HotellingT2#

class chemotools.outliers.HotellingT2(model: _BasePCA | _PLS | Pipeline, confidence: float = 0.95)[source]

Bases: _ModelResidualsBase

Calculate Hotelling’s T-squared statistics for PCA or PLS like 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)

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

References

[1] Johan A. Westerhuis, Stephen P. Gurden, Age K. Smilde

Generalized contribution plots in multivariate statistical process monitoring Chemometrics and Intelligent Laboratory Systems 51 2000 95–114 (2001).

Examples

>>> from chemotools.datasets import load_fermentation_train
>>> from chemotools.outliers import HotellingT2
>>> from sklearn.decomposition import PCA
>>> # Load sample data
>>> X, _ = load_fermentation_train()
>>> # Instantiate the PCA model
>>> pca = PCA(n_components=3).fit(X)
>>> # Initialize HotellingT2 with the fitted PCA model
>>> hotelling_t2 = HotellingT2(model=pca, confidence=0.95)
HotellingT2(model=PCA(n_components=3), confidence=0.95)
>>> hotelling_t2.fit(X)
>>> # Predict outliers in the dataset
>>> outliers = hotelling_t2.predict(X)
>>> # Calculate Hotelling's T-squared statistics
>>> t2_stats = hotelling_t2.predict_residuals(X)
fit(X: ndarray, y: ndarray | None = None) → HotellingT2[source]

Fit the model to the input data.

This step calculates the critical value for the outlier detection.

Parameters:

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

  • y (Ignored) – Not used, present for API consistency by convention.

Returns:

self – Fitted estimator with the critical threshold computed

Return type:

HotellingT2

predict(X: ndarray, y: ndarray | None = None) → ndarray[source]

Identify outliers in the input data.

Parameters:

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

  • y (None) – Ignored to align with API.

Returns:

Boolean array indicating outliers (-1) and inliers (1)

Return type:

ndarray of shape (n_samples,)

predict_residuals(X: ndarray, y: ndarray | None = None, validate: bool = True) → ndarray[source]

Calculate Hotelling’s T-squared statistics for input data.

Parameters:

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

  • y (None) – Ignored.

Returns:

Hotelling’s T-squared statistics for each sample

Return type:

ndarray of shape (n_samples,)

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