ecr — ECR — Elastic Component Regression

Group: Calibration transfer · Registry tolerance: 0.001

Description

Elastic Component Regression (Phase 50)

From the pls4all.sklearn.ECRegression docstring:

Elastic Component Regression (Liu 2013) — interpolates PCR (α=0) and PLS (α=1).

Registry note — Octave-bridged libPLS 1.95 ecr(X, y, A, 'center', alpha). Deterministic algorithm; small numerical differences arise only from the power-method tolerance and FP accumulation order.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

alpha

float

0.5

Elastic-net mixing weight (0 = pure L2, 1 = pure L1) applied to the PLS coefficient path.

Explanations

Bibliographic source

Liu, Y., Zhang, B. & Hu, J. (2013). Elastic Component Regression. Chemometrics and Intelligent Laboratory Systems 124, 73–79. — adapted in pls4all as a continuum/elastic blend.

Mathematical principle

ECR interpolates between PCR and PLS via a single parameter \(\alpha \in [0, 1]\) that mixes the two loading-weight criteria. The latent direction is \(\mathbf{w} \propto (1-\alpha)\mathbf{X}^{\top}\mathbf{X}\mathbf{w} + \alpha \mathbf{X}^{\top}\mathbf{y}\), which recovers PCR at \(\alpha = 0\) (the leading eigenvector of \(\mathbf{X}^{\top}\mathbf{X}\)) and PLS at \(\alpha = 1\) (proportional to \(\mathbf{X}^{\top}\mathbf{y}\)). Intermediate \(\alpha\) blends variance and covariance criteria; the optimum is typically located by cross-validation.

ECR is closely related to continuum regression with a different parameterisation, and in practice serves a similar purpose: when neither PCR nor PLS dominates RMSE on a given dataset, an interpolating method often wins by a small margin and offers a smooth tunable spectrum.

Implementation

n4m_ecr_fit. No widely installable reference; treated as paper_only in the registry.

MATLAB header (bindings/matlab/+pls4all/EcrRegression.m):

pls4all.EcrRegression  Elastic Component Regression (Liu 2009).

Usage

Direct n4m Python helper:

import n4m

res = n4m.ecr(X, y, n_components=4, alpha=0.6)
y_hat = res["predictions"]
coef = res["coefficients"]

Reusable sklearn-style wrapper:

from n4m.sklearn import NativeECRRegressor

model = NativeECRRegressor(n_components=4, alpha=0.6).fit(X, y)
y_hat = model.predict(X_test)

Every pls4all binding tab dispatches into the same C kernel; the external libraries listed at the bottom of the page are the parity references registered in benchmarks.parity_timing.registry. Switch tabs to read the same fit in your language. The R package now ships drop-in-compatible facades for the CRAN pls package (plsr, pcr, mvr) and for the mdatools::pls(x, y, ...) matrix idiom — those tabs appear only on the methods that have a meaningful equivalence.

pls4all bindings

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_ecr_fit(ctx, cfg, &x_view, &y_view, /* hyperparams */, &res);
/* … read coefficients / mask / scores via */
/* n4m_method_result_get_double_matrix / vector / scalar … */
n4m_method_result_destroy(res);
n4m_config_destroy(cfg);
n4m_context_destroy(ctx);

import pls4all
from pls4all._methods import ecr_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = ecr_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import ECRegression
mdl = ECRegression(n_components=2, alpha=0.5)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("ecr", X, y,
                      n_components = 4L, params = list(alpha = 0.5))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.ecr(X, y, 4);
% see header of bindings/matlab/+pls4all/ecr.m for full
% parameter surface:
%   res = ecr(X, Y, n_components, alpha)
yhat = predict(res, Xtest);

mdl  = pls4all.fit("ecr", X, y, "NumComponents", 4);
yhat = predict(mdl, Xtest);

Registry parity references 📐

  • 📐 ref.matlab_libpls (matlab · python) — libPLS 1.95 · relaxed (rmse_rel ≤ 1e-03) — 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

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 = pls4all binding 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; pls4all language bindings show binding parity against the C++ backend. Hover the icon for role and tolerance band.

BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-162.16 ms🏆
Python · pls4all
pls4all.python✓ bind2.24 ms
pls4all.sklearn✓ 4e-152.37 ms
R · pls4all
pls4all.R✓ bind5.88 ms
pls4all.R.formula✓ bind6.96 ms
pls4all.R.mdatools✓ bind7.41 ms
pls4all.R.pls✓ bind8.61 ms
MATLAB · external
📐ref.matlab_libplssource62.4 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-162.19 ms
Python · pls4all
pls4all.python✓ bind2.14 ms🏆
pls4all.sklearn✓ 4e-152.32 ms
R · pls4all
pls4all.R✓ bind5.03 ms
pls4all.R.formula✓ bind6.42 ms
pls4all.R.mdatools✓ bind6.40 ms
pls4all.R.pls✓ bind6.08 ms
MATLAB · external
📐ref.matlab_libplssource61.5 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-162.11 ms🏆
Python · pls4all
pls4all.python✓ bind2.16 ms
pls4all.sklearn✓ 4e-152.27 ms
R · pls4all
pls4all.R✓ bind5.42 ms
pls4all.R.formula✓ bind7.74 ms
pls4all.R.mdatools✓ bind6.53 ms
pls4all.R.pls✓ bind6.36 ms
MATLAB · external
📐ref.matlab_libplssource92.2 ms

See also: benchmark overview · methods index · interactive dashboard