cppls — Canonical Powered PLS (CPPLS)

Group: Core PLS · Registry tolerance: 1e-08

Description

CPPLS (Canonical Powered PLS, Indahl Liland & Næs 2009)

Registry note — R pls::cppls 2.9.0 Canonical Powered PLS (lower=upper=0.5 default reduces to NIPALS PLS1 with X-only deflation for q=1). pls4all matches at ~8e-16. SIMPLS column-σ^γ variant via cfg.solver = SIMPLS.

Parameters

Name	Type	Default	Notes
X	—	required	current public binding signature
y	—	required	current public binding signature
gamma	float	0.5	current public binding signature
n_components	int	2	current public binding signature

Explanations

Bibliographic source

Indahl, U. G., Liland, K. H. & Næs, T. (2009). Canonical partial least squares—a unified PLS approach to classification and regression problems. Journal of Chemometrics 23(9–10), 495–504. DOI 10.1002/cem.1243.

Mathematical principle

Canonical Powered PLS combines PLS covariance information with a canonical-correlation criterion so that multivariate or class-coded responses can guide a common latent space. In the current default implementation, components are extracted from the centred X–Y cross-product and X is deflated after each score. This is the CPPLS family implemented by R pls::cppls, rather than the unrelated 2005 \(\operatorname{sign}(X^Ty)|X^Ty|^\gamma\) formula formerly shown here.

Appropriate uses

Classification or multivariate calibration where Canonical Powered PLS response weighting is useful.

Limits and validation

In the default path gamma is recorded but does not alter the fit; only the legacy SIMPLS path applies a gamma-dependent column rescaling.

Implementation

The default Canonical Powered PLS path records gamma but does not currently use it in component extraction. Only the explicitly selected legacy SIMPLS branch applies gamma as a column-standard-deviation power rescaling; it still does not implement the formerly documented closed form.

Sources and provenance

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

API and bindings

C ABI (ABI 2): n4m_estimators_cppls_fit. Use the linked public header for the exact signature, configuration, and result handles.

Python (verified public re-export):

from n4m.estimators.regression.latent import cppls
result = cppls(X, y)

Source signature: cppls(X, y, *, gamma: float = 0.5, n_components: int = 2) (n4m/_impl/native.py).

R (source-verified): cppls(formula, data, ncomp = 2L, gamma = 0.5, na.action = stats::na.omit).

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

MATLAB / Octave (source-verified): cppls(X, Y, n_components, gamma).

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

Registry parity references 📐

• 📐 ref.r_pls (R · r) — pls 2.9.0 · strict (rmse_rel ≤ 1e-08) — R pls::cppls Canonical Powered PLS (Indahl, Liland & Næs 2009); default lower=upper=0.5 reduces to NIPALS PLS1 with X-only deflation for q=1.

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.

1 thread

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 8e-16	1.88 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.87 ms🏆
pls4all.sklearn	✓ 4e-15	1.97 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	4.57 ms
pls4all.R.formula	✓ bind	5.65 ms
pls4all.R.mdatools	⇄ +3e-02	6.07 ms
pls4all.R.pls	⇄ +3e-02	10.6 ms
R · external
📐ref.r_pls	source	9.91 ms

3 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 8e-16	1.78 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.79 ms
pls4all.sklearn	✓ 4e-15	1.97 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	4.38 ms
pls4all.R.formula	✓ bind	5.49 ms
pls4all.R.mdatools	⇄ +3e-02	6.44 ms
pls4all.R.pls	⇄ +3e-02	10.6 ms
R · external
📐ref.r_pls	source	9.85 ms

10 threads

Backend	Parity	200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 8e-16	1.69 ms🏆
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.80 ms
pls4all.sklearn	✓ 4e-15	1.95 ms
R · archived pls4all benchmark
pls4all.R	✓ bind	4.57 ms
pls4all.R.formula	✓ bind	5.38 ms
pls4all.R.mdatools	⇄ +3e-02	6.59 ms
pls4all.R.pls	⇄ +3e-02	11.1 ms
R · external
📐ref.r_pls	source	10.5 ms

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See also: benchmark overview · methods index · interactive dashboard