ds — Direct Standardisation

Group: Calibration transfer · Registry tolerance: 0.5

Description

DS — Direct Standardization (§13)

From the pls4all.sklearn.DSTransformer docstring:

Direct Standardization — full-band cross-instrument regression.

Registry note — Base R per-band lm.fit with window_half_width=0 — Direct Standardization is just per-band linear regression.

No tunable parameters declared at the binding level.

Explanations

Bibliographic source

Wang, Y., Veltkamp, D. J. & Kowalski, B. R. (1991). Multivariate instrument standardisation. Analytical Chemistry 63(23), 2750–2756.

Mathematical principle

Direct Standardisation (DS) learns a single global transfer matrix \(\mathbf{F}\) that maps secondary-instrument spectra back onto the primary instrument: \(\hat{\mathbf{X}}_{\mathrm{primary}} = \mathbf{X}_{\mathrm{secondary}} \mathbf{F}\). The matrix is fit by least squares on a small set of transfer-standard samples measured on both instruments, typically with a Tikhonov ridge for stability.

DS is the simplest member of the calibration-transfer family and works well when the inter-instrument response is approximately linear and stationary — i.e. when instrument differences amount to a constant linear transformation that is invariant across the spectrum. When the transformation varies across wavelength bands (common in dispersive vs FT spectrometers) the global transfer matrix produces band-mixing artefacts and PDS should be used instead.

A canonical workflow: fit DS on \(\le 30\) transfer standards, apply \(\mathbf{F}\) to all subsequent secondary-instrument spectra, then use a single PLS model fit only on primary data.

Implementation

n4m_ds_fit (TransformerMixin in tier 2). Reference: R chemometrics::stdize.

MATLAB header (bindings/matlab/+pls4all/ds.m):

pls4all.ds  Direct Standardization (calibration transfer).

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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_ds_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);

import pls4all
from pls4all._methods import ds_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = ds_fit(ctx, cfg, X, y, X_target=X_target)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import DSTransformer
mdl = DSTransformer(n_components=2)
mdl.fit(X, y, X_target=X_target)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("ds", X, y,
                      n_components = 2L)
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.ds(X, y, 2);
% see header of bindings/matlab/+pls4all/ds.m for full
% parameter surface:
%   res = ds(X_source, X_target)
yhat = predict(res, Xtest);

No idiomatic classdef wrapper — invoke pls4all.fit("ds", X, y, …) directly from the unified MEX factory.

Registry parity references 📐

  • 📐 ref.r_base (R · r) — base R 4.3.3 · qualitative (rmse_rel ≤ 5e-01) — Base R lm per spectral band — closest installable analog to Wang 1991 Piecewise Direct Standardization. With window_half_width=0 this reduces to Direct Standardization.

Benchmarks

Adaptive wall-clock per cell measured against full_matrix.csv. 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). 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.

BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-091.64 ms🏆
Python · pls4all
pls4all.python✓ bind2.09 ms
pls4all.sklearn✓ 9e-162.27 ms
R · pls4all
pls4all.R✓ bind10.2 ms
pls4all.R.formula✓ bind14.0 ms
pls4all.R.mdatools✓ bind11.4 ms
pls4all.R.pls✓ bind12.6 ms
R · external
📐ref.r_basesource31.0 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-093.32 ms
Python · pls4all
pls4all.python✓ bind1.57 ms🏆
pls4all.sklearn✓ 9e-161.72 ms
R · pls4all
pls4all.R✓ bind11.1 ms
pls4all.R.formula✓ bind11.8 ms
pls4all.R.mdatools✓ bind10.7 ms
pls4all.R.pls✓ bind13.0 ms
R · external
📐ref.r_basesource27.8 ms
BackendParity200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref 6e-091.42 ms🏆
Python · pls4all
pls4all.python✓ bind2.13 ms
pls4all.sklearn✓ 9e-161.72 ms
R · pls4all
pls4all.R✓ bind8.95 ms
pls4all.R.formula✓ bind9.70 ms
pls4all.R.mdatools✓ bind9.43 ms
pls4all.R.pls✓ bind10.1 ms
R · external
📐ref.r_basesource28.0 ms

See also: benchmark overview · methods index · interactive dashboard