# `wvc_select` — WVC — Weighted Variable Contribution
_Group_: **Variable selector** · _Registry tolerance_: `0.7`
## Description
WVC weighted-variable-component top-k
From the `pls4all.sklearn.WVCSelector` docstring:
> WVC-PLS — weighted variable contribution top-k selector.
> **Registry note** — R `plsVarSel::WVC_pls` top-k weighted-variable scoring. Mask RMSE-rel ~0=perfect, ~1=half disagree, ~1.41=disjoint; tolerance 0.7 enforces ~50% overlap.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `top_k` | `int` | `None` | Number of features to retain. |
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `normalize` | `bool` | `True` | Normalize per-variable scores to sum to one before ranking. |
## 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.
### Mathematical principle
WVC builds a **normalised weighted-variable-contribution** score from the SVD of the PLS components. Each feature's contribution to each component is weighted by the component's singular value (importance), then summed and normalised. Sort by WVC, take the top-$k$.
Compared to VIP, WVC uses SVD-based weighting which downweights components dominated by noise; this gives more stable rankings when $k$ is over-specified.
### Implementation
`n4m_wvc_select`.
MATLAB header (`bindings/matlab/+pls4all/wvc_select.m`):
```text
pls4all.wvc_select Weighted-vector correlation top-k selector.
```
### 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_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_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = wvc_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 WVCSelector
mdl = WVCSelector(top_k, n_components=2, normalize=True)
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_select", X, y,
n_components = 4L, params = list(top_k = 10L))
# 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.wvc_select(X, y, 4);
% see header of bindings/matlab/+pls4all/wvc_select.m for full
% parameter surface:
% res = wvc_select(X, Y, n_components, top_k, normalize)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("wvc_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 · qualitative (rmse_rel ≤ 7e-01) — R `plsVarSel::WVC_pls` — weighted-variable-component scoring.
:::
### 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**: qualitative — shape/smoke comparison only. The external library and pls4all do not produce numerically equivalent output for this method (see the MethodSpec notes); the `rmse_rel_tol ≤ 7e-01` budget is set wide on purpose. Treat ~ shape as *“we ran both, both finished”*, not as numerical agreement.
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 | ≈ | 2.59 ms | 7.54 ms🏆 | 38.8 ms | 236.7 ms | 1.58 ms🏆 | 2.75 ms | 18.3 ms🏆 | 207.1 ms🏆 | 1.3 s | 122.5 ms | 1.4 s | 7.0 s🏆 | 551.3 ms | 6.6 s🏆 |
pls4all.cpp.blas+omp | ≈ | 2.64 ms | 8.31 ms | 37.6 ms🏆 | 210.2 ms | 1.63 ms | 2.56 ms🏆 | 24.2 ms | 213.3 ms | 1.2 s🏆 | 103.7 ms | 1.4 s | 7.9 s | 577.0 ms | 7.7 s |
pls4all.cpp.omp | ≈ | 2.59 ms | 11.0 ms | 38.9 ms | 211.0 ms | 1.65 ms | 2.71 ms | 25.3 ms | 234.6 ms | 1.3 s | 90.9 ms🏆 | 1.4 s | 7.7 s | 537.8 ms | 7.1 s |
pls4all.cpp.ref | ≈ | 3.04 ms | 7.59 ms | 43.9 ms | 201.8 ms🏆 | 1.59 ms | 2.71 ms | 23.7 ms | 244.4 ms | 1.2 s | 106.1 ms | 1.4 s🏆 | 7.4 s | 518.3 ms🏆 | 7.5 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 2.58 ms🏆 | — | — | — | 1.70 ms | 3.69 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 2.71 ms | — | — | — | 1.93 ms | 5.19 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 12.5 ms | — | — | — | 6.24 ms | 10.7 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 19.2 ms | — | — | — | 6.38 ms | 8.54 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 17.6 ms | — | — | — | 7.20 ms | 9.48 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 20.0 ms | — | — | — | 6.77 ms | 10.2 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 4.46 ms | — | — | — | 2.80 ms | 5.94 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 7.03 ms | — | — | — | 3.07 ms | 6.33 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 30.5 ms | — | — | — | 17.2 ms | 15.9 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 | ~ shape | — | — | — | — | 2.52 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 1.68 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 1.66 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 1.72 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.60 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 3.44 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 4.94 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 6.25 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 6.20 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 6.53 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.50 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 4.78 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 15.6 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 | ~ shape | — | — | — | — | 1.48 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ~ shape | — | — | — | — | 1.47 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ~ shape | — | — | — | — | 1.46 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ~ shape | — | — | — | — | 1.46 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 1.58 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 1.59 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 3.86 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 4.65 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 4.63 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 4.42 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.37 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.65 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 12.0 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)