`so_pls` — Sequential and Orthogonalised PLS (SO-PLS)¶

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

Description¶

SO-PLS — Sequential & Orthogonalized multi-block PLS (§17)

From the pls4all.sklearn.SOPLSRegression docstring:

Sequential & Orthogonalised multi-block PLS (Næs et al. 2011).

Registry note — R multiblock::sopls 0.8.10 (Næs et al. 2011) canonical SO-PLS via fit$fitted at the full (k1,..,kB) slice. pls4all’s NIPALS-based SO-PLS matches to ~1e-13.

Parameters¶

Name	Type	Default	Notes
`n_components_per_block`	`—`	`None`	Per-block latent-component budget (one int per block).
`block_sizes`	`—`	`None`	Sequence of contiguous block widths defining the X-block partition (columns of X).

Explanations¶

Bibliographic source¶

Næs, T., Tomic, O., Mevik, B.-H. & Martens, H. (2011). Path modelling by sequential PLS regression. Journal of Chemometrics 25(1), 28–40.

Mathematical principle¶

SO-PLS extends MB-PLS by sequentially processing blocks in a user-specified order, orthogonalising each subsequent block against the scores extracted from the previous ones. Concretely: fit PLS on block 1, extract scores $\mathbf{T}_1$; orthogonalise block 2 to $\mathbf{T}_1$, fit PLS on the residual; and so on.

This makes each block’s contribution additive and interpretable — the unique variance in block $b$ that is predictive of $y$ given everything in blocks $1, \ldots, b-1$. Compared to MB-PLS (which fits all blocks simultaneously), SO-PLS encodes a domain hypothesis about which block is causally upstream of which.

Tuning: a per-block $k_b$ (number of components) plus the block order. The order matters; permuting blocks changes the attribution. Cross-validating the per-block $k_b$ is the standard procedure.

Implementation¶

n4m_so_pls_fit — requires n_components_per_block and block_sizes. Reference: CRAN multiblock 0.8.10.

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

pls4all.so_pls  Sequential & Orthogonalised multi-block PLS (Næs 2011).
 X: n × sum(block_sizes) concatenated multi-block matrix.
 n_components_per_block: int32 vector of length n_blocks.

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_so_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 so_pls_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = so_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 SOPLSRegression
mdl = SOPLSRegression(n_components_per_block=None, block_sizes=None)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

R · pls4all_method()

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("so_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.so_pls(X, y, 2);
% see header of bindings/matlab/+pls4all/so_pls.m for full
% parameter surface:
%   res = so_pls(X, Y, n_components_per_block, block_sizes)
yhat = predict(res, Xtest);

MATLAB · pls4all (classdef)

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

Registry parity references 📐

📐 ref.r_multiblock (R · r) — multiblock 0.8.10 · strict (rmse_rel ≤ 1e-06) — R multiblock::sopls 0.8.10 (Næs et al. 2011) canonical SO-PLS — in-sample fitted values via fit$fitted at the full (k1,..,kB) slice match pls4all’s canonical NIPALS SO-PLS to ~1e-15 in centered space.

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 7e-10	1.62 ms🏆
Python · pls4all
`pls4all.python`	✓ bind	1.67 ms
`pls4all.sklearn`	✓ bind	1.77 ms
R · pls4all
`pls4all.R`	✓ bind	3.26 ms
`pls4all.R.formula`	✓ bind	3.99 ms
`pls4all.R.mdatools`	✓ bind	4.00 ms
`pls4all.R.pls`	✓ bind	4.11 ms
R · external
📐`ref.r_multiblock`	source	981.7 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
`pls4all.cpp.blas+omp`	✓ ref 7e-10	1.66 ms🏆
Python · pls4all
`pls4all.python`	✓ bind	1.69 ms
`pls4all.sklearn`	✓ bind	2.44 ms
R · pls4all
`pls4all.R`	✓ bind	22.4 ms
`pls4all.R.formula`	✓ bind	31.5 ms
`pls4all.R.mdatools`	✓ bind	31.4 ms
`pls4all.R.pls`	✓ bind	34.4 ms
R · external
📐`ref.r_multiblock`	source	1.5 s

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
`pls4all.cpp.blas+omp`	✓ ref 7e-10	7.16 ms🏆
Python · pls4all
`pls4all.python`	✓ bind	11.3 ms
`pls4all.sklearn`	✓ bind	11.9 ms
R · pls4all
`pls4all.R`	✓ bind	11.3 ms
`pls4all.R.formula`	✓ bind	25.9 ms
`pls4all.R.mdatools`	✓ bind	10.3 ms
`pls4all.R.pls`	✓ bind	9.15 ms
R · external
📐`ref.r_multiblock`	source	4.0 s

nirs4all-methods

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`so_pls` — Sequential and Orthogonalised PLS (SO-PLS)¶

Description¶

Parameters¶

Explanations¶

Bibliographic source¶

Mathematical principle¶

Implementation¶

Usage¶

Benchmarks¶

so_pls — Sequential and Orthogonalised PLS (SO-PLS)¶

Description¶

Parameters¶

Explanations¶

Bibliographic source¶

Mathematical principle¶

Implementation¶

Usage¶

Benchmarks¶

`so_pls` — Sequential and Orthogonalised PLS (SO-PLS)¶