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.

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.

Implementation

n4m_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.

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

pls4all.on_pls  Orthogonal multi-block PLS (joint + unique loadings).
 n_components arg is unused by on_pls (it has its own block structure),
 but the dispatcher still requires it; we pass n_joint.

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

/* C ABI — libn4m */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_on_pls_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);

Python · pls4all (raw)

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

Python · pls4all.sklearn

from pls4all.sklearn import on_pls
result = on_pls(X, y, n_components=2)

R · pls4all_method()

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

MATLAB · pls4all (MEX)

res = pls4all.on_pls(X, y, 2);
% see header of bindings/matlab/+pls4all/on_pls.m for full
% parameter surface:
%   res = on_pls(X, Y, n_joint, n_unique_per_block, block_sizes)
yhat = predict(res, Xtest);

MATLAB · pls4all (classdef)

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

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

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-06).

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.

1 thread

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 2e-11	6.20 ms
Python · pls4all
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 · pls4all
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 · pls4all
pls4all.python	✓ bind	2.00 ms
pls4all.sklearn	✓ bind	16.0 ms
Python · external
📐ref.python_onpls	source	13.4 ms

---

See also: benchmark overview · methods index · interactive dashboard