pls_regression — n4m.estimators.regression.latent.pls_regression

Namespace: n4m.estimators.regression.latent · Fully-qualified: n4m.estimators.regression.latent.pls_regression · Catalog id: models.pls.pls_regression

API surface

C ABI (ABI 2): n4m_model_fit. Use the linked public header for the exact signature, configuration, and result handles.

R: no current source-verified entry point was found for this catalog method.

MATLAB / Octave: no current source-verified entry point was found for this catalog method.

Explanations

Bibliographic source

Wold, Sjöström & Eriksson (2001), PLS-regression: a basic tool of chemometrics, Chemometrics and Intelligent Laboratory Systems 58, 109–130, https://doi.org/10.1016/S0169-7439(01)00155-1; de Jong (1993), SIMPLS: an alternative approach to partial least squares regression, https://doi.org/10.1016/0169-7439(93)85002-X.

Mathematical principle

PLS regression extracts \(k\) latent components \(t_a = X w_a\) whose weights maximize the covariance between the (centered, optionally scaled) predictors and responses, deflates, and regresses \(Y\) on the scores. The fitted model is the affine predictor \(\hat Y = \bar y + (X-\bar x) B\) with \(B = W(P^T W)^{-1} Q^T\); NIPALS, SIMPLS, kernel, SVD and power solvers compute the same subspace up to numerical and single-response conventions.

Appropriate uses

General multivariate calibration of spectra to one or several responses, as the reference linear model and as a latent-score feature extractor ahead of another estimator.

Limits and validation

The component count must be chosen by validation on held-out data; solvers can differ at the last digits and SIMPLS deflates only the cross-covariance, so multi-response scores are not identical across solvers. Scaling choices change the fitted subspace.

Implementation

Generic role estimator models.pls.pls_regression (regressor and transformer) over n4m_model_fit; state is an N4MM model inside the N4ME format.

Sources and provenance

https://doi.org/10.1016/S0169-7439(01)00155-1; https://github.com/GBeurier/nirs4all-methods/blob/main/cpp/src/core/model.cpp

Catalog note

PLS regression through the N4MM model life cycle (n4m_model_fit) with a selectable solver; the general PLS estimator of the generic role surface.

See also: methods index.