PLSR-CPP — Functional Partial Least Squares Regression in C++

A clean, fast, and fully documented C++20 implementation of the NIPALS PLS1 algorithm applied to functional data, developed as part of the course Statistics and Data Analysis — M. Sc. in Data Science and Information Retrieval.

Includes realistic synthetic data *amplitude-modulated sine waves) and linear response generation, and a complete simulation study framework.

Perfect for teaching, research, benchmarking, or extending to real functional datasets (spectroscopy, chemometrics, FDA, etc.).

Scientific Motivation

We generate functional predictors

$$X_i(t_j) = A_i \cdot \sin(2\pi t_j) + \varepsilon_{ij}, \quad t_j \in [0,1], \quad i=1,\dots,N$$

with latent amplitude $A_i \sim \mathcal{U}[0.5, 2.5]$, and a scalar response

$$y_i = \beta_0 + \sum_{j=0}^{P-1} \beta_i(t_j) X_i(t_j) + \delta_i$$

This creates a strong linear relationship which PLSR recovers with just 1–2 components.

Features

• Modern C++20 + Eigen3 (header-only dependency)
• Classic NIPALS PLS1 implementation (Wold et al., 1984)
• Reproducible synthetic functional data (B-spline/Fourier-ready structure)
• Linear response
• Full Doxygen documentation with LaTeX formulas
• Cross-platform: Linux • macOS • Windows (MSVC, Clang, GCC)
• Extremely simple build system (just a smart Makefile wrapper around CMake)

Project Structure

plsr-cpp/
├── CMakeLists.txt
├── Makefile ← one-command magic
├── include/
│ ├── DataGenerator.hpp
│ ├── ResponseGenerator.hpp 
│ ├── fourier.hpp 
│ ├── bspline.hpp 
│ └── PLSR.hpp 
├── src/ ← implementations 
├── tests/ ← unit tests 
├── main.cpp ← full simulation demo 
├── results/ ← generated data & comparison 
├── LICENSE ← GPL-3.0 
└── README.md

Build & Run (All Platforms)

Prerequisites (same for Linux, macOS, Windows)

• A modern C++ compiler (GCC ≥ 10, Clang ≥ 10, MSVC ≥ 2019)
• CMake ≥ 3.16
• Eigen3 (header-only)

Installation of Eigen3

# Ubuntu/Debian
sudo apt install libeigen3-dev

# Arch Linux
sudo pacman -S eigen

# macOS (Homebrew)
brew install eigen

# Windows: use vcpkg
vcpkg install eigen3
# or Conan, or just drop the headers somewhere

One-command workflow (Linux & macOS)

cd plsr-cpp
make go          # builds + runs the full demo
make tests       # runs all unit tests

Other useful targets:

make setup      # first-time configuration
make build      # fast incremental rebuild
make run        # run the demo (same as `make make go`)
make clean      # remove build artifacts

Windows (Visual Studio or MinGW)

Open a terminal (PowerShell, CMD, or Git Bash) and run exactly the same make commands above if you have GNU Make installed.

Alternative: pure CMake (works everywhere)

mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release   # Linux/macOS
# or
cmake .. -G "Visual Studio 17 2022" -A x64   # Windows MSVC
cmake --build . --config Release --parallel
./main                 # Linux/macOS
./Release/main.exe     # Windows

Expected Output (in results/)

After running make go or ./build/main you will get:

results/
├── response.txt
└── coef_functions.txt

Authors

Dhiaa Eddine Bahri
dhya.bahri@proton.me
Main contributions: PLSR algorithm, project architecture, main integration and build system

Malek Rihani
malek.rihani090@gmail.com
Main contributions: Functional data and linear response generators

Academic year 2025-2026
M. Sc. in Data Science and Information Retrieval
University of Manouba — Higher Institute of Multimedia Arts

Citation

If you use this code in your research or teaching, please cite:

@software{plsr_cpp_2025,
  author       = {Bahri, Dhiaa Eddine and Rihani, Malek},
  title        = {PLSR-CPP: A C++20 implementation of NIPALS PLS1 for functional data},
  year         = 2025,
  publisher    = {GitHub},
  url          = {https://github.com/Disciple0fMarx/plsr-cpp}
}

Enjoy the power of supervised dimension reduction on functional data!