# `ecr` — ECR — Elastic Component Regression _Group_: **Calibration transfer** · _Registry tolerance_: `1e-08` ## 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** — 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 | |------|------|---------|-------| | `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_estimators_ecr_fit`. No widely installable reference; treated as `paper_only` in the registry. R roxygen note (`sklearn_extra.R::ecr`): > Elastic Component Regression — formula entry point. MATLAB header (`bindings/matlab/+pls4all/EcrRegression.m`): ```text pls4all.EcrRegression Elastic Component Regression (Liu 2009). ``` ### Usage 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** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_estimators_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); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python 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"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import ECRegression mdl = ECRegression(n_components=2, alpha=0.5) mdl.fit(X, y) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r 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. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- ecr_fit(X, Y, n_components, alpha = 0.5) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} R · pls4all (formula+S3) :sync: r-formula :class-label: lang-r ```r library(pls4all) fit <- ecr(y ~ ., data = train, ncomp = 4L) yhat <- predict(fit, newdata = test) summary(fit) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab 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); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab ```matlab mdl = pls4all.fit("ecr", X, y, "NumComponents", 4); yhat = predict(mdl, Xtest); ``` ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`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 Adaptive wall-clock per cell measured against [`full_matrix.csv`](../benchmarks/overview.md). 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`](../benchmarks/methodology.md)). 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. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)