# `variable_select_vip` — VIP (Variable Importance in Projection)
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
VIP top-k variable selection (§18 Phase 5a, method=0)
From the `pls4all.sklearn.VIPSelector` docstring:
> Variable Importance in Projection top-k selector (Favilla 2013).
Full Python sklearn-wrapper docstring
```text
Variable Importance in Projection top-k selector (Favilla 2013).
Parameters
----------
top_k : int
Number of features to keep.
n_components, solver, center_x, scale_x, tol, max_iter
Underlying PLS hyperparameters used for VIP scoring.
Notes
-----
Exposes ``vip_scores_`` as an alias for the generic ``scores_``
attribute, for callers used to the chemometrics naming convention.
```
> **Registry note** — R `plsVarSel::VIP` on `pls::plsr(method='kernelpls', scale=FALSE)`. pls4all pins the matching solver (`Solver.KERNEL_ALGORITHM`, `scale_x=False`, `scale_y=False`) and `compute_vip_scores` implements the same column-normalised W formula, so the selected-index masks agree bit-for-bit (`max_abs=0`).
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `top_k` | `int` | `None` | Number of features to retain. |
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `solver` | `str` | `'simpls'` | Inner algorithm: 'nipals', 'simpls', 'svd', 'kernel', 'orthogonal-scores', 'power', 'randomized-svd', 'wide-kernel'. |
| `center_x` | `bool` | `True` | Subtract the column mean of X before fitting. |
| `scale_x` | `bool` | `True` | Standardize X columns to unit variance before fitting. |
| `tol` | `float` | `1e-06` | Convergence tolerance for iterative solvers (NIPALS / power-iteration). |
| `max_iter` | `int` | `500` | Maximum iterations for iterative solvers. |
## Explanations
### Bibliographic source
Wold, S., Sjöström, M. & Eriksson, L. (2001). *PLS-regression: a basic tool of chemometrics*. Chemometrics and Intelligent Laboratory Systems 58(2), 109–130.
### Mathematical principle
VIP scores quantify each feature's contribution across all $k$ latent components of a PLS model, weighted by how much each component explains of $\mathbf{y}$: $\mathrm{VIP}_j = \sqrt{\frac{p}{\mathrm{SSY}} \sum_{a=1}^{k} w_{ja}^2 \, \mathrm{SSY}_a}$, where $w_{ja}$ is the loading weight of feature $j$ in component $a$ and $\mathrm{SSY}_a$ is the explained sum of squares of $\mathbf{y}$ in component $a$.
The normalisation guarantees $\sum_j \mathrm{VIP}_j^2 = p$, so the heuristic $\mathrm{VIP}_j > 1$ identifies features contributing more than their fair share. VIP is the workhorse of spectroscopic variable selection — simple, deterministic, fast, and well understood.
### Implementation
`n4m_feature_selection_variable_select_rank` with metric=VIP. Reference: R `plsVarSel 0.10.0`.
R roxygen note (`selectors.R::vip_select`):
> VIP (Variable Importance in Projection) ranker.
MATLAB header (`bindings/matlab/+pls4all/vip_select.m`):
```text
pls4all.vip_select VIP-based feature ranking.
res = pls4all.vip_select(X, Y, n_components, top_k)
Fits an internal SIMPLS model (store_scores=1) and ranks features by
their Variable Importance in Projection (VIP) scores.
```
### 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_variable_select_rank(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 variable_select_rank
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = variable_select_rank(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 VIPSelector
mdl = VIPSelector(top_k, n_components=2, solver='simpls', center_x=True, scale_x=True, tol=1e-06, max_iter=500)
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("variable_select_vip", 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} R · pls4all (raw fn)
:sync: r-raw
:class-label: lang-r
```r
library(pls4all)
res <- vip_select(model, X, top_k)
yhat <- pls4all_predict(res, X_test)
```
:::
:::{tab-item} MATLAB · pls4all (MEX)
:sync: matlab-mex
:class-label: lang-matlab
```matlab
res = pls4all.vip_select(X, y, 4);
% see header of bindings/matlab/+pls4all/vip_select.m for full
% parameter surface:
% res = vip_select(X, Y, n_components, top_k)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("variable_select_vip", 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::VIP` ranking on `pls::plsr(method='kernelpls', scale=FALSE)` — matches the pls4all kernel-PLS path used by `_variable_select_rank_pls4all(rank_method=0)`. The top-k indices are returned (1-based -> 0-based in the loader).
:::
### 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
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 2.55 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 2.47 ms |
pls4all.sklearn | ✓ J 1.00 | 1.97 ms🏆 |
| R · pls4all |
pls4all.R | ✓ J 1.00 | 6.19 ms |
pls4all.R.formula | ✓ J 1.00 | 6.51 ms |
pls4all.R.mdatools | ✓ J 1.00 | 6.61 ms |
pls4all.R.pls | ✓ J 1.00 | 5.86 ms |
| R · external |
📐ref.r_plsvarsel | source | 16.2 ms |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 8.22 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 7.47 ms |
pls4all.sklearn | ✓ J 1.00 | 2.74 ms🏆 |
| R · pls4all |
pls4all.R | ✓ J 1.00 | 25.1 ms |
pls4all.R.formula | ✓ J 1.00 | 11.1 ms |
pls4all.R.mdatools | ✓ J 1.00 | 9.03 ms |
pls4all.R.pls | ✓ J 1.00 | 17.2 ms |
| R · external |
📐ref.r_plsvarsel | source | 18.5 ms |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 200×40 (ms) |
| C++ native · libn4m |
pls4all.cpp.blas+omp | ✓ J 1.00 | 4.22 ms |
| Python · pls4all |
pls4all.python | ✓ J 1.00 | 4.15 ms |
pls4all.sklearn | ✓ J 1.00 | 3.66 ms🏆 |
| R · pls4all |
pls4all.R | ✓ J 1.00 | 5.24 ms |
pls4all.R.formula | ✓ J 1.00 | 6.31 ms |
pls4all.R.mdatools | ✓ J 1.00 | 6.76 ms |
pls4all.R.pls | ✓ J 1.00 | 6.29 ms |
| R · external |
📐ref.r_plsvarsel | source | 12.5 ms |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)