on_pls — OnPLS (Orthogonal N-block PLS)

Group: Multi-block / cross-modal · Registry tolerance: 1e-06

Description

OnPLS — Orthogonal multi-block decomposition (§18)

Registry note — Python OnPLS (tomlof/OnPLS, vendored in bindings/python/vendor/OnPLS). Canonical Löfstedt & Trygg 2011. Both impls predict the joint-component reconstruction of block 0.

No tunable parameters declared at the binding level.

Explanations

Bibliographic source

Löfstedt, T. & Trygg, J. (2011). OnPLS — a novel multiblock method for the modelling of predictive and orthogonal variation. Journal of Chemometrics 25(8), 441–455. Verified primary link: https://doi.org/10.1002/cem.1388.

Mathematical principle

OnPLS generalises OPLS to multiple blocks: it decomposes the joint structure into a globally predictive component shared by all blocks plus block-unique orthogonal components per block. This separates ‘integrated’ biology / chemistry information from block-specific noise.

The procedure iteratively refines a joint component by alternating projections and orthogonalisations across blocks. Compared to SO-PLS — which is asymmetric in block order — OnPLS is symmetric: no causal directionality is implied between blocks. This is the right choice when blocks are observation modalities of the same underlying process (e.g. transcriptomics + metabolomics + proteomics on the same biological samples).

The CRAN OnPLS package was archived in 2024 so the Python implementation is vendored at bindings/python/vendor/OnPLS/ to remove the dependency.

Appropriate uses

Multi-block exploratory modelling that separates globally joint, locally joint, and unique variation.

Limits and validation

Component interpretation is sensitive to block scaling and rank choices; predictive claims require external validation.

Implementation

n4m_estimators_on_pls_fit — requires n_joint, n_unique_per_block, block_sizes. The CRAN OnPLS package is archived; pls4all carries an in-tree vendored port for the parity reference.

Sources and provenance

Current implementation: cpp/src/core/extra_pls.cpp.

API and bindings

C ABI (ABI 2): n4m_estimators_on_pls_fit. Use the linked public header for the exact signature, configuration, and result handles.

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 (source-verified): on_pls_fit(X, Y, n_joint, n_unique_per_block, block_sizes).

The source signature has additional required inputs, so no example call is fabricated.

MATLAB / Octave (source-verified): on_pls(X, Y, n_joint, n_unique_per_block, block_sizes).

The source signature has additional required inputs, so no example call is fabricated.

Registry parity references 📐

• 📐 ref.python_onpls (python · python) — OnPLS github tomlof/OnPLS · strict (rmse_rel ≤ 1e-06) — Python OnPLS (Löfstedt & Trygg 2011). Vendored from GitHub because R multiblock 0.8.10 lacks onpls. Both impls return the joint-component reconstruction X̂_0.

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-06).

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.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-11	6.20 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	3.02 ms
pls4all.sklearn	✓ bind	2.69 ms🏆
Python · external
📐ref.python_onpls	source	12.2 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-11	1.81 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.91 ms
pls4all.sklearn	✓ bind	1.84 ms
Python · external
📐ref.python_onpls	source	9.46 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-11	1.91 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.00 ms
pls4all.sklearn	✓ bind	16.0 ms
Python · external
📐ref.python_onpls	source	13.4 ms

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