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spectrochempy.SVD¶

class SVD(**kwargs)[source]¶

Singular Value Decomposition (SVD).

The SVD is commonly written as \(X = U \Sigma V^{T}\).

This class has the attributes : U, s = diag(S) and VT=V \(^T\).

If the dataset contains masked values, the corresponding ranges are ignored in the calculation.

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.

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.
NMF: Non-Negative Matrix Factorization.
PCA: Perform Principal Components Analysis.
SIMPLISMA: SIMPLe to use Interactive Self-modeling Mixture Analysis.

Examples

>>> dataset = scp.read('irdata/nh4y-activation.spg')
>>> svd = scp.SVD()
>>> svd.fit(dataset)
<svd: U(55, 55), s(55), VT(55, 5549)>
>>> print(svd.ev.data)
[1.185e+04      634 ... 0.001089 0.000975]
>>> print(svd.ev_cum.data)
[   94.54     99.6 ...      100      100]
>>> print(svd.ev_ratio.data)
[   94.54    5.059 ... 8.687e-06 7.779e-06]

Attributes Summary

`U`	Return the left unitary matrix.
`VT`	Return a transpose matrix of the Loadings.
`X`	Return the X input dataset (eventually modified by the model).
`Y`	The `Y` input.
`components`	`NDDataset` with components in feature space (n_components, n_features).
`compute_uv`	Whether or not to compute U and VT in addition to s.
`config`	`traitlets.config.Config` object.
`cumulative_explained_variance`	Return Cumulative Explained Variance.
`ev`	Return a NDDataset of the explained variance.
`ev_cum`	Return Cumulative Explained Variance.
`ev_ratio`	Return Explained Variance per singular values.
`explained_variance`	Return a NDDataset of the explained variance.
`explained_variance_ratio`	Return Explained Variance per singular values.
`full_matrices`	If False , U and VT have the shapes (M, k) and (k, N), respectively, where k = min(M, N).
`log`	Return `log` output.
`n_components`	Number of components that were fitted.
`name`	Object name
`s`	Return Vector of singular values .
`singular_values`	Return a NDDataset containing singular values.
`sv`	Return a NDDataset containing singular values.

Methods Summary

`fit`(X)	Fit the SVD 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])	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

U¶

Return the left unitary matrix.

Its shape depends on full_matrices .

VT¶

Return a transpose matrix of the Loadings.

Its shape depends on full_matrices

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

Y¶: The Y input.

components¶

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

See also

get_components: Retrieve only the specified number of components.

compute_uv¶: Whether or not to compute U and VT in addition to s.

config¶: traitlets.config.Config object.

cumulative_explained_variance¶: Return Cumulative Explained Variance.

ev¶: Return a NDDataset of the explained variance.

ev_cum¶: Return Cumulative Explained Variance.

ev_ratio¶: Return Explained Variance per singular values.

explained_variance¶: Return a NDDataset of the explained variance.

explained_variance_ratio¶: Return Explained Variance per singular values.

full_matrices¶: If False , U and VT have the shapes (M, k) and (k, N), respectively, where k = min(M, N). Otherwise the shapes will be (M, M) and (N, N), respectively.

log¶: Return log output.

n_components¶: Number of components that were fitted.

name¶: Object name

s¶: Return Vector of singular values .

singular_values¶: Return a NDDataset containing singular values.

sv¶: Return a NDDataset containing singular values.

Methods Documentation

fit(X)[source]¶

Fit the SVD 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]¶

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 \(\hat{X}\)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.SVD