spectrochempy.PCA

class PCA(*, log_level='WARNING', warm_start=False, iterated_power='auto', n_components=None, n_oversamples=10, power_iteration_normalizer='auto', random_state=None, scaled=False, standardized=False, svd_solver='auto', tol=0.0, whiten=False)

Principal Component Anamysis (PCA).

The Principal Component Analysis analysis is using the sklearn.decomposition.PCA model.

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.

• iterated_power (an int or any of [‘auto’], optional, default: 'auto') – Number of iterations for the power method computed by svd_solver == ‘randomized’. Must be of range [0, infinity).

• n_components (any of [‘mle’] or an int or a float, optional, default: None) – Number of components to keep. if n_components is not set all components are kept:

  n_components == min(n_observations, n_features)
  

  If n_components == 'mle' and svd_solver == 'full' , Minka’s MLE is used to guess the dimension. Use of n_components == 'mle' will interpret svd_solver == 'auto' as svd_solver == 'full' . If 0 < n_components < 1 and svd_solver == 'full' , select the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by n_components. If svd_solver == 'arpack' , the number of components must be strictly less than the minimum of n_features and n_observations. Hence, the None case results in:

  n_components == min(n_observations, n_features) - 1.
  

• n_oversamples (int, optional, default: 10) – This parameter is only relevant when svd_solver="randomized" . It corresponds to the additional number of random vectors to sample the range of X so as to ensure proper conditioning. See randomized_svd for more details.

• power_iteration_normalizer (any value of [ 'auto' , 'QR' , 'LU' , 'none' ], optional, default: 'auto') – Power iteration normalizer for randomized SVD solver. Not used by ARPACK. See randomized_svd for more details.

• random_state (an int or a RandomState, optional, default: None) – Used when the ‘arpack’ or ‘randomized’ solvers are used. Pass an int for reproducible results across multiple function calls.

• scaled (bool, optional, default: False) – If True the data are scaled in the interval [0-1]: \(X' = (X - min(X)) / (max(X)-min(X))\).

• standardized (bool, optional, default: False) – If True the data are scaled to unit standard deviation: \(X' = X / \sigma\).

• svd_solver (any value of [ 'auto' , 'full' , 'arpack' , 'randomized' ], optional, default: 'auto') – If auto : The solver is selected by a default policy based on X.shape and n_components: if the input data is larger than 500x500 and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient ‘randomized’ method is enabled. Otherwise the exact full SVD is computed and optionally truncated afterwards. If full : run exact full SVD calling the standard LAPACK solver via scipy.linalg.svd and select the components by postprocessing If arpack : run SVD truncated to n_components calling ARPACK solver via scipy.sparse.linalg.svds . It requires strictly 0 < n_components < min(X.shape) If randomized : run randomized SVD by the method of Halko et al.

• tol (float, optional, default: 0.0) – Tolerance for singular values computed by svd_solver == ‘arpack’. Must be of range [0.0, infinity).

• whiten (bool, optional, default: False) – When True (False by default) the components_ vectors are multiplied by the square root of n_observations and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances. Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometime improve the predictive accuracy of the downstream estimators by making their data respect some hard-wired assumptions.

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.

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.
components	NDDataset with components in feature space (n_components, n_features).
config	traitlets.config.Config object.
iterated_power	Number of iterations for the power method computed by svd_solver == 'randomized'.
loadings	Return PCA loadings.
log	Return log output.
n_components	Number of components to keep. if n_components is not set all components are kept::.
n_oversamples	This parameter is only relevant when svd_solver="randomized" .
name	Object name
power_iteration_normalizer	Power iteration normalizer for randomized SVD solver.
random_state	Used when the 'arpack' or 'randomized' solvers are used.
scaled	\(X' = (X - min(X)) / (max(X)-min(X))\).
scores	Returns PCA scores.
standardized	\(X' = X / \sigma\).
svd_solver	If auto: The solver is selected by a default policy based on X.shape and n_components: if the input data is larger than 500x500 and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient 'randomized' method is enabled.
tol	Tolerance for singular values computed by svd_solver == 'arpack'.
whiten	When True (False by default) the components_ vectors are multiplied by the square root of n_observations and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances.

Methods Summary

fit(X)	Fit the PCA 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.
printev([n_components])	Print PCA figures of merit.
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.
scoreplot(self, *args[, colormap, ...])	2D or 3D scoreplot of observations.
screeplot([n_components])	Scree plot of explained variance + cumulative variance by PCA.
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.

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.

iterated_power

Number of iterations for the power method computed by svd_solver == ‘randomized’. Must be of range [0, infinity).

loadings

Return PCA loadings.

log

Return log output.

n_components

Number of components to keep. if n_components is not set all components are kept:

n_components == min(n_observations, n_features)

If n_components == 'mle' and svd_solver == 'full' , Minka’s MLE is used to guess the dimension. Use of n_components == 'mle' will interpret svd_solver == 'auto' as svd_solver == 'full' . If 0 < n_components < 1 and svd_solver == 'full' , select the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by n_components. If svd_solver == 'arpack' , the number of components must be strictly less than the minimum of n_features and n_observations. Hence, the None case results in:

n_components == min(n_observations, n_features) - 1.

n_oversamples

This parameter is only relevant when svd_solver="randomized" . It corresponds to the additional number of random vectors to sample the range of X so as to ensure proper conditioning. See randomized_svd for more details.

name

Object name

power_iteration_normalizer

Power iteration normalizer for randomized SVD solver. Not used by ARPACK. See randomized_svd for more details.

random_state

Used when the ‘arpack’ or ‘randomized’ solvers are used. Pass an int for reproducible results across multiple function calls.

scaled

\(X' = (X - min(X)) / (max(X)-min(X))\).

Type:

If True the data are scaled in the interval [0-1]

scores

Returns PCA scores.

standardized

\(X' = X / \sigma\).

Type:

If True the data are scaled to unit standard deviation

svd_solver

If auto: The solver is selected by a default policy based on X.shape and n_components: if the input data is larger than 500x500 and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient ‘randomized’ method is enabled. Otherwise the exact full SVD is computed and optionally truncated afterwards. If full : run exact full SVD calling the standard LAPACK solver via scipy.linalg.svd and select the components by postprocessing If arpack : run SVD truncated to n_components calling ARPACK solver via scipy.sparse.linalg.svds . It requires strictly 0 < n_components < min(X.shape) If randomized : run randomized SVD by the method of Halko et al.

tol

Tolerance for singular values computed by svd_solver == ‘arpack’. Must be of range [0.0, infinity).

whiten

When True (False by default) the components_ vectors are multiplied by the square root of n_observations and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances. Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometime improve the predictive accuracy of the downstream estimators by making their data respect some hard-wired assumptions.

Methods Documentation

fit(X)

Fit the PCA 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)

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="0.8.0") def parameters(self, default=False)

Alias for params method.

Deprecated since version 0.8.0: Use params instead.

params(default=False)

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)

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.

printev(n_components=None)

Print PCA figures of merit.

Prints eigenvalues and explained variance for all or first n_pc PC’s.

Parameters:

n_components (int, optional) – The number of components to print.

reconstruct(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).

Notes

Deprecated in version 0.6.

reduce(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.

Notes

Deprecated in version 0.6.

reset()

Reset configuration parameters to their default values.

scoreplot(self, *args, colormap='viridis', color_mapping='index', show_labels=False, labels_column=0, labels_every=1, **kwargs)

2D or 3D scoreplot of observations.

Plots the projection of each observation/spectrum onto the span of two or three selected principal components.

Parameters:

• *args (NDDataset and/or series of 2 or 3 ints or iterabble of 2 or 3 int, optional) – The NDDataset contains the sores to plot. If not provided PCA.scores is used. The 2 or 3 int are the PC on which the projection is shown. If not provided, default to [1,2], i.e. bidimensional plot on PCs #1 and #2.

• colormap (str) – A matplotlib colormap.

• color_mapping (‘index’ or ‘labels’) – If ‘index’, then the colors of each n_scores is mapped sequentially on the colormap. If labels, the labels of the n_observations are used for color mapping.

• show_labels (bool, optional, default: False) – If True each observation will be annotated with its label.

• labels_column (int, optional, default:0) – If several columns of labels are present indicates which column has to be used to show labels.

• labels_every (int, optional, default: 1) – Do not label all points, but only every value indicated by this parameter.

Returns:

Axes – The matplotlib axes.

Notes

• the markersize is defined from preferences (prefs) as the square of the prefs.lines.markersize.

screeplot(n_components=None, **kwargs)

Scree plot of explained variance + cumulative variance by PCA.

Explained variance by each PC is plot as a bar graph (left y axis) and cumulative explained variance is plot as a scatter plot with lines (right y axis).

Parameters:

• n_components (int) – Number of components to plot.

• **kwargs – Extra arguments: colors (default: [NBlue, NRed] ) to set the colors of the bar plot and scatter plot; ylims (default [(0, 100), "auto"]).

Returns:

list of Axes – The list of axes.

to_dict()

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.PCA

EFA example

EFA example

PCA example (iris dataset)

PCA example (iris dataset)

PCA analysis example

PCA analysis example