=0)
+    nmf32 = Estimator(random_state=0, tol=1e-3, **solver)
     W32 = nmf32.fit_transform(X.astype(np.float32))
-    nmf64 = NMF(solver=solver, random_state=0)
+    nmf64 = Estimator(random_state=0, tol=1e-3, **solver)
     W64 = nmf64.fit_transform(X)
 
-    assert_allclose(W32, W64, rtol=1e-6, atol=1e-5)
+    assert_allclose(W32, W64, atol=1e-5)
 
 
-def test_nmf_custom_init_dtype_error():
+@pytest.mark.parametrize("Estimator", [NMF, MiniBatchNMF])
+def test_nmf_custom_init_dtype_error(Estimator):
     # Check that an error is raise if custom H and/or W don't have the same
     # dtype as X.
     rng = np.random.RandomState(0)
@@ -705,12 +879,75 @@ def test_nmf_custom_init_dtype_error():
     W = rng.random_sample((20, 15))
 
     with pytest.raises(TypeError, match="should have the same dtype as X"):
-        NMF(init="custom").fit(X, H=H, W=W)
+        Estimator(init="custom").fit(X, H=H, W=W)
 
     with pytest.raises(TypeError, match="should have the same dtype as X"):
         non_negative_factorization(X, H=H, update_H=False)
 
 
+@pytest.mark.parametrize("beta_loss", [-0.5, 0, 0.5, 1, 1.5, 2, 2.5])
+def test_nmf_minibatchnmf_equivalence(beta_loss):
+    # Test that MiniBatchNMF is equivalent to NMF when batch_size = n_samples and
+    # forget_factor 0.0 (stopping criterion put aside)
+    rng = np.random.mtrand.RandomState(42)
+    X = np.abs(rng.randn(48, 5))
+
+    nmf = NMF(
+        n_components=5,
+        beta_loss=beta_loss,
+        solver="mu",
+        random_state=0,
+        tol=0,
+    )
+    mbnmf = MiniBatchNMF(
+        n_components=5,
+        beta_loss=beta_loss,
+        random_state=0,
+        tol=0,
+        max_no_improvement=None,
+        batch_size=X.shape[0],
+        forget_factor=0.0,
+    )
+    W = nmf.fit_transform(X)
+    mbW = mbnmf.fit_transform(X)
+    assert_allclose(W, mbW)
+
+
+def test_minibatch_nmf_partial_fit():
+    # Check fit / partial_fit equivalence. Applicable only with fresh restarts.
+    rng = np.random.mtrand.RandomState(42)
+    X = np.abs(rng.randn(100, 5))
+
+    n_components = 5
+    batch_size = 10
+    max_iter = 2
+
+    mbnmf1 = MiniBatchNMF(
+        n_components=n_components,
+        init="custom",
+        random_state=0,
+        max_iter=max_iter,
+        batch_size=batch_size,
+        tol=0,
+        max_no_improvement=None,
+        fresh_restarts=False,
+    )
+    mbnmf2 = MiniBatchNMF(n_components=n_components, init="custom", random_state=0)
+
+    # Force the same init of H (W is recomputed anyway) to be able to compare results.
+    W, H = nmf._initialize_nmf(
+        X, n_components=n_components, init="random", random_state=0
+    )
+
+    mbnmf1.fit(X, W=W, H=H)
+    for i in range(max_iter):
+        for j in range(batch_size):
+            mbnmf2.partial_fit(X[j : j + batch_size], W=W[:batch_size], H=H)
+
+    assert mbnmf1.n_steps_ == mbnmf2.n_steps_
+    assert_allclose(mbnmf1.components_, mbnmf2.components_)
+
+
 def test_feature_names_out():
     """Check feature names out for NMF."""
     random_state = np.random.RandomState(0)
@@ -719,3 +956,15 @@ def test_feature_names_out():
 
     names = nmf.get_feature_names_out()
     assert_array_equal([f"nmf{i}" for i in range(3)], names)
+
+
+def test_minibatch_nmf_verbose():
+    # Check verbose mode of MiniBatchNMF for better coverage.
+    A = np.random.RandomState(0).random_sample((100, 10))
+    nmf = MiniBatchNMF(tol=1e-2, random_state=0, verbose=1)
+    old_stdout = sys.stdout
+    sys.stdout = StringIO()
+    try:
+        nmf.fit(A)
+    finally:
+        sys.stdout = old_stdout