# `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_wvc_threshold_select`.
### 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_wvc_threshold_select_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 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} 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 · ✗ 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
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ≈ | 473.4 ms | 3.7 s | 4.6 s | 9.5 s🏆 | 431.2 ms | 421.5 ms | 3.7 s | 7.3 s | 31.3 s | 5.5 s🏆 | 30.5 s | 186.3 s | 11.5 s | 159.0 s |
pls4all.cpp.blas+omp | ≈ | 453.6 ms | 3.7 s | 4.5 s | 10.8 s | 433.2 ms | 411.6 ms | 4.0 s | 7.3 s🏆 | 30.1 s | 6.0 s | 32.3 s | 180.1 s🏆 | 11.4 s | 160.0 s |
pls4all.cpp.omp | ≈ | 459.1 ms | 3.6 s🏆 | 4.6 s | 10.4 s | 442.7 ms | 408.2 ms | 3.7 s | 7.8 s | 30.0 s🏆 | 5.5 s | 30.7 s | 190.3 s | 11.3 s | 167.1 s |
pls4all.cpp.ref | ≈ | 459.0 ms | 3.8 s | 4.4 s🏆 | 10.4 s | 430.2 ms | 403.4 ms | 3.4 s🏆 | 7.6 s | 30.2 s | 6.1 s | 28.8 s🏆 | 183.5 s | 11.2 s🏆 | 152.7 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 469.2 ms | — | — | — | 429.3 ms | 405.5 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 2.78 ms | — | — | — | 2.62 ms | 2.77 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 13.2 ms | — | — | — | 5.51 ms | 10.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 19.2 ms | — | — | — | 6.60 ms | 8.89 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 18.7 ms | — | — | — | 6.55 ms | 9.08 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 19.3 ms | — | — | — | 8.55 ms | 8.72 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 4.26 ms | — | — | — | 2.84 ms | 4.51 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 5.37 ms | — | — | — | 3.07 ms | 4.65 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 30.3 ms🏆 | — | — | — | 18.7 ms🏆 | 16.5 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 401.4 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 404.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 409.7 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 412.4 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 394.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.96 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.83 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 5.92 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.53 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 7.70 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 3.20 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.71 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 15.2 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (ms) | 250×50 (ms) | 500×50 (ms) | 500×500 (ms) | 500×2500 (ms) | 2500×50 (ms) | 2500×500 (ms) | 2500×2500 (ms) | 10000×50 (ms) | 10000×500 (ms) |
|---|
| C++ native · libn4m |
|---|
pls4all.cpp.blas | ✓ ref | — | — | — | — | 367.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 365.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 365.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 363.4 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 367.8 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.60 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 3.76 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 4.76 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 4.61 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 4.71 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.36 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.69 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 12.6 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
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_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)