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):

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

C ABI · libn4m

/* 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);

Python · pls4all (raw)

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"), …

Python · pls4all.sklearn

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)

R · pls4all_method()

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.

MATLAB · pls4all (MEX)

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);

MATLAB · pls4all (classdef)

No idiomatic classdef wrapper — invoke pls4all.fit("variable_select_sr", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

• 📐 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. 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). 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.

1 thread

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	542.8 ms
Python · pls4all
pls4all.python	✓ J 1.00	1.2 s
pls4all.sklearn	⇄ J 0.25	8.28 ms🏆
R · pls4all
pls4all.R	⇄ J 0.25	24.1 ms
pls4all.R.formula	⇄ J 0.25	11.2 ms
pls4all.R.mdatools	⇄ J 0.25	22.3 ms
pls4all.R.pls	⇄ J 0.25	31.6 ms
R · external
📐ref.r_plsvarsel	source	18.9 ms

3 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	780.0 ms
Python · pls4all
pls4all.python	✓ J 1.00	377.8 ms
pls4all.sklearn	⇄ J 0.25	2.81 ms🏆
R · pls4all
pls4all.R	⇄ J 0.25	20.2 ms
pls4all.R.formula	⇄ J 0.25	7.53 ms
pls4all.R.mdatools	⇄ J 0.25	8.89 ms
pls4all.R.pls	⇄ J 0.25	8.23 ms
R · external
📐ref.r_plsvarsel	source	11.4 ms

10 threads

Backend	Parity	200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ J 1.00	692.5 ms
Python · pls4all
pls4all.python	✓ J 1.00	1.3 s
pls4all.sklearn	⇄ J 0.25	5.57 ms🏆
R · pls4all
pls4all.R	⇄ J 0.25	6.01 ms
pls4all.R.formula	⇄ J 0.25	8.76 ms
pls4all.R.mdatools	⇄ J 0.25	6.96 ms
pls4all.R.pls	⇄ J 0.25	6.89 ms
R · external
📐ref.r_plsvarsel	source	12.7 ms

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See also: benchmark overview · methods index · interactive dashboard