# `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_feature_selection_variable_select_rank` with metric=SR. R roxygen note (`selectors.R::selectivity_ratio_select`): > Selectivity-ratio ranker. > @inheritParams vip_select > @return A list with `scores` and `selected_indices`. > @param model Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param top_k Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @export 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_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 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} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- selectivity_ratio_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.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  ·  ⇄ 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 1.00542.8 ms
Python · pls4all
pls4all.python✓ J 1.001.2 s
pls4all.sklearn⇄ J 0.258.28 ms🏆
R · pls4all
pls4all.R⇄ J 0.2524.1 ms
pls4all.R.formula⇄ J 0.2511.2 ms
pls4all.R.mdatools⇄ J 0.2522.3 ms
pls4all.R.pls⇄ J 0.2531.6 ms
R · external
📐ref.r_plsvarselsource18.9 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00780.0 ms
Python · pls4all
pls4all.python✓ J 1.00377.8 ms
pls4all.sklearn⇄ J 0.252.81 ms🏆
R · pls4all
pls4all.R⇄ J 0.2520.2 ms
pls4all.R.formula⇄ J 0.257.53 ms
pls4all.R.mdatools⇄ J 0.258.89 ms
pls4all.R.pls⇄ J 0.258.23 ms
R · external
📐ref.r_plsvarselsource11.4 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00692.5 ms
Python · pls4all
pls4all.python✓ J 1.001.3 s
pls4all.sklearn⇄ J 0.255.57 ms🏆
R · pls4all
pls4all.R⇄ J 0.256.01 ms
pls4all.R.formula⇄ J 0.258.76 ms
pls4all.R.mdatools⇄ J 0.256.96 ms
pls4all.R.pls⇄ J 0.256.89 ms
R · external
📐ref.r_plsvarselsource12.7 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)