# `aom_preprocess` — AOM (Adaptive Operator Mixture) preprocessing bank _Group_: **Diagnostic** · _Registry tolerance_: `1e-08` ## Description AOM preprocessing pipeline (§17 Phase 4) > **Registry note** — In-tree `nirs4all.operators.models.sklearn.aom_pls` is the sanctioned provider. pls4all currently exposes the preprocessing primitive, while nirs4all exposes the full AOM/POP estimator stack; parity is qualitative. ### Parameters | Name | Type | Default | Notes | |------|------|---------|-------| | `n_operators` | `int` | `3` | registry benchmark cell value | | `gating_mode` | `int` | `0` | registry benchmark cell value | ## Explanations ### Bibliographic source Beurier, G., Reiter, R., Noûs, C., Rouan, L. & Cornet, D. (2026). *Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: a large-scale benchmark of operator-adaptive PLS and Ridge models*. arXiv:2605.13587. https://arxiv.org/abs/2605.13587 — introduces operator-adaptive PLS (AOM-PLS / POP-PLS) and the bench against 50+ NIRS datasets that the git-pinned oracle `nirs4all.operators.models.sklearn.aom_pls` is calibrated against. ### Mathematical principle `aom_preprocess` is the **operator-bank primitive** that AOM-PLS and POP-PLS build on. Given the centered spectral matrix $\mathbf{X} \in \mathbb{R}^{n\times p}$ and a finite bank of strict-linear operators $\{\mathbf{A}_b\}_{b=1}^{M} \subset \mathbb{R}^{p\times p}$ — matrices fully determined by the wavelength grid (identity, Savitzky–Golay smooth/derivative, finite difference, polynomial detrending, Norris–Williams, Whittaker; SNV / MSC / EMSC / ASLS / OSC are excluded because they depend on $\mathbf{y}$ or on a reference spectrum) — `aom_preprocess` materializes the $M$ preprocessed views $\mathbf{X}_b = \mathbf{X}\mathbf{A}_b^{\top}$ and gates them. Two gating modes are supported: * **soft** ($\texttt{gating\_mode}=1$): equal-weight average $$\mathbf{X}_{\text{AOM}}^{\text{soft}} \;=\; \frac{1}{M}\sum_{b=1}^{M}\mathbf{X}\mathbf{A}_b^{\top}.$$ * **hard** ($\texttt{gating\_mode}=0$): deterministic first-operator selection, $$\mathbf{X}_{\text{AOM}}^{\text{hard}} \;=\; \mathbf{X}\mathbf{A}_{1}^{\top}.$$ Both modes preserve the **cross-covariance identity** exploited by the AOM/POP selectors: with $\mathbf{S} = \mathbf{X}^{\top}\mathbf{Y}$ and any $\mathbf{A}_b$ in the bank, $$\bigl(\mathbf{X}\mathbf{A}_b^{\top}\bigr)^{\top}\mathbf{Y} \;=\; \mathbf{A}_b\,\mathbf{S},$$ so a downstream PLS step can score the whole bank by $M$ cheap $O(pq)$ left actions instead of $M$ full $O(np)$ matrix products. The motivation is that **no single preprocessing is best on all calibrations** — different wavelength regions favour different transforms — and the AOM-PLS / POP-PLS selectors exploit that by picking, respectively, a global operator (one $b^{\star}$ for the whole model) or a per-component operator (one $b_a$ for each latent direction). Predictions on new spectra reuse the absorbed operator(s) through the recovered original-space coefficients — **no preprocessing replay at predict time**. ### Implementation `n4m_model_selection_aom_preprocessing_fit`. Reference: git-pinned oracle `nirs4all.operators.models.sklearn.aom_pls` (sanctioned exception). R roxygen note (`methods_extra.R::aom_preprocess`): > Adaptive Operator-Mixture preprocessing fit/transform. MATLAB header (`bindings/matlab/+pls4all/aom_preprocess.m`): ```text pls4all.aom_preprocess AOM preprocessing fit/transform. ``` ### 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_model_selection_aom_preprocessing_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 aom_preprocess_fit with pls4all.Context() as ctx, pls4all.Config() as cfg: res = aom_preprocess_fit(ctx, cfg, X, y) # 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 aom_preprocess result = aom_preprocess(X, y, n_components=2) ``` ::: :::{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("aom_preprocess", X, y, n_components = 2L, params = list(n_operators = 3L, gating_mode = 0L)) # 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 <- aom_preprocess(X, Y = NULL, n_operators = 1L, gating_mode = 0L) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab res = pls4all.aom_preprocess(X, y, 2); % see header of bindings/matlab/+pls4all/aom_preprocess.m for full % parameter surface: % res = aom_preprocess(X, Y, n_operators, gating_mode) yhat = predict(res, Xtest); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("aom_preprocess", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`nirs4all`** (python · python) — `nirs4all` in-tree · strict (rmse_rel ≤ 1e-08) — In-tree nirs4all AOM provider (sanctioned external reference). pls4all's current primitive exposes a small operator-bank preprocessing kernel, while nirs4all exposes the full AOM/POP estimator stack; the parity remains qualitative. ::: ### 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-08`). 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✓ ref1.85 ms
Python · pls4all
pls4all.python✓ bind1.76 ms
pls4all.sklearn✓ bind1.75 ms🏆
R · pls4all
pls4all.R✓ bind6.07 ms
pls4all.R.formula✓ bind7.96 ms
pls4all.R.mdatools✓ bind6.56 ms
pls4all.R.pls✓ bind7.33 ms
Python · external
📐nirs4allsource2.13 ms
::: :::{tab-item} 3 threads :sync: threads-3
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref2.95 ms
Python · pls4all
pls4all.python✓ bind1.74 ms🏆
pls4all.sklearn✓ bind3.37 ms
R · pls4all
pls4all.R✓ bind10.4 ms
pls4all.R.formula✓ bind35.7 ms
pls4all.R.mdatools✓ bind29.5 ms
pls4all.R.pls✓ bind32.9 ms
Python · external
📐nirs4allsource11.5 ms
::: :::{tab-item} 10 threads :sync: threads-10
BackendParity200×40 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref3.32 ms
Python · pls4all
pls4all.python✓ bind7.59 ms
pls4all.sklearn✓ bind4.10 ms
R · pls4all
pls4all.R✓ bind9.94 ms
pls4all.R.formula✓ bind9.00 ms
pls4all.R.mdatools✓ bind8.97 ms
pls4all.R.pls✓ bind8.32 ms
Python · external
📐nirs4allsource1.87 ms🏆
::: :::: --- _See also_: [benchmark overview](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)