spectrochempy.NMF

class NMF(*, log_level='WARNING', warm_start=False, alpha_H='same', alpha_W=0.0, beta_loss='frobenius', init=None, l1_ratio=0.0, max_iter=200, n_components=2, random_state=None, shuffle=False, solver='cd', tol=0.0001)[source][source]

Non-Negative Matrix Factorization (NMF).

Use sklearn.decomposition.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.

Parameters:

log_level (any of ["INFO", "DEBUG", "WARNING", "ERROR"], optional, default: "WARNING") – The log level at startup. It can be changed later on using the set_log_level method or by changing the log_level attribute.
warm_start (bool, optional, default: False) – When fitting repeatedly on the same dataset, but for multiple parameter values (such as to find the value maximizing performance), it may be possible to reuse previous model learned from the previous parameter value, saving time.

When warm_start is True, the existing fitted model attributes is used to initialize the new model in a subsequent call to fit.
alpha_H (a float or any of [‘same’], optional, default: 'same') – Constant that multiplies the regularization terms of H . Set it to zeroto have no regularization on H . If “same” (default), it takes the samevalue as alpha_W .
alpha_W (float, optional, default: 0.0) – Constant that multiplies the regularization terms of W . Set it to zero(default) to have no regularization on W .
beta_loss (a float or any of [‘frobenius’, ‘kullback-leibler’, ‘itakura-saito’], optional, default: 'frobenius') – Beta divergence to be minimized, measuring the distance between Xand 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.
init (any value of [ 'random' , 'nndsvd' , 'nndsvda' , 'nndsvdar' , 'custom' ], optional, 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.
l1_ratio (float, optional, 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.
max_iter (int, optional, default: 200) – Maximum number of iterations before timing out.
n_components (int, optional, default: 2) – Number of components to use.
random_state (an int or a RandomState, optional, default: None) – Used for initialisation (when init == ‘nndsvdar’ or ‘random’), and in Coordinate Descent. Pass an int, for reproducible results across multiple function calls.
shuffle (bool, optional, default: False) – If true, randomize the order of coordinates in the CD solver.
solver (any value of [ 'cd' , 'mu' ], optional, default: 'cd') – Numerical solver to use: - ‘cd’ is a Coordinate Descent solver. - ‘mu’ is a Multiplicative Update solver.
tol (float, optional, default: 0.0001) – Tolerance of the stopping condition.

See also

EFA: Perform an Evolving Factor Analysis (forward and reverse).
FastICA: Perform Independent Component Analysis with a fast algorithm.
IRIS: Integral inversion solver for spectroscopic data.
MCRALS: Perform MCR-ALS of a dataset knowing the initial \(C\) or \(S^T\) matrix.
PCA: Perform Principal Components Analysis.
SIMPLISMA: SIMPLe to use Interactive Self-modeling Mixture Analysis.
SVD: Perform a Singular Value Decomposition.

Initialize the BaseConfigurable class.

Parameters:

log_level (int, optional) – The log level at startup. Default is logging.WARNING.
**kwargs (dict) – Additional keyword arguments for configuration.

Attributes Summary

`X`	Return the X input dataset (eventually modified by the model).
`Y`	The `Y` input.
`alpha_H`	Constant that multiplies the regularization terms of `H` .
`alpha_W`	Constant that multiplies the regularization terms of `W` .
`beta_loss`	Beta divergence to be minimized, measuring the distance between Xand the dot product WH.
`components`	`NDDataset` with components in feature space (n_components, n_features).
`config`	`traitlets.config.Config` object.
`init`	Method used to initialize the procedure.
`l1_ratio`	The regularization mixing parameter, with 0 <= l1_ratio <= 1.
`log`	Return `log` output.
`max_iter`	Maximum number of iterations before timing out.
`n_components`	Number of components to use.
`name`	Object name
`random_state`	Used for initialisation (when `init` == 'nndsvdar' or 'random'), and in Coordinate Descent.
`shuffle`	If true, randomize the order of coordinates in the CD solver.
`solver`	Numerical solver to use: - 'cd' is a Coordinate Descent solver.
`tol`	Tolerance of the stopping condition.

Methods Summary

`fit`(X)	Fit the NMF model on X.
`fit_transform`(X[, Y])	Fit the model with `X` and apply the dimensionality reduction on `X`.
`get_components`([n_components])	Return the component's dataset: (selected n_components, n_features).
`inverse_transform`([X_transform])	Transform data back to its original space.
`parameters`([replace, removed, default])	Alias for `params` method.
`params`([default])	Return current or default configuration values.
`plotmerit`([X, X_hat])	Plot the input (`X`), reconstructed (`X_hat`) and residuals.
`reconstruct`([X_transform])	Transform data back to its original space.
`reduce`([X])	Apply dimensionality reduction to `X`.
`reset`()	Reset configuration parameters to their default values.
`to_dict`()	Return config value in a dict form.
`transform`([X])	Apply dimensionality reduction to `X`.

Attributes Documentation

X: Return the X input dataset (eventually modified by the model).

Y: The Y input.

alpha_H: Constant that multiplies the regularization terms of H . Set it to zeroto have no regularization on H . If “same” (default), it takes the samevalue as alpha_W .

alpha_W: Constant that multiplies the regularization terms of W . Set it to zero(default) to have no regularization on W .

beta_loss: Beta divergence to be minimized, measuring the distance between Xand 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.

components

NDDataset with components in feature space (n_components, n_features).

See also

get_components: Retrieve only the specified number of components.

config: traitlets.config.Config object.

init

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.

l1_ratio: 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.

log: Return log output.

max_iter: Maximum number of iterations before timing out.

n_components: Number of components to use.

name: Object name

random_state: Used for initialisation (when init == ‘nndsvdar’ or ‘random’), and in Coordinate Descent. Pass an int, for reproducible results across multiple function calls.

shuffle: If true, randomize the order of coordinates in the CD solver.

solver: Numerical solver to use: - ‘cd’ is a Coordinate Descent solver. - ‘mu’ is a Multiplicative Update solver.

tol: Tolerance of the stopping condition.

Methods Documentation

fit(X)[source][source]

Fit the NMF model on X.

Parameters:: X (NDDataset or array-like of shape (n_observations, n_features)) – Training data.
Returns:: self – The fitted instance itself.

See also

fit_transform: Fit the model with an input dataset X and apply the dimensionality reduction on X.
fit_reduce: Alias of fit_transform (Deprecated).

fit_transform(X, Y=None, **kwargs)[source]

Fit the model with X and apply the dimensionality reduction on X.

Parameters:

X (NDDataset or array-like of shape (n_observations, n_features)) – Training data.
Y (any) – Depends on the model.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

NDDataset – Dataset with shape (n_observations, n_components).

Other Parameters:

n_components (int, optional) – The number of components to use for the reduction. If not given the number of components is eventually the one specified or determined in the fit process.

get_components(n_components=None)

Return the component’s dataset: (selected n_components, n_features).

Parameters:: n_components (int, optional, default: None) – The number of components to keep in the output dataset. If None, all calculated components are returned.
Returns:: NDDataset – Dataset with shape (n_components, n_features)

inverse_transform(X_transform=None, **kwargs)

Transform data back to its original space.

In other words, return an input X_original whose reduce/transform would be X_transform.

Parameters:

X_transform (array-like of shape (n_observations, n_components), optional) – Reduced X data, where n_observations is the number of observations and n_components is the number of components. If X_transform is not provided, a transform of X provided in fit is performed first.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

NDDataset – Dataset with shape (n_observations, n_features).

Other Parameters:

n_components (int, optional) – The number of components to use for the reduction. If not given the number of components is eventually the one specified or determined in the fit process.

See also

reconstruct: Alias of inverse_transform (Deprecated).

parameters(replace="params", removed="0.7.1") def parameters(self, default=False)[source]: Alias for params method.

params(default=False)[source]

Return current or default configuration values.

Parameters:: default (bool, optional, default: False) – If default is True, the default parameters are returned, else the current values.
Returns:: dict – Current or default configuration values.

plotmerit(X=None, X_hat=None, **kwargs)[source]

Plot the input (X), reconstructed (X_hat) and residuals.

\(X\) and \(\hat{X}\) can be passed as arguments. If not, the X attribute is used for \(X`and :math:\)hat{X}`is computed by the inverse_transform method

Parameters:

X (NDDataset, optional) – Original dataset. If is not provided (default), the X attribute is used and X_hat is computed using inverse_transform.
X_hat (NDDataset, optional) – Inverse transformed dataset. if X is provided, X_hat must also be provided as compuyed externally.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

Axes – Matplotlib subplot axe.

Other Parameters:

colors (tuple or ndarray of 3 colors, optional) – Colors for X , X_hat and residuals E . in the case of 2D, The default colormap is used for X . By default, the three colors are NBlue , NGreen and NRed (which are colorblind friendly).
offset (float, optional, default: None) – Specify the separation (in percent) between the \(X\) , \(X_hat\) and \(E\).
nb_traces (int or 'all', optional) – Number of lines to display. Default is 'all'.
**others (Other keywords parameters) – Parameters passed to the internal plot method of the X dataset.

reconstruct(X_transform=None, **kwargs)[source]

Transform data back to its original space.

In other words, return an input X_original whose reduce/transform would be X_transform.

Parameters:

X_transform (array-like of shape (n_observations, n_components), optional) – Reduced X data, where n_observations is the number of observations and n_components is the number of components. If X_transform is not provided, a transform of X provided in fit is performed first.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

NDDataset – Dataset with shape (n_observations, n_features).

Other Parameters:

n_components (int, optional) – The number of components to use for the reduction. If not given the number of components is eventually the one specified or determined in the fit process.

See also

reconstruct: Alias of inverse_transform (Deprecated).

Notes

Deprecated in version 0.6.

reduce(X=None, **kwargs)[source]

Apply dimensionality reduction to X.

Parameters:

X (NDDataset or array-like of shape (n_observations, n_features), optional) – New data, where n_observations is the number of observations and n_features is the number of features. if not provided, the input dataset of the fit method will be used.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

NDDataset – Dataset with shape (n_observations, n_components).

Other Parameters:

n_components (int, optional) – The number of components to use for the reduction. If not given the number of components is eventually the one specified or determined in the fit process.

Notes

Deprecated in version 0.6.

reset()[source]: Reset configuration parameters to their default values.

to_dict()[source]

Return config value in a dict form.

Returns:: dict – A regular dictionary.

transform(X=None, **kwargs)

Apply dimensionality reduction to X.

Parameters:

X (NDDataset or array-like of shape (n_observations, n_features), optional) – New data, where n_observations is the number of observations and n_features is the number of features. if not provided, the input dataset of the fit method will be used.
**kwargs (keyword parameters, optional) – See Other Parameters.

Returns:

NDDataset – Dataset with shape (n_observations, n_components).

Other Parameters:

n_components (int, optional) – The number of components to use for the reduction. If not given the number of components is eventually the one specified or determined in the fit process.

Examples using spectrochempy.NMF

NMF analysis example