# `sparse_pls_da` — Sparse PLS-DA (Lê Cao 2008) _Group_: **Sparse** · _Registry tolerance_: `1e-08` ## 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_estimators_sparse_pls_da_fit`. Reference: Bioconductor `mixOmics::splsda`. R roxygen note (`methods_extra.R::sparse_pls_da_fit`): > Sparse PLS-DA classifier (`y_labels` is an integer vector of class IDs). > @param y_labels Integer vector. Class labels. > @param n_components Integer. Number of latent components. > @param sparsity_lambda Method-specific parameter. See the underlying `*_fit()` function for the exact semantics. > @param X Numeric matrix of predictors (rows = samples, cols = features). > @export MATLAB header (`bindings/matlab/+pls4all/sparse_pls_da.m`): ```text 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** ::::{tab-set} :class: pls4all-bindings :::{tab-item} C ABI · libn4m :sync: c :class-label: lang-c ```c /* C ABI — libn4m */ n4m_context_t* ctx = n4m_context_create(); n4m_config_t* cfg = n4m_config_create(); n4m_method_result_t* res = NULL; n4m_estimators_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); ``` ::: :::{tab-item} Python · pls4all (raw) :sync: python-raw :class-label: lang-python ```python 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"), … ``` ::: :::{tab-item} Python · pls4all.sklearn :sync: python-sklearn :class-label: lang-python ```python from pls4all.sklearn import SparsePLSDAClassifier mdl = SparsePLSDAClassifier(n_components=2, sparsity_lambda=0.05) mdl.fit(X, y) y_hat = mdl.predict(X_test) ``` ::: :::{tab-item} R · pls4all_method() :sync: r-dispatcher :class-label: lang-r ```r 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. ``` ::: :::{tab-item} R · pls4all (raw fn) :sync: r-raw :class-label: lang-r ```r library(pls4all) res <- sparse_pls_da_fit(X, y_labels, n_components, sparsity_lambda = 0.05) yhat <- pls4all_predict(res, X_test) ``` ::: :::{tab-item} MATLAB · pls4all (MEX) :sync: matlab-mex :class-label: lang-matlab ```matlab 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); ``` ::: :::{tab-item} MATLAB · pls4all (classdef) :sync: matlab-classdef :class-label: lang-matlab _No idiomatic classdef wrapper — invoke `pls4all.fit("sparse_pls_da", X, y, …)` directly from the unified MEX factory._ ::: :::: **Registry parity references** 📐 :::{card} :class-card: external-refs - 📐 **`ref.python_chun_keles_splsda`** (python · python) — `chun_keles_splsda` 1.0 · strict (rmse_rel ≤ 1e-08) — Sparse SIMPLS (Chun & Keles 2010) on dummy-coded class labels, followed by argmax over decision scores. Mirrors pls4all's `n4m_estimators_sparse_pls_da_fit` (default, cfg.sparse_simpls_legacy = 0) bit-for-bit. - 📐 **`ref.r_spls`** (R · r) — `spls` 2.3.2 · strict (rmse_rel ≤ 1e-08) — 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`](../benchmarks/overview.md). 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`](../benchmarks/methodology.md)). 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. ::::{tab-set} :class: parity-tabs :::{tab-item} 1 thread :sync: threads-1
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
::: :::{tab-item} 3 threads :sync: threads-3
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
::: :::{tab-item} 10 threads :sync: threads-10
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](../benchmarks/overview.md) · [methods index](index.md) · [interactive dashboard](../landing/dashboard.md)