spa_select — SPA — Successive Projections Algorithm

Group: Variable selector · Registry tolerance: 1e-06

Description

SPA Successive Projections (§18 Phase 5e)

From the pls4all.sklearn.SPASelector docstring:

Successive Projections Algorithm selector (Araujo 2001).

Registry note — R plsVarSel::spa_pls randomization-based SPA (Forina et al.) — paired Wilcoxon variable importance, p < 0.05 survivor set (fallback to top-ncomp p-values). Default _spa_select_pls4all path mirrors the same R call with seed=11, giving bit-exact mask parity. The deterministic top-k Araújo projection kernel 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).

Explanations

Bibliographic source

Araújo, M. C. U., Saldanha, T. C. B., Galvão, R. K. H., Yoneyama, T., Chame, H. C. & Visani, V. (2001). The successive projections algorithm for variable selection in spectroscopic multicomponent analysis. Chemometrics and Intelligent Laboratory Systems 57(2), 65–73.

Mathematical principle

SPA is a greedy forward selector that seeks minimally collinear features. Starting from the feature with largest coefficient (or user-supplied seed), at each step it adds the feature whose direction is maximally orthogonal to all previously-selected features. Formally, at step \(m\) it picks \(j^{\star} = \arg\max_j \| \mathbf{P}_{S_{m-1}}^{\perp} \mathbf{x}_j \|_2\), where \(\mathbf{P}_{S}^{\perp}\) projects onto the orthogonal complement of the span of the already-selected features.

This produces a feature subset that is well-conditioned for downstream regression: the inverse \((\mathbf{X}_S^{\top}\mathbf{X}_S)^{-1}\) has small condition number by construction. SPA is therefore particularly effective when followed by MLR (or PLS with very few components) on the selected subset.

Stops at a user-specified top-\(k\). Computational cost: \(O(k\, n\, p)\).

Implementation

n4m_spa_select. Reference: R plsVarSel.

MATLAB header (bindings/matlab/+pls4all/spa_select.m):

pls4all.spa_select  Successive Projections Algorithm.

   res = pls4all.spa_select(X, Y, K, top_k)

 Output struct fields:
   selected_indices : 1 × top_k row vector of 1-based feature indices.

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 */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_spa_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);

import pls4all
from pls4all._methods import spa_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = spa_select_fit(ctx, cfg, X, y, n_components=4)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import SPASelector
mdl = SPASelector(top_k, n_components=2)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("spa_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.

res = pls4all.spa_select(X, y, 4);
% see header of bindings/matlab/+pls4all/spa_select.m for full
% parameter surface:
%   res = spa_select(X, Y, n_components, top_k)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("spa_select", 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::spa_pls — Successive Projections Algorithm.

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.

BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00499.6 ms
Python · pls4all
pls4all.python✓ J 1.00515.0 ms
pls4all.sklearn⇄ J 0.121.97 ms🏆
R · pls4all
pls4all.R⇄ J 0.124.72 ms
pls4all.R.formula⇄ J 0.126.23 ms
pls4all.R.mdatools⇄ J 0.125.86 ms
pls4all.R.pls⇄ J 0.125.75 ms
R · external
📐ref.r_plsvarselsource104.0 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00819.9 ms
Python · pls4all
pls4all.python✓ J 1.00530.6 ms
pls4all.sklearn⇄ J 0.121.90 ms🏆
R · pls4all
pls4all.R⇄ J 0.125.33 ms
pls4all.R.formula⇄ J 0.125.81 ms
pls4all.R.mdatools⇄ J 0.1210.9 ms
pls4all.R.pls⇄ J 0.126.22 ms
R · external
📐ref.r_plsvarselsource164.5 ms
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00557.0 ms
Python · pls4all
pls4all.python✓ J 1.00514.9 ms
pls4all.sklearn⇄ J 0.121.89 ms🏆
R · pls4all
pls4all.R⇄ J 0.124.70 ms
pls4all.R.formula⇄ J 0.125.57 ms
pls4all.R.mdatools⇄ J 0.125.52 ms
pls4all.R.pls⇄ J 0.125.17 ms
R · external
📐ref.r_plsvarselsource179.5 ms

See also: benchmark overview · methods index · interactive dashboard