Optimal Transport for Multivariate Median Definition

Define a multivariate median for datasets where the median is not explicitly known.
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Table of Contents

1. 📄 About The Project
   • 🎯 Objective
   • 🌍 Context
   • 📁 Repository Structure
   • 📊 Dataset
2. 🚀 Getting Started
   • 🛠️ Installation
3. 📈 Usage
4. 📞 Contact

📄 About the project

This repository contains the results of a project focused on defining a multivariate median for datasets where the median is not explicitly known. The methodology leverages optimal transport in discrete and semi-discrete settings, where a known distribution (e.g., a uniformly distributed spherical distribution) is transported to the target distribution (e.g., the ANSUR II dataset). The results showcase detailed visualizations of transport processes, quantile contours, and algorithmic convergence.

🎯 Objective

The main goals of this project are:

1. Define a robust multivariate median for datasets lacking a direct median representation.
2. Utilize optimal transport theory to compute solutions for discrete and semi-discrete cases.
3. Analyze and visualize the resulting transports and their implications.

🌍 Context

This work was conducted during a two-month internship (June–July 2024) within the Image Optimisation et Probabilities Team at the Institut de Mathématiques de Bordeaux, supervised by Professor Jérémie BIGOT.

📁 Repository Structure

PY-Optimal-Transport-Median
├── README.md        # Overview and usage instructions.
├── social_preview.png        # Social Preview of the repo.
├── docs/        # Reference materials (papers, reports, etc.).
├── data/        # Dataset and its detailed analysis.
│   ├── analysis/        # Descriptive analysis of the database variables.
│   └── raw/        # Database used (ANSUR II Male and Female)
├── src/        # Jupyter notebooks and Python scripts.
│   ├── utils.py        # Reusable utility functions.
│   └── notebooks        # Four Jupyter notebooks illustrating key processes.
├── results/        # Outputs (e.g., figures, graphs).
└── reports/        # Final documents.
    ├── internship_report.pdf
    ├── summary_note.pdf
    └── presentation_slides.pptx

📊 Dataset

The ANSUR II dataset, located in the data/raw folder, serves as the primary resource for this project.

• Source: ANSUR II Dataset
• Description: Anthropometric data from military populations. A descriptive analysis of the dataset is provided in data/README.md.

🚀 Getting Started

🛠️ Installation

1. Clone the repo:

   git clone https://github.com/moranenzo/PY-Optimal-Transport-Median.git

2. Navigate to the project directory:

   cd PY-Optimal-Transport-Median

📈 Usage

Navigate to the src directory to explore:

• Detailed visualizations:
  • Distributions of the data.
  • Optimal transport processes between measures.
  • Quantile contours of target distributions.
• Step-by-step guides for:
  • Multivariate median computation.
  • Transport map visualizations.

To run a notebook:

1. Start Jupyter Notebook:

jupyter notebook

2. Open the desired notebook from src.

📞 Contact

Enzo MORAN - LinkedIn - [email protected]

Project Link: https://github.com/moranenzo/PY-Music-Genre-Classifier

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