# `lw_pls` — Locally-Weighted PLS (LW-PLS) _Group_: **Nonlinear / local** · _Registry tolerance_: `1e-08` ## Description LW-PLS — Locally-weighted PLS (§17 Phase 4) From the `pls4all.sklearn.LWPLSRegression` docstring: > Locally-weighted PLS (Næs & Centner 1998). > **Registry note** — In-tree `nirs4all.operators.models.sklearn.lwpls.LWPLS` is the sanctioned external reference. pls4all defaults to the Gaussian-weighted local PLS that matches nirs4all bit-for-bit (max_abs < 1e-13); the legacy k-NN cutoff variant is opt-in via cfg.solver = SIMPLS. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `n_neighbors` | `int` | `30` | Number of training neighbours used for each local prediction (LW-PLS). | ## Explanations ### Bibliographic source Centner, V. & Massart, D. L. (1998). *Optimisation in locally weighted regression*. Analytical Chemistry 70(19), 4206–4211. ### Mathematical principle Instead of fitting a single global PLS, LW-PLS refits a *per-prediction-point* local PLS using only the $k$-nearest calibration samples (in $\mathbf{X}$-space distance). This adapts the model to the local geometry around each query point and is effective on calibration sets that span heterogeneous regimes (e.g. a single instrument calibrated across several product classes). The neighbourhood weight typically combines distance (Gaussian or tricube kernel on the Euclidean / Mahalanobis distance) with the inverse residual variance from a preliminary global fit. The local PLS uses few components (typically 2–4) because the neighbourhood is small. Prediction cost is $O(n)$ for the neighbour search plus $O(k_{\mathrm{nn}} \cdot p \cdot k_{\mathrm{pls}})$ for the local fit, per query. KD-tree / ball-tree indices accelerate the neighbour search; pls4all uses an exhaustive scan because $p \gg n$ defeats most spatial indices for NIR data anyway. ### Implementation `n4m_estimators_lw_pls_fit`. Reference: sanctioned git-pinned port `nirs4all.operators.models.sklearn.lwpls`. R roxygen note (`methods_extra.R::lw_pls_fit`): > Locally-weighted PLS (Næs & Centner 1998). > @param n_components Integer. Number of latent components. > @param n_neighbors Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export MATLAB header (`bindings/matlab/+pls4all/lw_pls.m`): ```text pls4all.lw_pls Locally-weighted PLS (Næs & Centner 1998). ``` ### 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_lw_pls_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 lw_pls_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = lw_pls_fit(ctx, cfg, X, y, n_components=3) # 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 LWPLSRegression mdl = LWPLSRegression(n_components=2, n_neighbors=30) 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("lw_pls", X, y, n_components = 3L, params = list(n_neighbors = 30L)) # 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 <- lw_pls_fit(X, Y, n_components, n_neighbors = 30L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.lw_pls(X, y, 3); % see header of bindings/matlab/+pls4all/lw_pls.m for full % parameter surface: % res = lw_pls(X, Y, n_components, n_neighbors) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("lw_pls", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`nirs4all`** (python · python) — `nirs4all` in-tree · strict (rmse_rel ≤ 1e-08) — In-tree Python LW-PLS (sanctioned external reference). Locally-weighted PLS (Naes 1990 / Centner 1998). pls4all's default solver (NIPALS) implements the same Gaussian-weighted local PLS as the nirs4all reference, deriving the kernel bandwidth `lambda = max(1.0, 0.5 * n_neighbors)`. The legacy k-NN cutoff variant remains available via cfg.solver = SIMPLS. ::: ### 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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-1625.6 ms
Python · pls4all
pls4all.python✓ bind37.2 ms
pls4all.sklearn⇄ +1e+009.19 ms🏆
R · pls4all
pls4all.R⇄ +1e+0020.3 ms
pls4all.R.formula⇄ +1e+0023.2 ms
pls4all.R.mdatools⇄ +1e+0024.6 ms
pls4all.R.pls⇄ +1e+0023.2 ms
Python · external
📐nirs4allsource23.9 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-1610.8 ms
Python · pls4all
pls4all.python✓ bind10.3 ms
pls4all.sklearn⇄ +1e+004.44 ms🏆
R · pls4all
pls4all.R⇄ +1e+009.02 ms
pls4all.R.formula⇄ +1e+0010.0 ms
pls4all.R.mdatools⇄ +1e+0010.8 ms
pls4all.R.pls⇄ +1e+0011.1 ms
Python · external
📐nirs4allsource23.7 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 7e-1611.8 ms
Python · pls4all
pls4all.python✓ bind12.9 ms
pls4all.sklearn⇄ +1e+005.14 ms🏆
R · pls4all
pls4all.R⇄ +1e+009.85 ms
pls4all.R.formula⇄ +1e+009.03 ms
pls4all.R.mdatools⇄ +1e+0011.2 ms
pls4all.R.pls⇄ +1e+0012.1 ms
Python · external
📐nirs4allsource29.0 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)