Mini-Batch Non-Negative Matrix Factorization (NMF).
Added in version 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:
\[ \begin{align}\begin{aligned}L(W, H) &= 0.5 * ||X - WH||_{loss}^2\\ &+ alpha\_W * l1\_ratio * n\_features * ||vec(W)||_1\\ &+ alpha\_H * l1\_ratio * n\_samples * ||vec(H)||_1\\ &+ 0.5 * alpha\_W * (1 - l1\_ratio) * n\_features * ||W||_{Fro}^2\\ &+ 0.5 * alpha\_H * (1 - l1\_ratio) * n\_samples * ||H||_{Fro}^2,\end{aligned}\end{align} \]
where \(||A||_{Fro}^2 = \sum_{i,j} A_{ij}^2\) (Frobenius norm) and \(||vec(A)||_1 = \sum_{i,j} abs(A_{ij})\) (Elementwise L1 norm).
The generic norm \(||X - WH||_{loss}^2\) 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 User Guide.
Number of components. If None, all features are kept. If n_components='auto', the number of components is automatically inferred from W or H shapes.
Changed in version 1.4: Added 'auto' value.
Changed in version 1.6: Default value changed from None to 'auto'.
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 which must both be provided.
Number of samples in each mini-batch. Large batch sizes give better long-term convergence at the cost of a slower start.
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.
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.
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.
Maximum number of iterations over the complete dataset before timing out.
Constant that multiplies the regularization terms of W. Set it to zero (default) to have no regularization on W.
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.
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.
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.
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.
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.
Maximum number of iterations when solving for W at transform time. If None, it defaults to max_iter.
Used for initialisation (when init == ‘nndsvdar’ or ‘random’), and in Coordinate Descent. Pass an int for reproducible results across multiple function calls. See Glossary.
Whether to be verbose.
Factorization matrix, sometimes called ‘dictionary’.
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.
Frobenius norm of the matrix difference, or beta-divergence, between the training data X and the reconstructed data WH from the fitted model.
Actual number of started iterations over the whole dataset.
Number of mini-batches processed.
Number of features seen during fit.
n_features_in_,)
Names of features seen during 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
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_
Learn a NMF model for the data X.
Training vector, where n_samples is the number of samples and n_features is the number of features.
Not used, present for API consistency by convention.
Parameters (keyword arguments) and values passed to the fit_transform instance.
Returns the instance itself.
Learn a NMF model for the data X and returns the transformed data.
This is more efficient than calling fit followed by transform.
Data matrix to be decomposed.
Not used, present here for API consistency by convention.
If init='custom', it is used as initial guess for the solution. If None, uses the initialisation method specified in init.
If init='custom', it is used as initial guess for the solution. If None, uses the initialisation method specified in init.
Transformed data.
Get output feature names for transformation.
The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].
Only used to validate feature names with the names seen in fit.
Transformed feature names.
Get metadata routing of this object.
Please check User Guide on how the routing mechanism works.
A MetadataRequest encapsulating routing information.
Get parameters for this estimator.
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Parameter names mapped to their values.
Transform data back to its original space.
Added in version 0.18.
Transformed data matrix.
Returns a data matrix of the original shape.
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 Strategies to scale computationally: bigger data).
Data matrix to be decomposed.
Not used, present here for API consistency by convention.
If init='custom', it is used as initial guess for the solution. Only used for the first call to partial_fit.
If init='custom', it is used as initial guess for the solution. Only used for the first call to partial_fit.
Returns the instance itself.
Set output container.
See Introducing the set_output API for an example on how to use the API.
Configure output of transform and fit_transform.
"default": Default output format of a transformer
"pandas": DataFrame output
"polars": Polars output
None: Transform configuration is unchanged
Added in version 1.4: "polars" option was added.
Estimator instance.
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.
Estimator parameters.
Estimator instance.
Configure whether metadata should be requested to be passed to the partial_fit method.
Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with
enable_metadata_routing=True(seesklearn.set_config). Please check the User Guide on how the routing mechanism works.The options for each parameter are:
True: metadata is requested, and passed topartial_fitif provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it topartial_fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.The default (
sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.Added in version 1.3.
Metadata routing for H parameter in partial_fit.
Metadata routing for W parameter in partial_fit.
The updated object.
Transform the data X according to the fitted MiniBatchNMF model.
Data matrix to be transformed by the model.
Transformed data.
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