sparse_pls_da — Sparse PLS-DA (Lê Cao 2008)

Group: Sparse · Registry tolerance: 2.0

Description

Sparse PLS-DA (§7)

From the pls4all.sklearn.SparsePLSDAClassifier docstring:

Sparse PLS-DA classifier.

Registry note — R spls::splsda uses an LDA classifier on PLS scores; pls4all and SparsePlsDaPythonReference use argmax of the regression decision scores. Both emit one-hot predictions; differences appear only at the decision boundary.

Parameters

Name

Type

Default

Notes

n_components

int

2

Number of latent components extracted (k).

sparsity_lambda

float

0.05

L1 soft-threshold magnitude applied to the PLS weight vectors.

n_classes

int

3

registry benchmark cell value

Explanations

Bibliographic source

Lê Cao, K.-A., Rossouw, D., Robert-Granié, C. & Besse, P. (2008). A sparse PLS for variable selection when integrating omics data. Statistical Applications in Genetics and Molecular Biology 7(1).

Mathematical principle

Discriminant variant of sparse PLS. Encode class labels \(y \in \{0, 1, \ldots, C-1\}\) as a one-hot matrix \(\mathbf{Y} \in \{0, 1\}^{n \times C}\), fit a sparse PLS regression on it, then assign new samples to the class with the largest predicted score. The L1 penalty selects a discriminative subset of features along each latent direction.

In high-dimensional biomarker discovery (microarray, MALDI-TOF, NIR food classification) sparse PLS-DA is a standard since it simultaneously builds the discriminant and shortlists the candidate markers in a single regularised fit. Class probabilities follow from a softmax over the predicted score columns.

Implementation

n4m_sparse_pls_da_fit. Reference: Bioconductor mixOmics::splsda.

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

pls4all.sparse_pls_da  Sparse PLS-DA classifier (Chun & Keles 2010 + DA).
 y_labels: integer class IDs in {0, …, n_classes-1}.

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 */
n4m_context_t* ctx = n4m_context_create();
n4m_config_t*  cfg = n4m_config_create();
n4m_method_result_t* res = NULL;
n4m_sparse_pls_da_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);

import pls4all
from pls4all._methods import sparse_pls_da_fit
with pls4all.Context() as ctx, pls4all.Config() as cfg:
    res = sparse_pls_da_fit(ctx, cfg, X, y, n_components=4, y_labels=y_labels)
# then: res.matrix("predictions"), res.matrix("coefficients"),
# res.vector("mask"), res.scalar("intercept"), …

from pls4all.sklearn import SparsePLSDAClassifier
mdl = SparsePLSDAClassifier(n_components=2, sparsity_lambda=0.05)
mdl.fit(X, y)
y_hat = mdl.predict(X_test)

library(pls4all)
# Unified low-level dispatcher (May 2026 R cleanup):
res <- pls4all_method("sparse_pls_da", X, y,
                      n_components = 4L, params = list(sparsity_lambda = 0.05, n_classes = 3L))
# res is a named list with MethodResult arrays/scalars.
# selected_indices / top_k_intervals are 1-based.

res = pls4all.sparse_pls_da(X, y, 4);
% see header of bindings/matlab/+pls4all/sparse_pls_da.m for full
% parameter surface:
%   res = sparse_pls_da(X, y_labels, n_components, sparsity_lambda)
yhat = predict(res, Xtest);

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

Registry parity references 📐

  • 📐 ref.python_chun_keles_splsda (python · python) — chun_keles_splsda 1.0 · qualitative (rmse_rel ≤ 2e+00) — Sparse SIMPLS (Chun & Keles 2010) on dummy-coded class labels, followed by argmax over decision scores. Mirrors pls4all’s n4m_sparse_pls_da_fit (default, cfg.sparse_simpls_legacy = 0) bit-for-bit.

  • 📐 ref.r_spls (R · r) — spls 2.3.2 · qualitative (rmse_rel ≤ 2e+00) — R spls::splsda (Chun & Keles). Predictions returned as hard class labels by the package; we one-hot encode them to match pls4all’s soft-assignment prediction shape, so the parity check is on the classification boundary rather than continuous score values.

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-08).

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.

BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref7.43 ms
Python · pls4all
pls4all.python✓ bind4.50 ms
pls4all.sklearn⇄ +7e-012.45 ms🏆
R · pls4all
pls4all.R✓ bind7.20 ms
pls4all.R.formula✓ bind8.68 ms
pls4all.R.mdatools✓ bind8.43 ms
pls4all.R.pls✓ bind8.53 ms
Python · external
📐ref.python_chun_keles_splsdasource3.58 ms
R · external
📐ref.r_spls⇄ +1e+0082.9 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref12.7 ms
Python · pls4all
pls4all.python✓ bind8.19 ms
pls4all.sklearn⇄ +7e-015.55 ms🏆
R · pls4all
pls4all.R✓ bind23.8 ms
pls4all.R.formula✓ bind31.7 ms
pls4all.R.mdatools✓ bind37.4 ms
pls4all.R.pls✓ bind15.7 ms
Python · external
📐ref.python_chun_keles_splsdasource14.4 ms
R · external
📐ref.r_spls⇄ +1e+00117.9 ms
BackendParity200×50 (ms)
C++ native · libn4m
pls4all.cpp.blas+omp✓ ref7.83 ms
Python · pls4all
pls4all.python✓ bind7.59 ms
pls4all.sklearn⇄ +7e-013.94 ms🏆
R · pls4all
pls4all.R✓ bind12.2 ms
pls4all.R.formula✓ bind47.2 ms
pls4all.R.mdatools✓ bind26.4 ms
pls4all.R.pls✓ bind32.6 ms
Python · external
📐ref.python_chun_keles_splsdasource6.94 ms
R · external
📐ref.r_spls⇄ +1e+0091.2 ms

See also: benchmark overview · methods index · interactive dashboard