ecr — ECR — Elastic Component Regression

Group: Calibration transfer · Registry tolerance: 1e-08

Description

Elastic Component Regression (Phase 50)

Registry note — One-shot octave-cli libPLS 1.95 ecr(X, y, A, 'center', alpha). Deterministic; n4m’s power-method convergence is aligned to libPLS powermethod.m, matching it to ~1e-15.

Parameters

Name	Type	Default	Notes
X	—	required	current public binding signature
y	—	required	current public binding signature
alpha	float	0.5	current public binding signature
n_components	int	2	current public binding signature

Explanations

Bibliographic source

Li, H.-D., Liang, Y.-Z. & Xu, Q.-S. (2010). Uncover the path from PCR to PLS via elastic component regression. Chemometrics and Intelligent Laboratory Systems 104(2), 341–346. DOI 10.1016/j.chemolab.2010.08.003.

Mathematical principle

For each component the implementation forms \(\mathbf H=(1-\alpha)\mathbf X^T\mathbf X+\alpha(\mathbf X^T\mathbf Y)(\mathbf X^T\mathbf Y)^T\), takes its dominant eigenvector, computes the corresponding scores and loadings, and sequentially deflates X and Y. alpha therefore interpolates the implemented variance and squared-covariance criteria.

Appropriate uses

Supervised dimension reduction that explicitly blends X variance and X–Y covariance before regression.

Limits and validation

alpha changes the eigensystem and must be validated; endpoint interpretations assume the implemented scaling and sequential deflation.

Implementation

The earlier scalar formula mixing \(w^TX^TXw\) with \(w^TX^TY\) was dimensionally incomplete for multivariate Y. The matrix H above is the authoritative implemented criterion.

Sources and provenance

Current implementation: cpp/src/core/ecr.cpp.

API and bindings

C ABI (ABI 2): n4m_estimators_ecr_fit. Use the linked public header for the exact signature, configuration, and result handles.

Python (verified public re-export):

from n4m.estimators.regression.latent import ecr
result = ecr(X, y)

Source signature: ecr(X, y, *, alpha: float = 0.5, n_components: int = 2) (n4m/_impl/native.py).

R (source-verified): ecr(formula, data, ncomp = 2L, alpha = 0.5, na.action = stats::na.omit).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): ecr(X, Y, n_components, alpha).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 ref.matlab_libpls (matlab · python) — libPLS 1.95 · strict (rmse_rel ≤ 1e-08) — Octave-bridged libPLS 1.95 ecr(X, y, A, 'center', alpha). Predictions computed as X_predict @ B + y_mean using the fitted coefficient matrix and centring parameters.

Benchmarks

Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.

Adaptive wall-clock per cell measured against full_matrix.csv. Only backends that implement this method are listed; libraries without the method are omitted.

Verdict  ·  ✓ ref / ≈ ref / ~ shape mark a reference-gate pass at strict / relaxed / qualitative tolerance  ·  ✓ bind = archived binding-harness result agrees with the C++ baseline  ·  ⇄ cross-check = documented by-design selector/RNG/model, noncanonical API/facade convention, or secondary oracle  ·  ✗ divergent  ·  ⚠ error  ·  — not run. The fastest backend per column is marked 🏆.

Reference gate: strict — numeric equivalence (rmse_rel_tol ≤ 1e-08).

Rows tagged with 📐 are the canonical parity references for this method (declared in parity_timing.registry). C++ and external rows show reference parity; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.

1 thread

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 6e-16	2.16 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.24 ms
pls4all.sklearn	✓ 4e-15	2.37 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	5.88 ms
pls4all.R.formula	✓ bind	6.96 ms
pls4all.R.mdatools	✓ bind	7.41 ms
pls4all.R.pls	✓ bind	8.61 ms
MATLAB · external
📐ref.matlab_libpls	source	62.4 ms

3 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 6e-16	2.19 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.14 ms🏆
pls4all.sklearn	✓ 4e-15	2.32 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	5.03 ms
pls4all.R.formula	✓ bind	6.42 ms
pls4all.R.mdatools	✓ bind	6.40 ms
pls4all.R.pls	✓ bind	6.08 ms
MATLAB · external
📐ref.matlab_libpls	source	61.5 ms

10 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 6e-16	2.11 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.16 ms
pls4all.sklearn	✓ 4e-15	2.27 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	5.42 ms
pls4all.R.formula	✓ bind	7.74 ms
pls4all.R.mdatools	✓ bind	6.53 ms
pls4all.R.pls	✓ bind	6.36 ms
MATLAB · external
📐ref.matlab_libpls	source	92.2 ms

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See also: benchmark overview · methods index · interactive dashboard