chemometrics.AsymWhittaker

class chemometrics.AsymWhittaker(penalty, constraint_order=2, asym_factor=0.99)

Bases: TransformerMixin, BaseEstimator

Background correction X with an asymmetric Whittaker filter

AsymWhittaker smooths X with an asymmetric Whittaker filter. The filter estimates the background by a non-parametric line constraint by its derivative smoothness. penalty defines the penalty on non-smoothness.

Parameters

• penalty (float) – Scaling factor of the penalty term for non-smoothness.

• constraint_order (int) – Defines on which order of derivative the smoothness constraint acts on.

• asym_factor (float) – Relative weight of negative residuals. Positive residuals obtain a weight of 1-asym_factor. The default value is 0.99.

background_

Estimated background from last call to transform.

Type

(n, m) ndarray

Notes

AsymWhittaker uses sparse matrices for efficiency reasons. X may however be a full matrix. In contrast to the proposed algorithm by Eilers 1, no Cholesky decomposition is used. The reason is twofold. The Cholesky decomposition is not implemented for sparse matrices in Numpy/Scipy. Eilers uses the Cholesky decomposition to prevent Matlab from “reordering the sparse equation systems for minimal bandwidth”. Matlab seems to rely on UMFPACK for sparse matrix devision 2 which implements column reordering for sparsity preservation. As the sparse matrix we are working with is square and positive-definite, we can rely on the builtin factorize method, which solves with UMFPACK if installed, otherwise with SuperLU.

References

Application of whittaker smoother to spectroscopic data 1.

1(1,2)

Paul H. Eilers, A perfect smoother, Anal. Chem., vol 75, 14, pp. 3631-3636, 2003.

2

UMFPAC, https://en.wikipedia.org/wiki/UMFPACK, accessed 03.May.2020.

__init__(penalty, constraint_order=2, asym_factor=0.99)

Methods

__init__(penalty[, constraint_order, ...])
fit(X[, y])	Calculate regression matrix for later use.
fit_transform(X[, y])	Fit to data, then transform it.
get_params([deep])	Get parameters for this estimator.
set_params(**params)	Set the parameters of this estimator.
transform(X[, copy])	Do asymmetric Whittaker background subtraction

fit(X, y=None)

Calculate regression matrix for later use.

Parameters

• X ((n, m) ndarray) – Data to be pretreated. n samples x m variables (typically wavelengths)

• y – Ignored

fit_transform(X, y=None, **fit_params)

Fit to data, then transform it.

Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.

Parameters

• X (array-like of shape (n_samples, n_features)) – Input samples.

• y (array-like of shape (n_samples,) or (n_samples, n_outputs), default=None) – Target values (None for unsupervised transformations).

• **fit_params (dict) – Additional fit parameters.

Returns

X_new – Transformed array.

Return type

ndarray array of shape (n_samples, n_features_new)

get_params(deep=True)

Get parameters for this estimator.

Parameters

deep (bool, default=True) – If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params – Parameter names mapped to their values.

Return type

dict

set_params(**params)

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.

Parameters

**params (dict) – Estimator parameters.

Returns

self – Estimator instance.

Return type

estimator instance

transform(X, copy=True)

Do asymmetric Whittaker background subtraction

Parameters

• X ((n, m) ndarray) – Data to be pretreated. n samples x m variables (typically wavelengths)

• copy (bool (True default)) – Whether to genrate a copy of the input file or calculate in place.