# `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_pso_select`. Reference: Python `pyswarms` for the PSO core, wrapped against PLS CV-RMSE.
### 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_pso_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);
```
:::
:::{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} 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 · ✗ 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) | 80×25 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (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 | ✗ +1e+00 | 227.4 ms | 169.2 ms | 334.0 ms | 465.1 ms | 1.1 s | 238.7 ms | 317.1 ms🏆 | 1.2 s | 8.5 s | 670.7 ms | 9.1 s | 70.5 s | 3.2 s | 60.3 s |
pls4all.cpp.blas+omp | ✗ +1e+00 | 220.9 ms | 159.1 ms🏆 | 301.4 ms | 460.4 ms | 1.1 s | 244.7 ms | 340.7 ms | 1.1 s | 6.8 s🏆 | 709.1 ms | 7.8 s🏆 | 68.3 s🏆 | 3.1 s🏆 | 60.7 s |
pls4all.cpp.omp | ✗ +1e+00 | 220.4 ms | 182.6 ms | 302.3 ms | 444.2 ms🏆 | 1.0 s🏆 | 250.5 ms | 333.2 ms | 1.1 s🏆 | 8.5 s | 638.8 ms🏆 | 9.0 s | 69.4 s | 3.1 s | 59.8 s🏆 |
pls4all.cpp.ref | ✗ +1e+00 | 232.8 ms | 176.8 ms | 323.5 ms | 452.9 ms | 1.1 s | 244.8 ms | 340.7 ms | 1.1 s | 8.6 s | 659.7 ms | 9.1 s | 70.1 s | 3.2 s | 60.5 s |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 231.2 ms | 173.5 ms | — | — | — | 230.2 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 14.7 ms | 3.02 ms | — | — | — | 15.6 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 25.0 ms | 4.27 ms | — | — | — | 26.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 38.0 ms | 5.86 ms | — | — | — | 23.4 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 35.9 ms | 4.96 ms | — | — | — | 24.0 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 41.6 ms | 7.46 ms | — | — | — | 23.6 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 17.4 ms | 3.32 ms | — | — | — | 17.6 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 15.0 ms | 3.73 ms | — | — | — | 17.7 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_pyswarms | source | 218.3 ms🏆 | 166.6 ms | — | — | — | 210.3 ms🏆 | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 80×25 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (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 | — | 176.0 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | 181.1 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | 182.4 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | 180.0 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | 152.8 ms🏆 | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | 2.83 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | 4.22 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | 4.80 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | 4.69 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | 4.69 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | 3.10 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | 3.70 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_pyswarms | source | — | 172.1 ms | — | — | — | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 80×25 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (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 | — | 128.5 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | 127.9 ms🏆 | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | 131.1 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | 131.8 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | 128.0 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | 2.61 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | 3.52 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | 4.07 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | 4.09 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | 4.13 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | 2.97 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | 3.18 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_pyswarms | source | — | 135.9 ms | — | — | — | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)