# `interval_select` — iPLS — Interval PLS (moving-window) _Group_: **Variable selector** · _Registry tolerance_: `1e-06` ## Description Interval/iPLS forward selection (§18 Phase 5b) From the `pls4all.sklearn.IntervalSelector` docstring: > Forward interval PLS (iPLS, Nørgaard 2000). > **Registry note** — R `mdatools::ipls(method='forward')`. Default `_interval_select_pls4all` path mirrors the same R call with identical interval grid and venetian CV, giving bit-exact mask parity. The C++ contiguous-fold kernel is opt-in via `legacy=True`. ### 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. | | `step` | `int` | `5` | Stride between consecutive forward-iPLS intervals. | | `n_folds` | `int` | `3` | Number of cross-validation folds used inside the selector. | | `interval_step` | `int` | `2` | registry benchmark cell value | ## 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. ### Mathematical principle Slide a fixed-width window of $w$ consecutive wavelengths across the spectrum, fit PLS on each window alone, evaluate by CV-RMSE. The window with the lowest CV-RMSE is returned as the selected interval. iPLS is the simplest **interval** selector — it returns a single contiguous band rather than scattered wavelengths. The output is therefore directly interpretable as a spectroscopic feature (functional group, electronic transition, …). For multi-band selection use biPLS or siPLS. The window width $w$ is the main tunable; cross-validating $w$ jointly with the window position is the standard extension. ### Implementation `n4m_feature_selection_interval_select`. Reference: R `plsVarSel`. R roxygen note (`methods_extra.R::interval_select`): > Interval selector (iPLS). > @param n_components Integer. Number of latent components. > @param interval_width Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param step Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @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_interval_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 interval_select_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = interval_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 IntervalSelector mdl = IntervalSelector(n_components=2, interval_width=10, step=5, 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("interval_select", X, y, n_components = 4L, params = list(interval_width = 5L, interval_step = 2L)) # 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 <- interval_select(X, Y, n_components, interval_width = 10L, step = 1L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.interval_select(X, y, 4); % see header of bindings/matlab/+pls4all/interval_select.m for full % parameter surface: % res = interval_select(X, Y, n_components, interval_width, step) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("interval_select", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.r_mdatools`** (R · r) — `mdatools` 0.15.0 · strict (rmse_rel ≤ 1e-06) — R `mdatools::ipls` forward-iPLS — returns the union of selected interval variables. pls4all's `interval_select` uses a slightly different scoring (fold-RMSE on a fixed validation plan), so set/index overlap is the metric of interest. ::: ### 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
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.001.5 s
Python · pls4all
pls4all.python✓ J 1.001.5 s
pls4all.sklearn⇄ J 0.503.75 ms🏆
R · pls4all
pls4all.R⇄ J 0.5010.9 ms
pls4all.R.formula⇄ J 0.5011.7 ms
pls4all.R.mdatools⇄ J 0.5013.9 ms
pls4all.R.pls⇄ J 0.5010.3 ms
R · external
📐ref.r_mdatoolssource632.3 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.002.0 s
Python · pls4all
pls4all.python✓ J 1.002.0 s
pls4all.sklearn⇄ J 0.503.95 ms🏆
R · pls4all
pls4all.R⇄ J 0.508.51 ms
pls4all.R.formula⇄ J 0.509.33 ms
pls4all.R.mdatools⇄ J 0.507.09 ms
pls4all.R.pls⇄ J 0.509.36 ms
R · external
📐ref.r_mdatoolssource706.6 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ J 1.001.1 s
Python · pls4all
pls4all.python✓ J 1.00994.2 ms
pls4all.sklearn⇄ J 0.502.26 ms🏆
R · pls4all
pls4all.R⇄ J 0.505.63 ms
pls4all.R.formula⇄ J 0.506.68 ms
pls4all.R.mdatools⇄ J 0.506.61 ms
pls4all.R.pls⇄ J 0.507.03 ms
R · external
📐ref.r_mdatoolssource507.0 ms
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)