# `vissa_select` — VISSA — Variable Iterative Space-Shrinkage
_Group_: **Variable selector** · _Registry tolerance_: `1e-06`
## Description
VISSA-PLS — Variable Iterative Space Shrinkage (§49)
From the `pls4all.sklearn.VISSASelector` docstring:
> Variable Iterative Subspace Shrinkage Approach (Deng 2014).
> **Registry note** — Python `auswahl.VISSA 0.9.0` (LSX-UniWue) — canonical Deng 2014 implementation via weighted binary matrix sampling. Default `_vissa_select_pls4all` path mirrors the same auswahl call with seed=11, giving bit-exact mask parity. The C++ splitmix64 VISSA kernel is opt-in via `legacy=True`.
### Parameters
| Name | Type | Default | Notes |
|------|------|---------|-------|
| `n_components` | `int` | `2` | Number of latent components extracted (k). |
| `n_iterations` | `int` | `10` | Number of selection iterations or Monte-Carlo passes. |
| `n_submodels` | `int` | `60` | Number of bootstrap sub-models drawn per VISSA iteration. |
| `ratio_kept` | `float` | `0.1` | Fraction of top-scoring features retained at each VISSA shrinkage step. |
| `threshold` | `float` | `0.5` | Inclusion-probability cut-off below which features are dropped. |
| `floor_probability` | `float` | `0.05` | Lower bound applied to per-feature inclusion probabilities to avoid premature pruning. |
| `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
Deng, B. C., Yun, Y. H., Liang, Y. Z. & Yi, L. Z. (2014). *A new strategy to prevent over-fitting in partial least squares models based on model population analysis*. Analytica Chimica Acta 880, 32–41.
### Mathematical principle
VISSA evaluates a **population of random subsets** of the same size, refines the population by selecting the best by CV-RMSE, and iteratively shrinks the search space toward features that survive in many high-performing subsets. Features that appear in many top subsets are deemed important; the search converges to a consensus subset.
Different from CARS in that the search space is shrunken **by consensus over a population** rather than by exponential decay over iterations. This gives smoother convergence and less sensitivity to single high-leverage subsets.
### Implementation
`n4m_vissa_select`.
### 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_vissa_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 vissa_select_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
res = vissa_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 VISSASelector
mdl = VISSASelector(n_components=2, n_iterations=10, n_submodels=60, ratio_kept=0.1, threshold=0.5, floor_probability=0.05, 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("vissa_select", X, y,
n_components = 3L, params = list(n_iterations = 10L, n_submodels = 60L, ratio_kept = 0.1, threshold = 0.5, floor_probability = 0.05, 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("vissa_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("vissa_select", X, y, …)` directly from the unified MEX factory._
:::
::::
**Registry parity references** 📐
:::{card}
:class-card: external-refs
- 📐 **`ref.python_auswahl`** (python · python) — `auswahl` 0.9.0 · strict (rmse_rel ≤ 1e-06) — Python `auswahl.VISSA` from LSX-UniWue 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 VISSA 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 | 2.6 s | 1.5 s | 3.5 s | 3.9 s🏆 | 9.2 s | 2.3 s | 3.3 s | 11.1 s | 77.0 s | 8.4 s | 63.1 s | 489.0 s🏆 | 22.4 s | 315.4 s |
pls4all.cpp.blas+omp | ✗ +1e+00 | 2.5 s🏆 | 1.6 s | 3.5 s | 4.0 s | 8.6 s🏆 | 2.4 s | 3.2 s🏆 | 11.5 s | 78.3 s | 8.9 s | 63.0 s | 490.6 s | 21.8 s | 322.7 s |
pls4all.cpp.omp | ✗ +1e+00 | 2.6 s | 1.5 s | 3.5 s | 4.1 s | 9.0 s | 2.2 s🏆 | 3.4 s | 11.0 s | 79.2 s | 8.4 s | 62.2 s🏆 | 490.5 s | 21.6 s🏆 | 319.2 s |
pls4all.cpp.ref | ✗ +1e+00 | 2.5 s | 1.4 s🏆 | 3.6 s | 3.9 s | 9.1 s | 2.3 s | 3.3 s | 9.6 s🏆 | 76.2 s🏆 | 7.9 s🏆 | 62.6 s | 492.5 s | 22.2 s | 314.9 s🏆 |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | 3.2 s | 1.5 s | — | — | — | 2.5 s | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | 55.5 ms | 8.52 ms | — | — | — | 43.4 ms | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | 78.1 ms | 10.4 ms | — | — | — | 62.6 ms | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | 88.5 ms | 13.8 ms | — | — | — | 62.3 ms | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | 97.8 ms | 12.2 ms | — | — | — | 59.8 ms | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | 84.1 ms | 10.8 ms | — | — | — | 71.6 ms | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | 50.4 ms | 8.82 ms | — | — | — | 45.1 ms | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | 47.1 ms | 9.82 ms | — | — | — | 49.0 ms | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | 2.8 s | 1.6 s | — | — | — | 2.3 s | — | — | — | — | — | — | — | — |
:::
:::{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 | — | 1.0 s | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | 1.0 s | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | 1.0 s | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | 1.0 s | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | 842.6 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | 15.0 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | 13.6 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | 14.3 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | 12.8 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | 16.1 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | 9.86 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | 12.6 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | 782.0 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 | — | 298.7 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.blas+omp | ✓ ref | — | 304.7 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.omp | ✓ ref | — | 299.9 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.cpp.ref | ✓ ref | — | 303.0 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · pls4all |
|---|
pls4all.python | ✓ bind | — | 309.2 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.sklearn | ✗ +1e+00 | — | 8.07 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| R · pls4all |
|---|
pls4all.R | ✗ +1e+00 | — | 9.95 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.formula | ✗ +1e+00 | — | 10.3 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.mdatools | ✗ +1e+00 | — | 10.2 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.R.pls | ✗ +1e+00 | — | 10.3 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| MATLAB · pls4all |
|---|
pls4all.matlab | ✗ +1e+00 | — | 8.35 ms | — | — | — | — | — | — | — | — | — | — | — | — |
pls4all.matlab.classdef | ✗ +1e+00 | — | 8.85 ms | — | — | — | — | — | — | — | — | — | — | — | — |
| Python · external |
|---|
📐ref.python_auswahl | source | — | 230.4 ms🏆 | — | — | — | — | — | — | — | — | — | — | — | — |
:::
::::
---
_See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)