opls — Orthogonal PLS (OPLS)¶
Group: Core PLS · Registry tolerance: 1e-08
Description¶
Orthogonal PLS (Trygg & Wold 2002)
Registry note — Bioconductor
ropls::oplsis the external OPLS reference; convergence and orthogonal-component conventions may differ.
Parameters¶
Name |
Type |
Default |
Notes |
|---|---|---|---|
|
|
|
registry benchmark cell value |
Explanations¶
Bibliographic source¶
Trygg, J. & Wold, S. (2002). Orthogonal projections to latent structures (O-PLS). Journal of Chemometrics 16(3), 119–128. DOI 10.1002/cem.695.
Mathematical principle¶
OPLS rotates the standard PLS latent space so that a single direction captures all \(\mathbf{Y}\)-correlated variation while the remaining components capture \(\mathbf{Y}\)-orthogonal structural variation in \(\mathbf{X}\). The resulting decomposition \(\mathbf{X} = \mathbf{t}_p\mathbf{p}_p^{\top} + \mathbf{T}_o\mathbf{P}_o^{\top} + \mathbf{E}\) separates the predictive component \(\mathbf{t}_p\) from the orthogonal block \(\mathbf{T}_o\), which absorbs spectroscopic baselines, scatter and other nuisance factors that confound interpretation of the predictive loading.
Numerically OPLS proceeds by NIPALS-deflating \(\mathbf{X}\) against directions orthogonal to \(\mathbf{X}^{\top}\mathbf{y}\) before each new predictive component is extracted. Predictions are identical to those of a one-component PLS on the orthogonal-corrected \(\mathbf{X}\); the value is in the interpretation of the loadings, not in better predictions per se.
OPLS shines in metabolomics and process spectroscopy where the spectra carry strong systematic but non-predictive variation; in those settings the single-vector predictive loading is far easier to relate to biology / chemistry than a multi-component PLS loading matrix.
Appropriate uses¶
Separating X variation correlated with Y from orthogonal spectral variation for interpretation and linear prediction.
Limits and validation¶
Orthogonal filtering is supervised and must be fitted inside each validation fold; it does not make the final predictor nonlinear.
Implementation¶
Algorithm.OPLS + Solver.NIPALS + Deflation.ORTHOGONAL. Reference: Bioconductor ropls::opls. Note: orthogonal-component ordering and the criterion that stops orthogonal extraction differ between implementations — exact bit parity is not expected, but RMSE-rel parity within ~1e-3 is.
Sources and provenance¶
Current implementation: cpp/src/core/extra_pls.cpp.
API and bindings¶
C ABI: no standalone exported symbol is declared for this method.
Python: no current AST-verified public n4m re-export was found for this method. The linked C ABI above is the documented surface in this checkout.
R: no current source-verified entry point was found for this catalog method.
MATLAB / Octave: no current source-verified entry point was found for this catalog method.
Registry parity references 📐
📐
ref.r_ropls(R · r) —roplsBioc · strict (rmse_rel ≤ 1e-08) — Bioconductorropls::opls— OPLS reference. Permutations and plotting are disabled in benchmark timing; ropls still requires crossvalI >= 1 for a finite Q2 path.
Benchmarks¶
Archived measurement identity. Backend labels in this table are the raw IDs recorded when the benchmark ran (including historical pls4all.* IDs). They preserve measurement provenance and do not describe a current public Python, R, or MATLAB binding; use the source-verified API and bindings section above for current entry points.
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 = archived binding-harness result 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; archived language-harness rows show binding parity against the C++ backend. Hover the icon for role and tolerance band.
| Backend | Parity | 200×50 (ms) |
|---|---|---|
| C++ native · libn4m | ||
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.87 ms🏆 |
| Python · archived pls4all benchmark | ||
pls4all.python | ✓ bind | 1.88 ms |
pls4all.sklearn | ✓ bind | 2.12 ms |
| R · archived pls4all benchmark | ||
pls4all.R | ✓ 2e-14 | 4.35 ms |
pls4all.R.formula | ✓ 2e-14 | 5.13 ms |
pls4all.R.mdatools | ✓ 2e-14 | 5.23 ms |
pls4all.R.pls | ✓ 2e-14 | 5.40 ms |
| R · external | ||
📐ref.r_ropls | source | 15.4 ms |
| Backend | Parity | 200×50 (ms) |
|---|---|---|
| C++ native · libn4m | ||
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.96 ms |
| Python · archived pls4all benchmark | ||
pls4all.python | ✓ bind | 1.79 ms🏆 |
pls4all.sklearn | ✓ bind | 2.14 ms |
| R · archived pls4all benchmark | ||
pls4all.R | ✓ 2e-14 | 6.22 ms |
pls4all.R.formula | ✓ 2e-14 | 5.57 ms |
pls4all.R.mdatools | ✓ 2e-14 | 7.12 ms |
pls4all.R.pls | ✓ 2e-14 | 7.88 ms |
| R · external | ||
📐ref.r_ropls | source | 16.0 ms |
| Backend | Parity | 200×50 (ms) |
|---|---|---|
| C++ native · libn4m | ||
pls4all.cpp.blas+omp | ✓ ref 5e-15 | 1.73 ms🏆 |
| Python · archived pls4all benchmark | ||
pls4all.python | ✓ bind | 1.81 ms |
pls4all.sklearn | ✓ bind | 1.94 ms |
| R · archived pls4all benchmark | ||
pls4all.R | ✓ 2e-14 | 4.17 ms |
pls4all.R.formula | ✓ 2e-14 | 5.09 ms |
pls4all.R.mdatools | ✓ 2e-14 | 5.39 ms |
pls4all.R.pls | ✓ 2e-14 | 5.17 ms |
| R · external | ||
📐ref.r_ropls | source | 16.0 ms |
See also: benchmark overview · methods index · interactive dashboard