# `variable_select_sr` — Selectivity Ratio
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
Selectivity-Ratio top-k (§18 Phase 5a, method=2)
From the `pls4all.sklearn.SelectivityRatioSelector` docstring:
> Selectivity Ratio top-k selector (Rajalahti 2009).
> **Registry note** — R `plsVarSel::SR` on `pls::plsr(method='simpls', scale=FALSE)`. Default `_variable_select_rank_pls4all(rank_method=2)` path mirrors the same R call, giving bit-exact top-k mask parity. SR is deterministic (no RNG), so no seed pinning is required. The C++ `variable_select_rank` SR path (per-feature X-energy reconstruction) is opt-in via `legacy=True`.
### 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
Rajalahti, T., Arneberg, R., Berven, F. S., Myhr, K.-M., Ulvik, R. J. & Kvalheim, O. M. (2009). *Biomarker discovery in mass spectral profiles by means of selectivity ratio plot*. Chemometrics and Intelligent Laboratory Systems 95(1), 35–48.
### Mathematical principle
Selectivity Ratio (SR) measures the relative explained-to-residual variance of each feature along the **target-projected** PLS direction: $\mathrm{SR}_j = \mathrm{Var}(\hat{x}_j) / \mathrm{Var}(x_j - \hat{x}_j)$, where $\hat{x}_j$ is the projection of feature $j$ onto the target-projected loading vector $\mathbf{p}_{\mathrm{tp}}$ (a single direction in $\mathbf{X}$ space that captures all $\mathbf{Y}$-correlated variation).
High SR means a feature's variance is dominated by its $y$-correlated part; low SR means the feature's variance is mostly orthogonal to $y$ (noise / interferent / matrix). SR therefore separates predictive features from structurally-correlated nuisance features.
Unlike VIP, SR works with a single direction (the target projection), which means it scales gracefully to very many components and is interpretable as a univariate diagnostic per feature.
### Implementation
`n4m_variable_select_rank` with metric=SR.
MATLAB header (`bindings/matlab/+pls4all/selectivity_ratio_select.m`):
```text
pls4all.selectivity_ratio_select Selectivity-ratio feature ranking.
res = pls4all.selectivity_ratio_select(X, Y, n_components, top_k)
Fits an internal SIMPLS model (store_scores=1) and ranks features by
the Selectivity Ratio (SR) statistic.
```
### 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_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 SelectivityRatioSelector
mdl = SelectivityRatioSelector(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_sr", 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.selectivity_ratio_select(X, y, 4);
% see header of bindings/matlab/+pls4all/selectivity_ratio_select.m for full
% parameter surface:
% res = selectivity_ratio_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_sr", 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::SR` selectivity ratio on a fitted `pls::plsr` model. Top-k indices.
:::
### 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 | ≈ | 413.7 ms | 616.2 ms🏆 | 899.9 ms | 1.9 s | 431.6 ms | 452.0 ms | 654.9 ms | 1.4 s | 5.3 s | 903.8 ms | 4.2 s🏆 | 28.7 s🏆 | 1.7 s | 25.7 s |
pls4all.cpp.blas+omp | ≈ | 408.7 ms | 623.5 ms | 881.8 ms🏆 | 1.9 s🏆 | 435.6 ms | 445.4 ms | 643.0 ms | 1.4 s | 5.3 s | 900.4 ms🏆 | 4.3 s | 28.9 s | 1.7 s | 25.7 s🏆 |
pls4all.cpp.omp | ≈ | 417.0 ms | 632.8 ms | 887.1 ms | 1.9 s | 418.4 ms | 453.3 ms | 636.6 ms🏆 | 1.4 s | 5.2 s🏆 | 918.3 ms | 4.3 s | 28.9 s | 1.7 s | 25.8 s |
pls4all.cpp.ref | ≈ | 419.0 ms | 633.5 ms | 895.8 ms | 1.9 s | 424.4 ms | 460.0 ms | 653.7 ms | 1.4 s🏆 | 5.5 s | 908.3 ms | 4.3 s | 28.8 s | 1.7 s🏆 | 25.8 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 400.5 ms | — | — | — | 426.6 ms | 445.4 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 2.70 ms | — | — | — | 2.18 ms | 3.10 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 12.7 ms | — | — | — | 6.23 ms | 13.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 23.2 ms | — | — | — | 6.78 ms | 14.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 20.3 ms | — | — | — | 7.10 ms | 11.9 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 23.1 ms | — | — | — | 8.66 ms | 11.3 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 6.75 ms | — | — | — | 2.62 ms | 4.67 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 4.69 ms | — | — | — | 3.22 ms | 6.86 ms | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | 17.7 ms🏆 | — | — | — | 16.7 ms🏆 | 16.8 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 | — | — | — | — | 400.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 407.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 406.3 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 402.6 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 402.0 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.96 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 6.35 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 6.51 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 6.39 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 7.58 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 4.13 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 3.19 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 11.5 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 | — | — | — | — | 371.5 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | — | — | — | 370.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | — | — | — | 368.1 ms | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | — | — | — | 368.1 ms | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 371.9 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | — | — | — | 1.95 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | — | — | — | 4.54 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | — | — | — | 4.72 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | — | — | — | 4.74 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | — | — | — | 4.82 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | — | — | — | 2.36 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | — | — | — | 2.70 ms | — | — | — | — | — | — | — | — | — |
| R · external |
|---|
📐ref.r_plsvarsel | source | — | — | — | — | 10.4 ms🏆 | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)