# `wvc_threshold_select` — WVC-threshold selection _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description WVC threshold-based selection (§18 Phase 5r) From the `pls4all.sklearn.WVCThresholdSelector` docstring: > Threshold-/factor-based WVC-PLS selector. > **Registry note** — R `plsVarSel::WVC_pls` with explicit median-scaled threshold. Default `_wvc_threshold_select_pls4all` path mirrors the same R call, giving bit-exact mask parity. The C++ min-selected kernel is opt-in via `legacy=True`. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `normalize` | `bool` | `True` | Normalize per-variable scores to sum to one before ranking. | | `score_threshold` | `float` | `0.0` | Absolute lower bound on WVC scores for retention. | | `threshold_factor` | `float` | `1.0` | Multiplier applied to the mean WVC score to define the dynamic threshold. | | `min_selected` | `int | None` | `None` | Lower bound on the surviving feature count after thresholding. | ## Explanations ### Bibliographic source Andries, J. P. M. & Vander Heyden, Y. (2011). *Improved variable reduction in partial least squares modelling based on predictive-property-ranked variables and adaptation of partial least squares complexity*. Analytica Chimica Acta 705(1–2), 292–305. https://doi.org/10.1016/j.aca.2011.06.037 — same paper as `wvc_select`; introduces both the top-$k$ ranking and the threshold / factor-of-mean rules used here. ### Mathematical principle Apply fixed-threshold and factor-of-mean rules over WVC scores, with a minimum-selected fallback. Two selection rules are evaluated and the lowest-CV-RMSE one returned: (1) WVC > absolute threshold $\tau$, or (2) WVC > $f \cdot \overline{\mathrm{WVC}}$ (factor-of-mean). The factor-of-mean rule is dataset-adaptive; the absolute rule is more conservative. The minimum-selected fallback (e.g. retain at least 10 features) prevents empty selections on flat-WVC datasets. ### Implementation `n4m_feature_selection_wvc_threshold_select`. R roxygen note (`methods_extra.R::wvc_threshold_select`): > WVC-threshold selector. > @param n_components Integer. Number of latent components. > @param normalize Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param threshold Numeric. Convergence / pruning threshold. > @param threshold_factor Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param min_selected 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 ### 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_feature_selection_wvc_threshold_select(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 wvc_threshold_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = wvc_threshold_select_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 WVCThresholdSelector mdl = WVCThresholdSelector(n_components=2, normalize=True, score_threshold=0.0, threshold_factor=1.0, min_selected=None) 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("wvc_threshold_select", X, y, n_components = 4L, params = list(threshold_factor = 0.5, min_selected = 5L)) # 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 <- wvc_threshold_select(X, Y, n_components, normalize = TRUE, threshold = 0.0, threshold_factor = 1.0, min_selected = 1L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.fit("wvc_threshold_select", X, y, "NumComponents", 4); yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("wvc_threshold_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.r_plsvarsel`** (R · r) — `plsVarSel` 0.10.0 · strict (rmse_rel ≤ 1e-06) — R `plsVarSel::WVC_pls` with explicit threshold — picks features whose weighted-variable scores exceed the median × threshold-factor. ::: ### 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-06`). 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✓ J 1.00336.1 ms
Python · pls4all
pls4all.python✓ J 1.00344.7 ms
pls4all.sklearn⇄ J 0.691.67 ms🏆
R · pls4all
pls4all.R⇄ J 0.694.07 ms
pls4all.R.formula⇄ J 0.694.66 ms
pls4all.R.mdatools⇄ J 0.694.59 ms
pls4all.R.pls⇄ J 0.695.51 ms
R · external
📐ref.r_plsvarselsource13.0 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00304.2 ms
Python · pls4all
pls4all.python✓ J 1.00301.0 ms
pls4all.sklearn⇄ J 0.691.57 ms🏆
R · pls4all
pls4all.R⇄ J 0.694.31 ms
pls4all.R.formula⇄ J 0.694.42 ms
pls4all.R.mdatools⇄ J 0.694.35 ms
pls4all.R.pls⇄ J 0.694.40 ms
R · external
📐ref.r_plsvarselsource12.7 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00340.2 ms
Python · pls4all
pls4all.python✓ J 1.00329.0 ms
pls4all.sklearn⇄ J 0.691.61 ms🏆
R · pls4all
pls4all.R⇄ J 0.694.06 ms
pls4all.R.formula⇄ J 0.694.70 ms
pls4all.R.mdatools⇄ J 0.695.14 ms
pls4all.R.pls⇄ J 0.695.45 ms
R · external
📐ref.r_plsvarselsource13.5 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)