QResiduals#

class chemotools.outliers.QResiduals(model: _BasePCA | _PLS | Pipeline, confidence: float = 0.95, method: Literal['chi-square', 'jackson-mudholkar', 'percentile'] = 'jackson-mudholkar')[source]

Bases: _ModelResidualsBase

Calculate Q residuals (Squared Prediction Error - SPE) for PCA or PLS models.

Parameters:

  • model (Union[ModelType, Pipeline]) – A fitted PCA/PLS model or Pipeline ending with such a model.

  • confidence (float, default=0.95) – Confidence level for statistical calculations (between 0 and 1).

  • method (str, default="jackson-mudholkar") – The method used to compute the confidence threshold for Q residuals. Options: - “chi-square” : Uses the first two moments of the residual eigenvalues (mean and variance) to compute a moment-matched chi-square threshold for Q residuals [1, 3]. - “jackson-mudholkar” : Uses the first three moments of the residual eigenvalues to calculate an analytical threshold based on Jackson & Mudholkar’s approximation [2, 3]. - “percentile” : Uses the empirical percentile of the observed Q residuals to set a non-parametric threshold.

Variables:

  • estimator (ModelType) – The fitted model of type _BasePCA or _PLS.

  • transformer (Optional[Pipeline]) – Preprocessing steps before the model.

  • n_features_in (int) – Number of features in the input data.

  • n_components (int) – Number of components in the model.

  • n_samples (int) – Number of samples used to train the model.

  • critical_value (float) – The calculated critical value for outlier detection.

fit(X, y=None)

Fit the Q Residuals model by computing residuals from the training set. Calculates the critical threshold based on the chosen method.

predict(X)

Identify outliers in the input data based on Q residuals threshold.

predict_residuals(X, y=None, validate=True)

Calculate Q residuals (Squared Prediction Error - SPE) for input data.

_calculate_critical_value(X)

Calculate the critical value for outlier detection using the specified method.

References

[1] Box, G. E. P. (1954).

Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25(2), 290–302.

[2] Jackson, J. E., & Mudholkar, G. S. (1979).

Control procedures for residuals associated with principal component analysis. Technometrics, 21(3), 341–349.

[3] Johan A. Westerhuis, Stephen P. Gurden, Age K. Smilde (2001)

Generalized contribution plots in multivariate statistical process monitoring Chemometrics and Intelligent Laboratory Systems 51 95–114 (2000)

Examples

>>> from chemotools.datasets import load_fermentation_train
>>> from chemotools.outliers import QResiduals
>>> from sklearn.decomposition import PCA
>>> X, _ = load_fermentation_train()
>>> pca = PCA(n_components=3).fit(X)
>>> # Initialize QResiduals with the fitted PCA model
>>> q_residuals = QResiduals(model=pca, confidence=0.95)
>>> q_residuals.fit(X)
>>> # Predict outliers in the dataset
>>> outliers = q_residuals.predict(X)
>>> # Calculate Q-residuals
>>> q_residuals_stats = q_residuals.predict_residuals(X)

Attributes

critical_value_

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