pls_qda — PLS-QDA

Group: Classification & GLM · Registry tolerance: 1e-06

Description

PLS-QDA (§5) — quadratic discriminant on PLS scores

Registry note — sklearn PLSRegression(scale=False) -> QuadraticDiscriminantAnalysis(reg_param=0.0) pipeline. pls4all’s default now mirrors this convention: NIPALS PLS scores via the C kernel, then sklearn-style QDA predict_proba in Python. The legacy single-pass C++ kernel (SIMPLS + identity-covariance log-posterior) is opt-in via legacy=True.

Parameters

Name	Type	Default	Notes
n_components	int	4	registry benchmark cell value
n_classes	int	3	registry benchmark cell value

Explanations

Bibliographic source

Pérez-Enciso, M. & Tenenhaus, M. (2003). Prediction of clinical outcome with microarray data: a partial least squares discriminant analysis (PLS-DA) approach. Human Genetics 112, 581–592. DOI 10.1007/s00439-003-0921-9.

Mathematical principle

PLS first supplies a low-dimensional supervised score space. QDA then estimates a separate mean and regularized covariance for each class and compares Gaussian discriminant scores including the empirical log class prior.

Appropriate uses

Classification on PLS scores when class-specific covariance matrices are supported by enough samples.

Limits and validation

Class priors are empirical in the current implementation; class-specific covariance estimates can be singular or unstable for small classes.

Implementation

Current priors are observed class proportions; there is no uniform-prior or caller-supplied-prior option on this path. Covariance regularization remains necessary when class samples are few.

Sources and provenance

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

API and bindings

C ABI (ABI 2): n4m_estimators_pls_qda_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): pls_qda_fit(X, y_labels, n_components).

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

MATLAB / Octave (source-verified): pls_qda(X, y_labels, n_components).

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

Registry parity references 📐

• 📐 ref.python_scikit_learn (python · python) — scikit-learn 1.8.0 · strict (rmse_rel ≤ 1e-06) — sklearn PLSRegression(scale=False) -> QuadraticDiscriminantAnalysis(reg_param=0.0) pipeline. pls4all’s default PLS-QDA reuses the same convention: NIPALS PLS scores from the C kernel, then sklearn-style QDA in Python. Bit-for-bit parity (max_abs < 1e-6).

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 5e-16	2.65 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	2.12 ms
pls4all.sklearn	⇄ +2e+00	2.11 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	4.06 ms
pls4all.R.formula	⇄ +2e+00	4.67 ms
pls4all.R.mdatools	⇄ +2e+00	5.46 ms
pls4all.R.pls	⇄ +2e+00	4.99 ms
Python · external
📐ref.python_scikit_learn	source	2.36 ms

3 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 5e-16	1.94 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	1.92 ms
pls4all.sklearn	⇄ +2e+00	1.64 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	8.84 ms
pls4all.R.formula	⇄ +2e+00	18.1 ms
pls4all.R.mdatools	⇄ +2e+00	18.2 ms
pls4all.R.pls	⇄ +2e+00	13.5 ms
Python · external
📐ref.python_scikit_learn	source	6.90 ms

10 threads

Backend	Parity	200×30 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp	✓ ref 5e-16	5.99 ms
Python · archived pls4all benchmark
pls4all.python	✓ bind	4.32 ms
pls4all.sklearn	⇄ +2e+00	1.49 ms🏆
R · archived pls4all benchmark
pls4all.R	⇄ +2e+00	3.90 ms
pls4all.R.formula	⇄ +2e+00	5.11 ms
pls4all.R.mdatools	⇄ +2e+00	5.10 ms
pls4all.R.pls	⇄ +2e+00	5.08 ms
Python · external
📐ref.python_scikit_learn	source	2.39 ms

---

See also: benchmark overview · methods index · interactive dashboard