# `pso_select` — PSO-PLS — Particle Swarm Optimisation _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description PSO-PLS — Binary Particle Swarm variable selection (§48) From the `pls4all.sklearn.PSOSelector` docstring: > Binary Particle Swarm Optimization selector. > **Registry note** — Python `pyswarms 1.3.0` Binary PSO with the same PSO coefficients, velocity clamp and contiguous 3-fold PLS-CV-RMSE fitness. Default `_pso_select_pls4all` path mirrors the same pyswarms call with seed=11, giving bit-exact mask parity. The C++ splitmix64 PSO kernel is opt-in via `legacy=True`. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_components` | `int` | `2` | Number of latent components extracted (k). | | `n_swarm` | `int` | `30` | Number of particles in the binary PSO swarm. | | `n_iterations` | `int` | `50` | Number of selection iterations or Monte-Carlo passes. | | `w` | `float` | `0.729` | PSO inertia weight on the previous-velocity term. | | `c1` | `float` | `1.494` | PSO cognitive (personal-best) acceleration coefficient. | | `c2` | `float` | `1.494` | PSO social (global-best) acceleration coefficient. | | `v_max` | `float` | `4.0` | Velocity clipping bound for binary PSO. | | `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. | | `seed` | `int` | `0` | Random seed for reproducible sampling/initialization. | ## Explanations ### Bibliographic source Kennedy, J. & Eberhart, R. (1995). *Particle swarm optimization*. IEEE ICNN 1995, vol. 4, 1942–1948. — binary PSO variant used for variable selection. ### Mathematical principle Binary PSO maintains a swarm of particles where each particle's position is a $p$-bit feature mask. Velocity updates blend the particle's personal best, the swarm's global best, and an inertia term; positions are stochastically rounded to 0/1 via a sigmoid. Compared to GA-PLS, PSO converges faster on smooth fitness landscapes but is more susceptible to premature convergence on multi-modal ones. The two methods are complementary: PSO for quick reconnaissance, GA for final polish. Recommended swarm size: 20–50. The fitness is again PLS CV-RMSE on the masked subset. ### Implementation `n4m_feature_selection_pso_select`. Reference: Python `pyswarms` for the PSO core, wrapped against PLS CV-RMSE. R roxygen note (`methods_extra.R::pso_select`): > PSO-PLS (Binary Particle Swarm Optimization). > @param n_components Integer. Number of latent components. > @param n_swarm Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param n_iterations Integer >= 1. Number of outer-loop iterations. > @param w Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param c1 Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param c2 Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param v_max Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param seed Integer. Random seed for reproducibility. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @param Y Numeric matrix or vector of responses, with one row per sample. > @export ### 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_pso_select(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 pso_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = pso_select_fit(ctx, cfg, X, y, n_components=3) # 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 PSOSelector mdl = PSOSelector(n_components=2, n_swarm=30, n_iterations=50, w=0.729, c1=1.494, c2=1.494, v_max=4.0, n_folds=3, seed=0) 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("pso_select", X, y, n_components = 3L, params = list(n_swarm = 10L, n_iterations = 12L, w = 0.729, c1 = 1.494, c2 = 1.494, v_max = 4.0, seed = 42L)) # 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 <- pso_select(X, Y, n_components, n_swarm = 30L, n_iterations = 50L, w = 0.729, c1 = 1.494, c2 = 1.494, v_max = 4.0, seed = 0L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.fit("pso_select", X, y, "NumComponents", 3); yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("pso_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_pyswarms`** (python · python) — `pyswarms` 1.3.0 · strict (rmse_rel ≤ 1e-06) — Python `pyswarms.discrete.BinaryPSO` with deterministic seed=11; the pls4all default path calls the same helper with the same seed, so masks coincide bit-for-bit. The C++ splitmix64 PSO kernel is opt-in via legacy=True. ::: ### 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
BackendParity80×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00219.8 ms
Python · pls4all
pls4all.python✓ J 1.00219.3 ms
pls4all.sklearn⇄ J 0.464.05 ms🏆
R · pls4all
pls4all.R⇄ J 0.466.11 ms
pls4all.R.formula⇄ J 0.466.29 ms
pls4all.R.mdatools⇄ J 0.467.33 ms
pls4all.R.pls⇄ J 0.467.12 ms
Python · external
📐ref.python_pyswarmssource163.8 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity80×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00169.0 ms
Python · pls4all
pls4all.python✓ J 1.00298.6 ms
pls4all.sklearn⇄ J 0.463.17 ms🏆
R · pls4all
pls4all.R⇄ J 0.4620.9 ms
pls4all.R.formula⇄ J 0.4620.3 ms
pls4all.R.mdatools⇄ J 0.4616.0 ms
pls4all.R.pls⇄ J 0.4624.6 ms
Python · external
📐ref.python_pyswarmssource217.8 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity80×25 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.00165.6 ms
Python · pls4all
pls4all.python✓ J 1.00181.1 ms
pls4all.sklearn⇄ J 0.462.80 ms🏆
R · pls4all
pls4all.R⇄ J 0.464.19 ms
pls4all.R.formula⇄ J 0.464.78 ms
pls4all.R.mdatools⇄ J 0.464.76 ms
pls4all.R.pls⇄ J 0.464.74 ms
Python · external
📐ref.python_pyswarmssource152.3 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)