# `sipls_select` — siPLS — Synergy Interval PLS
_Group_: **Variable selector** · _Registry tolerance_: `0.7`
· _Parity reference_: **paper-only** (Nørgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L. & Engelsen, S. B. (2000). Interval partial least-squares regression (iPLS). Appl. Spectrosc. 54(3), 413-419. (No widely installable R / Python port of siPLS' synergistic combinations; smoke-tested only.))
## Description
siPLS synergistic interval selection (§18 Phase 5q)
From the `pls4all.sklearn.SiPLSSelector` docstring:
> siPLS — synergistic interval combinations (Nørgaard 2000).
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `interval_width` | `int` | `10` | Width (in variables) of each contiguous spectral interval. |
| `combination_size` | `int` | `2` | Number of intervals combined into the synergistic siPLS subset. |
| `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. |
## Explanations
### Bibliographic source
Nørgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L. & Engelsen, S. B. (2000). *Interval partial least-squares regression (iPLS): a comparative chemometric study with an example from near-infrared spectroscopy*. Applied Spectroscopy 54(3), 413–419 — same paper as `interval_select`; siPLS is the synergy-combinations extension proposed in §3.
### Mathematical principle
Exhaustively score every combination of $m$ fixed-size intervals (out of $I$ total) by CV-RMSE; return the best combination. This captures **synergy** — pairs (or triples) of intervals that work well together even if neither alone is the best single interval.
Combinatorial cost is $\binom{I}{m}$ which is manageable only for small $m$ (typically $m \le 4$ with $I \le 20$, giving up to ~5000 combinations). For larger search spaces use biPLS or interval-GA.
siPLS is the natural extension of iPLS when single-interval performance is unsatisfactory: it explicitly looks for complementary bands.
### Implementation
`n4m_sipls_select`. Reference: R `plsVarSel`.
### 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_sipls_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 sipls_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = sipls_select_fit(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 SiPLSSelector
mdl = SiPLSSelector(n_components=2, interval_width=10, combination_size=2, n_folds=3)
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("sipls_select", X, y,
n_components = 4L, params = list(interval_width = 5L, combination_size = 2L))
# 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.sipls_select(X, y, 4);
% see header of bindings/matlab/+pls4all/sipls_select.m for full
% parameter surface:
% res = sipls_select(X, Y, n_components, interval_width, combination_size)
yhat = predict(res, Xtest);
```
:::
:::{tab-item} MATLAB · pls4all (classdef)
:sync: matlab-classdef
:class-label: lang-matlab
_No idiomatic classdef wrapper — invoke `pls4all.fit("sipls_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📜 **Paper-only** — no executable parity reference; the `pls4all` implementation is verified by a smoke fit only. Canonical citation: Nørgaard, L., Saudland, A., Wagner, J., Nielsen, J. P., Munck, L. & Engelsen, S. B. (2000). Interval partial least-squares regression (iPLS). Appl. Spectrosc. 54(3), 413-419. (No widely installable R / Python port of siPLS' synergistic combinations; smoke-tested only.)
:::
### 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 🏆.
::::{tab-set}
:class: parity-tabs
:::{tab-item} 1 thread
:sync: threads-1
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (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) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 20.7 ms🏆 | — | — | — | 2.64 ms🏆 | 5.35 ms | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | 21.8 ms | — | — | — | 2.99 ms | 4.81 ms🏆 | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | 28.4 ms | — | — | — | 6.79 ms | 12.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | 35.3 ms | — | — | — | 7.58 ms | 10.5 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | 35.6 ms | — | — | — | 7.83 ms | 11.2 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | 37.0 ms | — | — | — | 7.70 ms | 12.0 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | 21.7 ms | — | — | — | 3.46 ms | 9.03 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | 26.7 ms | — | — | — | 4.07 ms | 9.78 ms | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 3 threads
:sync: threads-3
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (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) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 2.44 ms🏆 | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 2.64 ms | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 6.17 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 9.10 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 7.35 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 7.28 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | — | — | — | — | 3.36 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | — | — | — | — | 5.87 ms | — | — | — | — | — | — | — | — | — |
:::
:::{tab-item} 10 threads
:sync: threads-10
| Backend | Parity | 50×250 (ms) | 100×50 (ms) | 100×500 (ms) | 100×2500 (ms) | 200×40 (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) |
|---|
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | — | — | — | 4.20 ms | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✓ bind | — | — | — | — | 2.50 ms🏆 | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✓ bind | — | — | — | — | 5.28 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✓ bind | — | — | — | — | 6.22 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✓ bind | — | — | — | — | 5.59 ms | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✓ bind | — | — | — | — | 6.13 ms | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✓ bind | — | — | — | — | 3.14 ms | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✓ bind | — | — | — | — | 3.56 ms | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)